Cross- sectional diagram of the roadway. Energy Generated: Power asphalts used to provide electrical power to street lights. The set up involved piezoelectric devices lay beneath asphalt roads.
Very high frequency response. Simple to use as they have small dimensions and large measuring range. It is not suitable for measurement in static condition.
Since the device operates with the small electric charge, they need high impedance cable for electrical interface. The output may vary according to the temperature variation of the crystal. The experiment involves 1 Km stretch power asphalt with vehicle passing rate of in 16 h.
Based on this experiment, the total electrical energy generated range between KWh - Kwh. Assuming there are 10 individual street lights. In contrary, energy efficiency always increases with more speed.
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Did you find this document useful? Is this content inappropriate? Within the fibril, collagen molecules arrange themselves in a quasi-hexagonally packing fashion.
Each collagen molecules consist of three polypeptide chains that wind together to form a right-handed triple- helix. Each molecule lies parallel to its neighbour in a staggered manner such that each molecule sits approximately 64 to 67 nm above or below its neighbouring molecule in the fibril.
This shift gives the fibrils their characteristic repeating D-band structure Adapted from The complexity of collagen fibers makes it difficult to establish the origin of its piezoelectricity.
The fibrils are highly oriented and have a crystalline arrangement 16 — attributes well associated with piezoelectricity.
The molecules are packed in a quasi- hexagonal fashion which can be described by point group 6 C6 in Schoenflies notation As discussed in Section 2.
The origin of piezoelectricity in collagen therefore may be the induced polarization or displacement of hydrogen bonds in the collagen polypeptide chains resulting from a shear stress or electric field, respectively The early work on collagen piezoelectricity quantified its piezoelectric activity; a piezoelectric d14 coefficient of 8 x cgs.
PFM has been used more recently to probe collagen at its different hierarchical levels. At the nanoscale, individual collagen fibrils demonstrate shear piezoelectricity. The piezoelectric tensor of collagen measured via PFM reports higher piezoelectric coefficients than those obtained via macroscopic measurements 28, 41, The piezoelectric effect in collagen is sufficient to construct a successful collagen-based gramophone 18 illustrating its potential as an electromechanical transducer.
Amino acids are chains of simple compounds connected by peptide bonds. X-ray diffraction XRD or nuclear magnetic resonance NMR can determine the crystal structure of amino acids in their crystalline form.
Based on their symmetry, 19 of the 20 protein amino acid crystals may demonstrate piezoelectric behaviour, as they are non- centrosymmetric. Vasilescu et al. Later work by Lemanov focused on crystals of amino acids and their compounds While many of the reports were qualitative, one study calculated the piezoelectric dcoefficient of L-argenine phosphate as 8. These studies indicate that the classical symmetry requirements of piezoelectricity hold for amino acids too.
Similarly, while racemic amino acids should be achiral, classical piezoelectricity is still permissible in some cases — as long as they belong to non- centrosymmetric groups.
Such is the case for DL-alanine which although a racemic variety, belongs to the piezoelectric point group mm2 The explanation for the absence of piezoelectricity in some amino acids whose symmetry supports piezoelectricity is simple; the experimental setup was not sensitive enough to overcome the effects of damping within the amino acid crystals Piezoelectricity in Phospholipids Phospholipids make up the flexible barrier between the cell and its environment.
Like amino acids, they are chiral and demonstrate piezoelectricity. Interestingly, it was by comparing phospholipids with liquid crystals that an understanding of how piezoelectricity is supported in phospholipids arose Jakli, a liquid crystallographer, noted these strong parallels and hypothesized that chiral phospholipids would demonstrate piezoelectricity while racemic phospholipids would not There are two broad categories of liquid crystals - nematics and smectics, as illustrated in Figure 2.
Adapted from The molecules of nematic liquid crystals do not have any positional ordering — however, they maintain an alignment parallel to a common director axis, Figure 2. Smectic liquid crystals are more ordered. Each layer of molecules is ordered with a well-established interlayer spacing The molecules in a SmA liquid crystal have their long axis pointing in the direction normal to the layer axis.
The molecules in a SmC liquid crystal have their long axis tilted at an angle from the layer axis If a liquid crystal is chiral it is denoted with an asterisks. Each molecule has a dipole moment normal to the tilt plane. The spontaneous polarisation Ps associated with each dipole precesses around the direction normal to the layer forming a helix. Meyer hypothesised that chiral liquid crystals would demonstrate piezoelectricity because of their low symmetry and this has since been confirmed experimentally By drawing parallels with liquid crystals, the crystal symmetry of a phospholipid bilayer can be described.
