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MICROPHONES

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A microphone, sometimes referred to as a mike or mic (pronounced "mike"), is an acoustic to electric transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, tape recorders, hearing aids, motion picture production, live and recorded audio engineering, in radio and television broadcasting and in computers for recording voice, VoIP and numerous other computer applications.

An Oktava condenser microphone

## Invention

The word "microphone" (Greek mikros "small" and phone "sound") originally referred to a mechanical hearing aid for small sounds.[1]

The invention of a practical microphone was crucial to the early development of the telephone system. Emile Berliner invented the first microphone on March 4, 1877, but the first useful microphone was invented by Alexander Graham Bell. Many early developments in microphone design took place in Bell Laboratories.

## Principle of operation

All microphones capture sound waves with a thin, flexible diaphragm (or ribbon in the case of ribbon microphones). The vibrations of this element are then converted by various methods into an electrical signal that is an analog of the original sound. Most microphones in use today use electromagnetic generation (dynamic microphones), capacitance change (condenser microphones) or piezoelectric generation to produce the signal from mechanical vibration.

## Microphone varieties

### Capacitor or condenser microphones

In a capacitor microphone, also known as a condenser microphone, the diaphragm acts as one plate of a capacitor, and the vibrations produce changes in the distance between the plates. Since the plates are biased with a fixed charge (Q), the voltage maintained across the capacitor plates changes with the vibrations in the air, according to the capacitance equation:

$Q = C \cdot V$

where Q = charge in coulombs, C = capacitance in farads and V = potential difference in volts. The capacitance of the plates is inversely proportional to the distance between them for a parallel-plate capacitor.:

$C \propto \frac{A}{d}$

Capacitor microphones can be expensive and require a power supply, commonly provided from mic inputs as phantom power, but give a high-quality sound signal and are now the preferred choice in laboratory and studio recording applications.

### Electret capacitor microphones

An electret microphone is a relatively new type of condenser microphone invented at Bell laboratories in 1962 by Gerhard Sessler and Jim West [2], and often simply called an electret microphone. An electret is a dielectric material that has been permanently electrically charged or polarised. The name comes from electrostatic and magnet; a static charge is embedded in an electret by alignment of the static charges in the material, much the way a magnet is made by aligning the magnetic domains in a piece of iron. They are used in many applications, from high-quality recording and lavalier use to built-in microphones in small sound recording devices and telephones. Though electret mikes were once considered low-cost and low quality, the best ones can now rival capacitor mikes in every respect (apart from low noise) and can even have the long-term stability and ultra-flat response needed for a measuring microphone. Unlike other condenser microphones, they require no polarising voltage, but normally contain an integrated preamplifier which does require power (often incorrectly called polarizing power or bias). This preamp is frequently phantom powered in sound reinforcement and studio applications. While few electret microphones rival the best DC-polarized units in terms of noise level, this is not due to any inherent limitation of the electret. Rather, mass production techniques needed to produce electrets cheaply don't lend themselves to the precision needed to produce the highest quality microphones.

### Dynamic microphones

In a dynamic microphone a small movable induction coil, positioned in the magnetic field of a permanent magnet, is attached to the diaphragm. When sound enters through the windscreen of the microphone, the sound wave vibrations move the diaphragm. When the diaphragm vibrates, the coil moves in the magnetic field, producing a varying current in the coil through electromagnetic induction. The principle is exactly the same as in a loudspeaker, only reversed. Dynamic microphones are robust, relatively inexpensive, and resistant to moisture, and for this reason they are widely used on-stage by singers. They tend to have a poor low-frequency response, which is advantageous for reducing handling noise as a vocal mic, but tends to exclude them from other uses.