Adapted from When the phospholipid is undisturbed, the net polarisation of the phospholipid is zero as illustrated by the top view schematic in Figure 2. Subjecting the phospholipid to a shear stress distorts the helix, inducing a net polarisation as depicted in Figure 2.
Tourmaline crystals and poled barium titanate ceramics are examples of pyroelectrics materials. Three conditions must be satisfied in order to be pyroelectric.
Firstly, the molecular structure of the material must have a non-zero dipole moment. This means that on a molecular scale, the units or building blocks of pyroelectric materials possess a dipole moment.
The way in which these building blocks are stacked together must be in a manner that does not result in individual dipole moments cancelling out one another. Secondly, the material must have no centre of symmetry. Finally, the material must either possess no axis of rotational symmetry or else have a single axis of rotational symmetry that is not included in an inversion axis Ten of the 32 crystal groups, called polar groups, satisfy these criteria.
The spontaneous polarisation, Ps, is the dipole moment per unit volume. It defines the amount of charge, Q, that develops around a material of area, A. Lang proposed a simple thought experiment that allows the nature of pyroelectricity to be understood. If the material were free to float in air, charges at its surfaces would attract and bind to free charges in the atmosphere. The net effect would be a neutral surface charge, Figure 2.
When the temperature is constant, the spontaneous polarisation remains unaltered and an ammeter connected in series with the sample would read zero current, Figure 2. However, if the material is pyroelectric, a change in temperature affects its dipoles, either shifting their atomic positions or affecting their interatomic bonding. The result is a change of spontaneous polarisation. In response, the free charges within the material must redistribute themselves to compensate for the change in bound charges.
The net result is a flow of current, I, measured by the ammeter, Figure 2. Equation 2. Heating and cooling should be linear to avoid inducing false- pyroelectric currents.
Chapter 3 outlines precautions to distinguish between primary, secondary and tertiary pyroelectric effects. This was the first report of pyroelectricity in biological materials.
Other early works in the field found pyroelectricity in plant leaves and the integument of cockroach insects The number of studies investigating pyroelectricity in biological materials is far less than the number of studies investigating their piezoelectric properties. One reason for this may be that because pyroelectricity has no physiological significance in the way that bone-piezoelectricity does, there has been less interest. Secondly, the difficulties of measuring pyroelectricity accurately, especially in biological materials, may be a barrier that has prevented researchers from uncovering pyroelectricity in other biological materials.
Biological materials may degrade or denature when exposed to heating. Also, there size, shape and environment may pose challenges for creating electrode contacts.
The high content of water in biological materials can also affect the reproducibility of data Despite these challenges, there is some evidence that pyroelectricity persists down to the smallest biological building blocks.
He also recognised that the polar symmetry of many amino acids would support pyroelectricity. Hence, while studying the piezoelectric effect in amino acids and their compounds, he reported that a number of them also showed pyroelectricity.
Unfortunately, he did not publish details of the measurement approach, only commenting that the pyroelectric coefficient was not very high. In the same way that the symmetry assigned to hydroxyapatite erroneously dismissed it as non-piezoelectric, so too was the pyroelectric properties of hydroxyapatite kept hidden until recently. Originally, pyroelectricity in bone was attributed its polar collagen component. It was believed that hydroxyapatite played no role in bone pyroelectricity.
Soon after, Lang et al. In ferroelectric materials, a sufficiently high electric field reverses the direction of the electric dipoles, re-orientating the direction of its spontaneous polarisation Typically, ferroelectric materials are characterised by high dielectric constants and a Curie point, above which the material adopts a non-polar state.
The Sawyer-Tower circuit is the classical method of measuring ferroelectricity. Ferroelectric samples measured in this way demonstrate characteristic hysteresis loops, Figure 2. This hysteresis loop determines the spontaneous polarisation, remnant polarisation polarisation at zero electric field and coercive field field required to reverse the spontaneous polarisation of the sample.
Also for samples that are ferroelectric, measurements of the strain induced due to the applied field reveal a characteristic butterfly loop, Figure 2. The poling process involves heating the material above the Curie temperature. Applying a high DC voltage causes the dipoles to align in the direction of the applied field. The result is an overall net polarization. During cooling, the DC voltage remains in place, preventing the majority of dipoles from returning to their original state.