### Ribbon microphones

In ribbon microphones a thin, usually corrugated metal ribbon is suspended in a magnetic field. The ribbon is electrically connected to the microphone's output, and its vibration within the magnetic field generates the electrical signal. Basic ribbon microphones detect sound in a bidirectional (also called figure-eight) pattern because the ribbon, which is open to sound both front and back, responds to the pressure gradient rather than the sound pressure. Though the symmetrical front and rear pickup can be a nuisance in normal stereo recording, the high side rejection can be used to advantage by positioning a ribbon mic horizontally, for example above cymbals, so that the rear lobe picks up only sound from the ceiling. Other directional patterns are produced by enclosing one side of the ribbon in an acoustic trap or baffle, allowing sound to reach only one side. Ribbon mics give very high quality sound reproduction, and were once valued for this reason, but a good low-frequency response can be obtained only if the ribbon is suspended very loosely, and this makes them fragile. Protective wind screens can reduce the danger of damaging the ribbon, but will somewhat reduce the bass response at large miking distances.

Ribbon microphones don't require phantom power; in fact, this voltage can damage these microphones.

Inside the Oktava 319 condenser microphone

### Carbon microphones

A carbon microphone, formerly used in telephone handsets, is a capsule containing carbon granules pressed between two metal plates. A voltage is applied across the metal plates, causing a small current to flow through the carbon. One of the plates, the diaphragm, vibrates in sympathy with incident sound waves, applying a varying pressure to the carbon. The changing pressure deforms the granules, causing the contact area between each pair of adjacent granules to change, and this causes the electrical resistance of the mass of granules to change. The changes in resistance cause a corresponding change in the voltage across the two plates, and hence in the current flowing through the microphone, producing the electrical signal. Carbon microphones were once commonly used in telephones; they have extremely low-quality sound reproduction and a very limited frequency response range, but are very robust devices. Unlike other microphone types, the carbon microphone can also be used as a type of amplifier, using a small amount of sound energy to produce a larger amount of electrical energy. Carbon microphones found use as early telephone repeaters, making long distance phone calls possible in the era before vacuum tubes. These repeaters worked by mechanically coupling a magnetic telephone receiver to a carbon microphone: the faint signal from the receiver was transferred to the microphone, with a resulting stronger electrical signal to send down the line.

### Piezo microphones

A piezo (pronounced "pee-ay-zo" or "pie-ee-zo") microphone uses the phenomenon of piezoelectricity—the ability of some materials to produce a voltage when subjected to pressure—to convert vibrations into an electrical signal. Piezo transducers are often used as contact microphones to amplify acoustic instruments for live performance, or to record sounds in unusual environments (underwater, for instance).

An example of this is Rochelle salt (potassium sodium tartrate), which is a piezoelectric crystal that works as a transducer both ways; it is also commonly used as a slimline loudspeaker component.

### Laser microphones

A laser microphone is an exotic application of laser technology. It consists of a laser beam that must be reflected off a glass window or another rigid surface that vibrates in sympathy with nearby sounds. This device essentially turns any vibrating surface near the source of sound into a microphone. It does this by measuring the distance between itself and the surface extremely accurately; the tiny fluctuations in this distance become the electrical signal of the sounds picked up. Laser microphones are new, very rare and expensive, and are most commonly portrayed in the movies as spying devices.

### Speakers as microphones

A loudspeaker is the exact opposite of a microphone, since it's a transducer that turns an electrical signal into sound waves. However, because a conventional speaker is constructed much like a dynamic microphone (with a diaphragm, coil and magnet), speakers can actually work "in reverse" as microphones. The result, though, is a microphone with poor quality, limited frequency response (particularly at the high end), and poor sensitivity.

In practical use, speakers are sometimes used as microphones in such applications as intercoms or walkie-talkies, where high quality and sensitivity are not needed. However, there is at least one other novel application of this principle; using a medium-size woofer placed closely in front of a "kick" (bass drum) in a drum set to act as a microphone. This has been commercialized with the Yamaha "Subkick".[3]

## Other microphone types

A pressure gradient microphone is a microphone in which both sides of the diaphragm are exposed to the incident sound and the microphone is therefore responsive to the pressure differential (gradient) between the two sides of the membrane. Sound incident parallel to the plane of the diaphragm produces no pressure differential, giving pressure-gradient microphones their characteristic figure-eight directional patterns. They are also called "velocity microphones", since the output voltage is proportional to the air particle velocity.

A lavalier microphone is made for hands-free operation. These small microphones are worn on the body and held in place either with a lanyard worn around the neck or a clip fastened to clothing. The cord may be hidden by clothes and either run to an RF transmitter in a pocket or clipped to a belt (for mobile use), or run directly to the mixer (for stationary applications).

A wireless microphone is one which does not use a cable. It usually transmits its signal using a small FM radio transmitter to a nearby receiver connected to the sound system, but it can also use infrared light if the transmitter and receiver are within sight of each other.

A contact microphone is designed to pick up vibrations directly from a solid surface or object, as opposed to sound vibrations carried through air. One use for this is to detect sounds of a very low level, such as those from small objects or insects. The microphone commonly consists of a magnetic (moving coil) transducer, contact plate and contact pin. The contact plate is placed against the object from which vibrations are to be picked up; the contact pin transfers these vibrations to the coil of the transducer. Contact microphones have been used to pick up the sound of a snail's heartbeat and the footsteps of ants. A portable version of this microphone has recently been developed.

A throat microphone is a variant of the contact microphone, used to pick up speech directly from the throat, around which it is strapped. This allows the device to be used in areas with ambient sounds that would otherwise make the speaker inaudible.

A parabolic microphone uses a parabolic reflector to collect and focus sound waves onto a microphone receiver, in much the same way that a parabolic antenna (e.g. satellite dish) does with radio waves. Typical uses of this microphone, which has unusually focused front sensitivity and can pick up sounds from many meters away, include nature recording, outdoor sporting events, eavesdropping, law enforcement, and even espionage. Parabolic microphones are not typically used for standard recording applications, because they tend to have poor low-frequency response as a side effect of their design.

## Connectivity

### Connectors

The most common connectors used by microphones are:

• Male XLR connector on professional microphones

• 1/4'' mono phone plug (UK "jack plug") on consumer (less expensive) microphones

• 3.5 mm mono mini phone plug on very inexpensive and computer microphones

Some microphones use other connectors, such as TRS, 5-pin XLR, or stereo mini phone plug on some stereo microphones. Some lavaliers have a proprietary connector to connect them to their transmitter. Since 2005, professional-quality microphones with USB connections have begun to appear, designed for direct recording into computer-based software studios.

### Impedance matching

Microphones have an electrical characteristic called impedance, measured in ohms (Ω) that depends on the design. Low impedance is considered under 600 Ω. Medium impedance is considered between 600 Ω and 10 kΩ. High impedance is above 10 kΩ. Most professional microphones are low impedance, about 200 Ω. Less expensive models have an impedance of at least 600 Ω. Low-impedance microphones are preferred over high impedance on long-run cables for two reasons: one is that using a high-impedance mike with a long cable is likely to result in loss of high frequency signal; the other is that long high-impedance cables tend to pick up more hum (and possibly radio-frequency interference (RFI) as well).

To get the best sound, the impedances of the microphone and the equipment to which it is connected must match. There are transformers (called matching transformers) that adapt impedances, such as DI units. In general, any XLR microphone can be connected to any mixer with XLR inputs, and any plug microphone can be connected to any jack plug that is marked as a microphone input, but it can't be connected to a line input.

## Directionality

A microphone's directionality or polar pattern indicates how sensitive it is to sounds arriving at different angles about its central axis. The polar pattern represents the locus of points that produce the same signal level output in the microphone if a given sound pressure level is generated from that point.

An omnidirectional microphone's response is generally considered to be a perfect sphere in three dimensions. In the real world, this is not the case. As with directional microphones, the polar pattern for an "omnidirectional" microphone is a function of frequency. The body of the microphone is not infinitely small and, as a consequence, it tends to get in its own way with respect to sounds arriving from the rear, causing a slight flattening of the polar response. This flattening increases as the diameter of the microphone (assuming it's cylindrical) reaches the wavelength of the frequency in question. Therefore, the smallest diameter microphone will give the best omnidirectional characteristics at high frequencies. The wavelength of sound at 10 kHz is about an inch (2.5 cm) so the smallest measuring microphones are often 1/4" (6 mm) in diameter, which practically eliminates directionality even up to the highest frequencies. Omnidirectional microphones, unlike cardioids, do not employ resonant cavities as delays, and so can be considered the "purest" mikes in terms of low coloration; they add very little to the original sound. Being pressure-sensitive they can also have a very flat low-frequency response down to 20 Hz or below. Pressure-sensitive mikes also respond much less to wind noise than directional (velocity sensitive) mikes.