After cooling and removing the DC voltage, a remnant polarisation persists. Poling thus, induces an artificial anisotropic condition necessary to induce piezoelectricity. Joseph Valasek formally reported observations of ferroelectricity in samples of Rochelle Salt in The majority of ferroelectrics are solid, bulk materials, often containing lead components.
The discovery of piezoelectricity and ferroelectricity in PVDF extended ferroelectrics to applications that require flexibility and biocompatibility PFM has emerged as a tool capable of probing the ferroelectric properties of materials. Li et al. Liu et al. Ferroelectric switching in elastin is suppressed by glucose, an observation that may have physiological significance Heredia et al. Similarly, Lang et al.
These examples fulfil the long held promise that biological materials might show ferroelectric behaviour. Studies such as these serve to motivate further research in to the area of biological-ferroelectrics.
Eventually perhaps, a true physiological significance of ferroelectricity in biological materials will be uncovered. A connected series of amino acids forms a peptide. A longer chain of amino acids arranged in biologically functional manner is called a protein. Proteins can be grouped in to three categories, fibrous, globular and integral membrane proteins.
Lysozyme is a globular protein. Sir Alexander Fleming is famously associated with the discovery of penicillin in However, before that in , he made another significant discovery — that of lysozyme. By accident, a drop of nasal mucus fell on to a plate of bacteria and he noticed that it caused lysis of the bacteria Lysozyme is effective in protecting us against infection and is used as a preservative in the food industry ; however, it is not suitable as an anti-biotic.
Although, it has not contributed to medicine in the way that penicillin has, the discovery of lysozyme has left a remarkable imprint. Ninety-five years on from its initial discovery, lysozyme has become the protein of choice in structural biochemistry, owing to its small size and stability. It is also found abundantly in hen egg whites.
As Fleming discovered, its function is to protect against infection by breaking down the cell wall of gram-positive bacteria. Alternating N-acetylglucosamine NAG and N-acetylmuramic acid NAM residues are linked together to form the peptidoglycan layer of the bacterial cell wall. The weakened bacterial cell wall then collapses under its own internal pressure Lysozyme is small in size — The ribbon diagram in Figure 2.
The ribbon diagram begins at the red C-terminus and follows the colour of the spectrum until it reaches the blue N-terminus. The hydrophobic groups are buried within and the hydrophilic groups are on the outside giving lysozyme its hydrophobic exterior and hydrophilic interior. Compared to other protein types, globular proteins crystallise easily.
Blake et al. Uniquely, lysozyme crystals can grow in more than one form. The Protein Data Bank , a depository of thousands of protein structures, reports findings of tetragonal, monoclinic, orthorhombic, triclinic and hexagonal crystals of lysozyme Optical microscopy images of lysozyme crystal polymorphs are shown in Figure 2. Diffraction studies reveal a lot of information about lysozyme.
In the simplest sense, diffraction experiments determine the unit cell parameters of the protein crystal. In addition, these measurements add to our understanding of protein molecular packing arrangements, folding mechanisms and hydration shell properties. Diffraction data also reveals similarities and disparities between lysozymes from different sources. Structurally, lysozyme from hen egg whites, human, bacteriophage and bacterial sources are similar. However, lysozyme from the fungus species Chalarosis is different, having no sequence homology with avian, mammalian or phage lysozymes.
It does share some sequence similarities with the bacterial form of lysozyme Diffraction studies can also aid our understanding of how lysozyme binds to N- acetylglucosamine residues in bacterial cells While diffraction has emerged as a powerful tool in protein structural biochemistry, it may not always determine the best symmetry fit for a given protein. For protein crystals especially, artefacts such as twinning and pseudo-symmetry operations are common.
This occurs when more than one protein molecule sit in each asymmetric unit. As diffraction systems and software are become increasingly sophisticated with automatic fitting programs, the risk of a protein being incorrectly assigned to an incorrect space group also increases In this scenario, the non-crystallographic symmetry axis in the software program is biased towards the crystallographic axis The extent to which misassignment of space group symmetry occurs may be significant; Zhart et.
Nucleation can be controlled by seeding, or by the application of a localized voltage or magnetic field AFM has been used to study the growth mechanisms of lysozyme in its triclinic 51 , tetragonal 52 , monoclinic 53 and orthorhombic 54 forms.