A unidirectional microphone is sensitive to sounds from only one direction. The diagram above illustrates a number of these patterns, with the microphone capsule being represented as a red dot. The top of the diagram is the front of the mic. The sound intensity for a particular frequency is plotted for angles radially from 0 to 360°. (Professional diagrams show these scales and include multiple plots at different frequencies. These diagrams just provide an overview of the typical shapes and their names.)

The most common unidirectional mike is a cardioid microphone, so named because the sensitivity pattern is heart-shaped. A hyper-cardioid is similar but with a tighter area of front sensitivity and a tiny lobe of rear sensitivity. These two patterns are commonly used as vocal or speech mikes, since they are good at rejecting sounds from other directions. Because they employ internal cavities to provide front-back delay, directional mikes tend to have more coloration than omnis, and they also suffer from low-frequency roll-off. These problems are overcome to a large extent by careful design, but only the best cardioids can begin to approach the performance of a tiny low-cost omni in terms of absolute accuracy. This is not always recognised, but is the price paid for directionality, often needed to exclude ambient reverberation wherever very close placement is impossible.

Figure 8 or bi-directional mikes receive sound from both the front and back of the element. Most ribbon microphones are of this pattern.

Shotgun microphones are the most highly directional. They have small lobes of sensitivity to the left, right, and rear but are significantly more sensitive to the front. This results from placing the element inside a tube with slots cut along the side; wave-cancellation eliminates most of the off-axis noise. Shotgun microphones are commonly used on TV and film sets, and for location recording of wildlife.

An omnidirectional microphone is a pressure transducer; the output voltage is proportional to the air pressure at a given time.

On the other hand, a figure-8 pattern is a pressure gradient transducer; the output voltage is proportional to the difference in pressure on the front and on the back side. A sound wave arriving from the back will lead to a signal with a polarity opposite to that of an identical sound wave from the front. Moreover, shorter wavelengths (higher frequencies) are picked up more effectively than lower frequencies.

A cardioid microphone is effectively a superposition of an omnidirectional and a figure-8 microphone; for sound waves coming from the back, the negative signal from the figure-8 cancels the positive signal from the omnidirectional element, whereas for sound waves coming from the front, the two add to each other. A hypercardioid microphone is similar, but with a slightly larger figure-8 contribution.

Since directional microphones are (partially) pressure gradient transducers, their sensitivity is dependent on the distance to the sound source. This is known as the proximity effect, a bass boost at distances of a few centimeters.

## Measurements and specifications

Because of differences in their construction, microphones have their own characteristic responses to sound. This difference in response produces non-uniform phase and frequency responses. In addition, mics are not uniformly sensitive to sound pressure, and can accept differing levels without distorting. Although for scientific applications microphones with a more uniform response are desirable, this is often not the case for music recording, as the non-uniform response of a microphone can produce a desirable coloration of the sound. There is an international standard for microphone specifications (IEC 60268-4), but very few manufacturers adhere to it.

A frequency response diagram plots the microphone sensitivity in decibels over a range of frequencies (typically at least 0–20 kHz), generally for perfectly on-axis sound (sound arriving at 0° to the capsule). Frequency response may be less informatively stated textually like so: "20 Hz–20 kHz ±3 dB". This is interpreted as a (mostly) linear plot between the stated frequencies, with variations in amplitude of no more than 3 dB plus or minus. However, one cannot determine from this information how smooth the variations are, nor in what parts of the spectrum they occur. Note that commonly-made statements such as "20 Hz–20 kHz" are meaningless without a decibel measure.

The self-noise or equivalent noise level is the sound level that creates the same output voltage as the inherent noise of the microphone. This represents the lowest point of the microphone's dynamic range, and is particularly important should you wish to record sounds that are quiet. The measure is often stated in dBA, which is the equivalent loudness of the noise on a decibel scale frequency-weighted for how the ear hears, for example: "15 dBA SPL" (SPL means sound pressure level relative to 20 micropascals). The lower the number the better. Some microphone manufacturers state the noise level using ITU-R 468 noise weighting, which more accurately represents the way we hear noise, but gives a figure some 11 to 14 dB higher. A quiet microphone will measure typically 20 dBA SPL or 32 dB SPL 468-weighted.

The maximum SPL (sound pressure level) the microphone can accept is measured for particular values of total harmonic distortion (THD), typically 1%. This is generally inaudible, so one can safely use the mic at this level without harming the recording. Example: "142 dB SPL peak (<1% THD)". The higher the value, the better.

The clipping level is perhaps a better indicator of maximum useable level as the 1% THD figure usually quoted under max SPL is really a very mild level of distortion, quite inaudible especially on brief high peaks. Harmonic distortion from microphones is usually of low-order (mostly third harmonic) type, and hence not very audible even at 3-5%. Clipping, on the other hand, usually caused by the diaphram reaching its absolute displacement limit (or by the preamplifier), will produce a very harsh sound on peaks, and should be avoided if at all possible. For some mikes the clipping level may be much higher than the max SPL.

The dynamic range of a mike is the difference in SPL between the noise floor and the maximum SPL. If stated on its own, for example "120 dB", it conveys significantly less information than having the self-noise and maximum SPL figures individually.

Sensitivity indicates how well the mike converts acoustic pressure to output voltage. A high sensitivity mike creates more voltage and so will need less amplification at the mixer or recording device. This is a practical concern but not directly an indication of the mike's quality, and in fact the term sensitivity is something of a misnomer, 'transduction gain' being perhaps more meaningful, (or just "output level") because true sensitivity will generally be set by the noise floor, and too much "sensitivity" in terms of output level will compromise the clipping level. There are two common measures. The (preferred) international standard is made in mV per pascal at 1 kHz. A higher value indicates greater sensitivity. The older American method is referred to a 1 V/Pa standard and measured in plain dB, resulting in a negative value. Again, a higher value indicates greater sensitivity, so −60  dB is more sensitive than −70 dB.

## Measurement microphones

Some microphones are intended for use as standard measuring microphones for the testing of speakers and checking noise levels etc. These are calibrated transducers and will usually be supplied with a calibration certificate stating absolute sensitivity against frequency.

### Microphone calibration techniques

#### Pistonphone apparatus

A pistonphone is an acoustical calibrator (sound source) using a closed coupler to generate a precise sound pressure for the calibration of instrumentation microphones. The principle relies on a piston mechanically driven to move at a specified rate on a fixed volume of air to which the microphone under test is exposed. The air is assumed to be compressed adiabatically and the SPL in the chamber can be calculated from PV = const. The Piston phone method only works at low frequencies but can be accurate and is related to an easily calculable sound pressure level. The standard test frequency is usually around 250 Hz.

#### Reciprocal method

This method relies on the reciprocity of one or more microphones in a group of 3 to be calibrated. It can still be used when only one of the microphones is reciprocal (exhibits equal response when used as a microphone or as a loudspeaker).

## Microphone techniques

There exist a number of well-developed microphone techniques used for miking musical, film, or voice sources. Choice of technique depends on a number of factors, including:

• The collection of extraneous noise. This can be a concern, especially in amplified performances, where audio feedback can be a significant problem. Alternatively, it can be a desired outcome, in situations where ambient noise is useful (hall reverberation, audience reaction).

• Choice of a signal type: Mono, stereo or multi-channel.

• Type of sound-source: Acoustic instruments produce a very different sound than electric instruments, which are again different from the human voice.

• Situational circumstances: Sometimes a microphone should not be visible, or having a microphone nearby is not appropriate. In scenes for a movie the microphone may be held above the pictureframe, just out of sight. In this way there is always a certain distance between the actor and the microphone.

• Processing: If the signal is destined to be heavily processed, or "mixed down", a different type of input may be required.

• The use of a windshield as well as a pop shield, designed to reduce vocal plosives.

### Basic techniques

There are several classes of microphone placement for recording and amplification.