In typical experiments, protein crystals are grown either directly on glass petri dishes or transferred from sitting drop wells to a petri dish. The protein crystal sits in a droplet of the mother liquor to prevent it from drying out.
After some time, the protein crystals settle and adhere to the base of the dish. This allows the AFM tip to scan across their surface without the sample protein moving. AFM has revealed growth spirals, rounded steps, impurity pinning and 3D nucleation on the surface of lysozyme crystals. At low supersaturation levels, screw dislocations are the growth mechanism that result in spirals at the crystal surface shown in Figure 2. In the latter stages of the liquid-AFM study, two-dimensional nucleation becomes the dominant growth mechanism.
Further nucleation creates islands that merge with the spiral steps forming bulges on the spirals until eventually no evidence of the spiral step is left, Figure 2. During adsorption, lysozyme changes its conformational state. Depending on the orientation of the molecule, the conformational change can result in a change of height that is detectable by AFM.
Height images of lysozyme adsorbed on to mica demonstrated spikes that may correspond to induced changes in protein conformation. These spikes were not present in images of proteins with inhibited enzyme activity There have been very few attempts to extend PFM to the realm of liquid environments. The major difficulty is that most liquids are highly conductive and decompose even at low voltages One approach is to use insulating probes that have a conductive apex.
In this case, the voltage is localised, reducing stray currents and electromechanical artefacts Other studies have investigated the feasibility of liquid PFM in contact and intermittent contact modes for samples of PZT and periodically poled lithium niobate.
Surprisingly, Rodriguez et al. This observation is one that will limit the usefulness of the technique for scanning biological materials in liquid environments. Rodriguez et al. The quality of the images reduced when collected in a liquid environment compared to images collected in an ambient environment, perhaps because of increased damping effects. Yet, the contrast between piezoelectric intertubular and non-piezoelectric peritubular regions was still evident As the physiological environment of many biological materials, including proteins, is a liquid one, further work in this area could realise high-resolution PFM in biological samples under native conditions.
They reported that two-thirds of this water is structurally the same as ordinary water and the remaining one-third bound water is only slightly different In the range of the frequency sweep, there was no indication of any impedance resonance that would point towards piezoelectricity. Determining the dielectric constant of a protein is not a trivial task. The presence of an aqueous environment complicates both experimental and theoretical studies. In the literature, values for the dielectric constant of lysozyme range between 2 and Smith used long molecular dynamics simulations to show that an intermediate value for the dielectric constant of 30 may be most appropriate More recently, Li et al.
In terms of measuring electro-mechanical properties of lysozyme, the literature survey only uncovered one study. A publication from Ortore et al.
Even at ambient pressures, this difference persists. At ambient pressure, protein surface charges create an electric field that increases the hydration water density via electrostriction.
Interestingly, as the pressure is increased the hydration water density also increases in a manner that is analogous to the direct piezoelectric effect. A plot generated from literature data of the mean surface charge density as a function of the hydrostatic pressure is linear, but with a large y- intercept. Although incorrect units are derived, they calculate a strikingly high value for the effective piezoelectric coefficient, reporting a value of pC N We further hypothesis that the same symmetry restrictions that govern classical crystalline materials govern crystals of lysozyme also.
As the symmetry increase from triclinic through to tetragonal, the corresponding piezoelectric tensor becomes more constricted. We predict that monoclinic crystals of lysozyme will demonstrate longitudinal d22 , transverse d21 and d23 , and shear d14, d16, d25, d34 and d36 piezoelectric coefficients.
Hexagonal crystals of lysozyme have the potential to demonstrate only the shear piezoelectric coefficientss d14 and d25, which should be of equal magnitude and of opposite sign. Orthorhombic crystals of lysozyme may potentially demonstrate shear piezoelectric coefficients d14, d25 and d In its most common form point group tetragonal crystals of lysozyme may demonstrate only shear piezoelectric coefficients d14 and d25, which should be of equal magnitude and of opposite sign.
Observed in the bulk and at the nanoscale, the properties of piezoelectricity, pyroelectricity and ferroelectricity, seem to persist at all hierarchical levels. The exact mechanisms behind each are not always clear. Lysozyme is an ideal case-study material for several reasons. Like all natural proteins, it is chiral and non-centrosymmetric. Additionally, crystallising lysozyme in its various forms allows one to investigate how symmetry affects its physical properties. The following chapter will look at the methods of measuring dielectric properties in biological materials, highlighting the challenges involved.
Firstly, we introduce the principles of protein crystal growth. Then, the structural characterisation of protein crystals will be discussed with a particular focus on synchrotron diffraction. Next, we review the state-of-the-art methods of piezoelectric measurement and justify the selection of two methods the Berlincourt Method and Piezoresponse Force Microscopy for investigating piezoelectricity in proteins.
This chapter also discusses Switching-Spectroscopy PFM for investigations of ferroelectricity at the nanoscale. Finally, techniques for measuring pyroelectricity are reviewed in order to select a suitable method of measuring pyroelectricity in lysozyme crystals. In addition, the choice of salt, pH, ionic strength, protein concentration and any additives is critical to the realization of protein crystals. Unfortunately, the set of parameters required is unique to each protein, making protein crystallisation a challenging endeavour.
With so many parameters at play, screening methods identify suitable parameters that are optimised later. The simple process of salt crystallisation is a good place to begin to understand how proteins crystallise. In both cases the laws of thermodynamics apply and supersaturation proceeds crystal nucleation. To induce supersaturation in a salt solution, the solution is heated to increase its solubility. As the solution cools, its solubility decreases allowing it to become supersaturated.
The solution now contains more salt molecules than it would under normal conditions. It is no longer in equilibrium and seeks to find a more favourable thermodynamic state. The free-energy of the system is minimised when the salt begins to crystallise. Reaching this supersaturated state triggers crystal nucleation. Although temperature can be used to vary the solubility of salts, using temperature to vary the solubility of proteins is unwise, as it may cause denaturation. Instead, precipitants are added which bind to water molecules in the solute — reducing the number of water molecules available to the protein.
In effect, this reduces the protein solubility or thought about in another way, increases the effective protein concentration. Figure 3. Protein crystallisation is a two-stage process. Nucleation occurs during the first stage and crystal growth occurs in the second stage. Both stages require supersaturation conditions; however, nucleation needs a higher degree of saturation.
Therefore, the protein must first be pushed into the highly supersaturated labile zone where rapid nucleation happens. The protein must not stay in this zone for too long as a surplus of crystal nuclei impedes the growth of large crystals. Instead, the protein is pushed to the lower-supersaturated metastable zone.
In this zone, nucleation ceases and the existing crystals grow in size. There are various crystallisation techniques to control these processes so that good quality, large crystals can be grown for further studies. Initially, the concentration of precipitant in the reservoir is higher than that in the drop — setting up a concentration gradient.
Water from the drop evaporates, falling in to the reservoir below. Therefore, the volume of the drop decreases, and consequently the protein concentration within the drop increases. Eventually, the protein will supersaturate, initialising crystallisation. Both methods are relatively simple but the sitting drop has a slight disadvantage in that crystals may become stuck to the bottom of the well. However, the realisation made by Laue, Friedrich and Knipping in Munich in — that crystals diffract X- rays — would greatly extend the applications of X-rays and facilitate our understanding of the atomic structure of crystals.
The father and son team, W. Bragg and W. Bragg, developed the technique of X-ray diffraction, earning a Nobel Prize for their efforts in Another important contributor at the time was P. Ewald who devised a means of interpreting the geometry of the diffraction pattern using a construct called the reciprocal lattice described below. In , J.
Bernal and D. Crawfoot-Hodgkin discovered that protein crystals would diffract X-rays It took until to decipher a method of solving the protein structure from the diffraction pattern; myoglobin was the first protein to have its structure solved The anode also acts as the target.
X-rays are produced when high-speed electrons strike the target material often made of chromium, copper or molybdenum. Only a small portion of electrons are converted to X-rays during the collision. The remaining energy is dissipated as heat. A synchrotron is a powerful source of X-rays.
A schematic of a synchrotron is shown in Figure 3. Electrons produced by an electron gun are pre-accelerated in the booster ring before entering the storage ring.
The electrons are made to bend around the ring by strong magnets. Electrons circling the ring experience centripetal force and are accelerated to relativistic speeds producing X-rays.
Additionally, X-ray beams from synchrotron sources are of high intensity, allowing diffraction experiments to be performed on small crystals in a reasonable timeframe before degradation occurs. The shortest distance between atoms in a crystal is the length of a covalent bond, i. Thus, radiation in the visible spectrum approximately nm to nm will not diffract passing through a crystal. A higher energy radiation source is required. X-rays fulfil this criterion as their energy is in the range to eV.