• In close miking, a directional microphone is placed relatively close to an instrument or sound source. This serves to eliminate extraneous noise, including room reverberation, and is commonly used when attempting to record a number of separate instruments while keeping the signals separate, or when trying to avoid feedback in an amplified performance. This technique was first used by Les Paul on his version of "The Tennessee Waltz" with Mary Ford.

• In ambient or distant miking, a microphone—typically a sensitive one—is placed at some distance from the sound source. The goal of this technique is to get a broader, natural mix of the sound source or sources, along with ambient sound, including reverberation from the room or hall.

### Stereo recording techniques

There are two essential components to placing objects (phantom sources) in the stereo sound-field between the loudspeakers. These are the level difference Δ L, the relative loudness, and the time-delay difference Δ t, the difference in arrival time. The "interaural" signals (binaural ILD and ITD) at the ears are not the stereo microphone signals which are coming from the loudspeakers, and are called "interchannel" signals (Δ L and Δ t). These signals are normally not mixed. Loudspeaker signals are different from the sound arriving at the ear. See the section "Binaural recording for earphones".

#### Conventional stereo recording for loudspeakers

The following microphone techniques can be used to capture the live "soundstage":

• The X-Y technique involves the coincident placement of two directional (cardioid) microphones. When two directional microphones are placed coincidentally, typically at a 90° angle (or greater) to each other (typically with each microphone pointing to a side of the soundstage), a stereo effect is achieved simply through intensity differences between the sound entering each microphone. Due to the lack of time-of-arrival stereo information, the stereo effect in X-Y recordings has less ambience. The main advantage is that the signal is mono-compatible, i.e., the signal is suitable for playback on non-stereo devices such as AM radio. If two bi-directional (figure 8) microphones are used instead of cardioid microphones, this technique is known as a Blumlein pair .

• The Mid-Side (M-S) technique is a special case of X-Y and uses a directional cardioid or an omnidirectional pressure microphone (M) and a bidirectional (figure-8) microphone (S), placed at a 90° angle to each other with the directional microphone facing the soundstage. The outputs of these microphones are mixed in such a way as to generate sum and difference signals between the outputs. The S signal is added to the M for one channel, and is subtracted (by reversing phase and adding) to generate the other channel. M-S has two advantages: when the stereo signal is combined into mono, the signal from the S microphone cancels out entirely, leaving only the mono recording from the directional M microphone; additionally, M-S recordings can be "remixed" after recording to alter or even remove the stereo spread. The M-S technique with an omnidirectional M microphone is equivalent to X-Y with two cardioids at a 180° angle.

• Near-coincident recording is a variant of the X-Y technique and incorporates interchannel time delay by placing the microphones several inches apart. The ORTF stereo technique of the Office de Radiodiffusion Télévision Française (Radio France), calls for a pair of cardioid microphones placed 17 cm apart at an angle of 110°. In the NOS stereo technique of the Nederlandse Omroep Stichting (Holland Radio), the angle is 90° and the distance is 30 cm. The choice between one and the other depends on the recording angle of the microphone system, not on the distance to and the width of the sound source. This technique leads to a realistic stereo effect and has reasonable mono-compatibility. These interchannel signals have nothing to do with interaural signals which come only from artificial head recordings. Even the spacing of 17 cm has nothing to do with human ear distance. The ORTF and NOS engineers did not think in those terms, because this microphone system was developed for a set of stereo loudspeakers, not for earphones.

• The A-B technique uses two omnidirectional microphones at a moderate distance from each other (20 centimeters up to a few meters). Stereo information consists of large time-of-arrival distances and some sound level differences. With excessively large distances, the stereo image can be perceived as somewhat unnatural, as if the left and right channel are independent sound sources without an even spread from left to right. A-B recordings are not so good for mono playback because the time-of-arrival differences can lead to certain frequency components being canceled out and others being amplified, the so-called comb-filtering effect, but the stereo sound can be really convincing. If wide A-B is used for large orchestras, the center can be filled with another microphone. Then one gets the famous "Decca tree", which has brought us many good sounding recordings.