The corresponding wavelength range for X-rays is 10 nm to 0. While this interpretation is not incorrect, it is cumbersome requiring six angles, three lattice spacings and three integers to determine the direction of the diffracted beam In the Bragg interpretation, atoms within the crystal are imagined to form layers or planes as in Figure 3.
The distance between planes is known as the inter-planar spacing and is denoted by dhkl, where hkl are miller indices. From Figure 3. Thus, Equation 3. Two abstract constructs that facilitate the interpretation of the diffraction pattern are shown in Figure 3. The Ewald sphere of 1 radius is drawn around the crystal.
As shown in Figure 3. Conversely, if the Bragg equation is not met, the lattice point will not intersect the sphere. Structural determination of the crystal involves two steps.
In the first step, the lattice parameters of the unit cell are calculated from the geometry of the diffraction pattern. In the second step, the distribution of atoms within the structure from the relative intensities of the diffractions spots is determined. The intensity of the diffraction spots is directly proportional to the square of the structure factor, Fhkl. While the Bragg equation considers a single atom to reside at each lattice point, it does not specify the scattering power of the each atom.
To a large extend it is the electrons within the atom that contribute to scattering. Thus, the structure factor is the ratio of the sum of the atomic scattering amplitudes fn to the amplitude scattered by a single atom.
The structure factor contains information about the amplitude and phase of the scattered waves Equation 3. That is, if the intensity of the diffraction pattern is known, the positions of the atoms within the unit cell can be determined. As mentioned above, the intensity of the diffraction spot is proportional to the square 2 of Fhkl. In crystallography, this is known as the phase problem. However, if the crystal does not have a centre of symmetry, as is the case of protein crystals, this solution is not valid.
Other methods of solving the phase problem include molecular replacement which makes use of the atomic co-ordinates of similar protein structure , isomorphic replacement which uses heavy-atom substitution and anomalous dispersion which uses the anomalous scattering that occurs at the absorption edge These methods allow the phase information to be determined from some a priori knowledge of the molecular structure.
Each method has advantages and limitations. This section reviews methods of measuring piezoelectricity, and justifies the choice of methods used in this work. The resonance method is a dynamic method of piezoelectric measurement. It measures the frequencies at which the material demonstrates a mechanical piezoelectric response to an applied AC voltage.
Piezoelectric materials each have a characteristic frequency at which it will vibrate freely, called the resonance frequency, and another frequency at which they resist vibration most effectively, called the anti- resonance frequency.
Both the resonance and anti-resonance frequencies are characteristic of the sample, from which the piezoelectric coefficients of the sample are accurately calculated. With careful consideration of sample geometry, electroding, shielding and the clamping arrangement, the resonance method measures piezoelectricity with great accuracy and repeatability However, the resonance method is not ideally suited to thin-film measurement.
In thin- films, the relationship between the piezoelectric and elastic properties and their resonant frequencies is not well established Additionally, piezoelectric resonance in thin-films occurs in the gigahertz range, outside the scope of most commercial impedance analysers. The technique works well for bulk samples, establishing a complete piezoelectric tensor.
However, achieving this requires the sample to be prepared in different geometries: as a disc, a plate and a cylinder In many cases, including in this work, satisfying this requirement is unfeasible. This resolution is sufficient to measure the small voltage-induced strains in piezoelectric materials. By knowing the voltage applied, one can calculate the piezoelectric coefficient of the sample This method has successfully measured the piezoelectric coefficient of bulk , thin-film , and biological samples While laser-interferometry is suitable for measuring piezoelectricity in thin-films, this type of measurement brings its own challenges.
A single-beam interferometer only monitors the displacement from the front surface of the sample. In this case, the bending artificially enlarges the deformation measured by the interferometer Simply strengthening the bond between the sample and substrate may not always be appropriate as it creates a clamping effect in the transverse direction Double- beam interferometry provides a convenient solution, monitoring both the front and back surfaces of the sample simultaneously , , Using laser interferometry to detect protein piezoelectricity would be challenging as the method works best with flat, well-polished samples.
However, laser interferometry has been used to study conformational changes and crystal growth processes in proteins. In terms of piezoelectric measurements, the effect of water on the piezoelectric properties of collagen were revealed by laser-interferometry In this project, the cost of purchasing or custom building a laser-interferometry system was not feasible.
Owing to the limitations and constraints of both the resonance method and laser- interferometry, these were not pursued further in this research project. As such, the Berlincourt method and PFM, emerged as two viable techniques for investigating protein piezoelectricity. The next section discusses the basic principle of each, as well as their suitability and limitations in greater depth. The original design was static; a known weight placed on top of the sample caused a charge to develop due to the piezoelectric effect.
Static measurements, however, suffer from thermal drift. For this reason, a quasi-static version of the method soon became the norm. The schematic in Figure 3. The piezoelectric coefficient, d, is calculated by employing the second constitutive equation from Appendix D Equation D.
This results in a simple equation that forms the basis of the Berlincourt method. The simplicity of the Berlincourt method is its main advantage. Taking measurements is quick and requires little sample preparation.
Unlike the resonance method, only one type of sample geometry is required However, the direct method has its limitations. The geometry of the sample, the magnitude of the preload force, the magnitude and the frequency of the oscillating force, the geometry of the electrodes as well as the temperature and humidity of the environment, can all affect the accuracy and consistency of the measurement , Thin-film samples are particularly challenging and often require modification of the method.
The Berlincourt method relies on the comparison between the test sample and a reference material. Therefore, the measurement is inherently dependent on the accuracy by which the piezoelectric coefficient of the reference material was established Modifying the classical Berlincourt method overcomes many of these challenges.
In cases where non-uniform loading or point loading is a concern, a pneumatic loading method is useful , In cases where the substrate heavily influences the measurement often true for thin films , the contribution of the substrate to the measured piezoelectric co-efficient can be altered by varying the geometry of the support substrate.
In this way, by using several different substrate geometries, the contribution of substrate effects to the piezoelectric coefficient of the sample can be determined mathematically Alternatively, finite element analysis can compensate for substrate effects by determine a calibration factor that relates the charge-force ratio to the true dcoefficient of the sample In this work, a commercial piezometer based on the Berlincourt method was available for the piezoelectric study.
While many factors may affect the overall measurement, careful consideration of these limitations as outlined in the IEEE standard and the National Physics Laboratory guide allows for accurate and reliable measurements. This advancement earned its creators a Nobel Prize in Today, SPM is an umbrella term capturing a range of techniques that measure forces van der Waals, electrostatic, magnetic and electrical properties at the nanoscale.
AFM generates topographical images with atomic-level resolution by rastering an ultra-sharp tip across the surface of a sample. Because of its high resolution, AFM has extensive applications in the semiconductor industry, as well as in material, polymer and biological sciences. This allows 3 rd and 4 th order tensors to be expressed as 6x3 and 6x6 matrices. The polarization vector , established during manufacture by a high DC voltage applied to the electrodes, is represented by an arrow pointing from the positive to the negative poling electrode.
This information is conveyed by a dot or stripe on the electrode surface held at high voltage during the poling process. It is helpful to remember that the polarization arrow represents the force exerted on a positive charge by a positive potential field. Thus, it signifies the direction a positively charged particle would displace when influenced by a nearby positive charge. It should be kept in mind that electron flow moves in the opposite direction.
Piezoelectric coefficients , relating input parameters to output parameters, use double subscripts. The first subscript denotes the direction of the electric field E or dielectric displacement D, and the second subscript refers to the direction of mechanical stress T or strain S. The piezoelectric charge coefficient is a 3 rd order tensor that can be expressed as a 3x6 matrix that correlates the charge displaced unit area with electrodes short circuited , associated with an applied stress, according to the relation:.
The first subscript gives the direction of the charge motion associated with the applied stress. The second subscript gives the direction of mechanical stress. D33 relates the ratio of charge motion along the 3-axis to the stress applied along the 3-axis, assuming the electrodes are shorted, and no other stresses are present.
D31 relates the charge flow along the 3-axis to the stress along the 1-axis or 2-axis under similar conditions. The piezoelectric voltage coefficient , g, is a 3 x 6 matrix and correlate the electric field, E, developed with electrodes open circuited , associated with an applied stress, T, according to the relation:. The first subscript gives the direction of the electric field associated with the applied stress.
Piezoelectric coefficients, used to relate input parameters to output parameters, use double subscripts. The piezoelectric strain coefficients , d ij , correlate the strain produced by an applied electric field according to the relation:.
The first subscript gives the direction of the electric field associated with the applied voltage. The second subscript gives the direction of mechanical strain. The coupling coefficient, k lower case , is an indication of the materials ability to convert electrical energy to mechanical energy. Specifically, the square of the coupling coefficient equals the ratio of mechanical energy output to the electrical energy input.
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