• The Blumlein shuffler technique uses two microphones spaced around 20 cm (head width), and these are usually, but not necessarily, omnidirectional. A special "Blumlein shuffler" circuit integrates the difference signal, before matrixing it to produce an output in which phase (time delay) information has been converted to amplitude difference. This is a purist technique for providing true stereo from binaural capture, permitting omnidirectional microphones to be used (with their low coloration and flat low-frequency response) for true stereo. It has been little used, probably because of the lack of commercial shufflers. While offering very realistic stereo, it can emphasise low frequencies picked up from the sides unless the shuffler incorporates rolloff in the difference path. A central baffle, in the form of a foam disc suspended between the microphones, provides level separation above 2 kHz where the shuffling has to be phased out.

• The Baffled Omnidirectional technique uses a pair of near-coincident omnidirectional microphones with an absorptive baffle between them and is closely related to binaural technique. Stereo information consists primarily of time-of-arrival differences between the microphones and intensity differences from the baffle. The Jecklin Disk, described by the Swiss radio technician Juerg Jecklin, uses of a 30 cm flat circular sound absorbing baffle arranged vertically with the faces perpendicular to the sound source. Pressure microphones are placed 16.5 cm apart, directly left and right of the disk's center. The KFM Sphere, described by Guenther Theile, consists of two pressure microphones mounted on opposite sides of a 20 cm sphere. The microphones are mounted flush with the surface and arranged with the 0-axis perpendicular to the sound source.

### Surround Microphone Techniques

• The Double MS Technique was developed by Chris Wittig and Neil Muncy, and uses a front-facing mid-side microphone pair of direct sound pickup and a rear MS pair facing away from the front. The rear pair is placed at or just beyond the critical distance of the room where the reverberant sound level equals the direct sound level. The matrixed outputs feed front-left, front-right, rear-left, and rear-right speakers.

• The Surround Ambience Microphone Array was developed by Gunther Theile of the Institute for Rundfunktechnik (IRT). Four cardioid microphones are placed 90 degrees to each other and 21 to 25cm apart. No center channel is described.

• The Spider Microphone Array uses a special mike mount with five arms that radiate out from a center point, like a star. At the end of each arm is a condenser microphone aiming outward from the center. Two examples: The Microtech Gefell INA 5 uses five M930 mics in shock mounts. In the SPL Atmos 5.1/ASM 5 Surround Recording System, five Brauner condenser mikes feed a five channel mixing console, which adjusts the mic polar patterns and offers panning, bass management, and surround monitoring. SPL's Web site is www.spl-usa.com Both systems use the Ideal Cardioid Arrangement (ICA 5, ITU-775 specification), developed by Volker Henkels and Ulf Herrmann.

## Microphone manufacturers

• AKG Acoustics

• Audio Engineering Associates

• Audio-Technica

• Audix

• Behringer

• Beyerdynamic

• Blue Microphones

• Brauner Microphones

• Brüel & Kjær

• DPA Microphones (formerly known as B&K)

• Earthworks

• Electro-Voice

• Feilo

• Groove Tubes

• Josephson Engineering

• Lauten Audio

• M-Audio

• Manley Labs

• MicFactory

• Microtech-Gefell GmbH

• Milab

• MXL

• Georg Neumann GmbH

• Oktava

• Røde Microphones

• Royer Labs

• Samson Technologies

• Sanken

• Schoeps

• SE Electronics

• Sennheiser

• ShinyBox Audio

• Shure Incorporated

• Sonic Studios

• Soundelux Microphones

• SoundField

• Studio Projects

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text:
# Why is del operator coordinate free?

In solving Laplace equation $\Delta u=0$, every textbook will tell you to transform $\Delta=\partial_{xx}+\partial_{yy}$ into polar coordinate form $\Delta_p$(What it looks like doesn't matter here). Then it sets $\Delta_p v(r,\theta)=0$. How can you be sure that $u(x,y)=v(r(x,y),\theta(x,y))$?

I think the problem does not only exist in Laplacian operator case. So my question is "is Del operator coordinate free, in what sense and why?"

-
Yu can think on the "Laplacian" operator as the trace of the Hessian and, as long it is a trace of an operator, it is coordinate free. –  matgaio May 1 '12 at 21:12
There is a more intrinsic view of partial (and, more generally, directional) derivatives as linear functional on the space os smooth real functions. You can think this way: for each $p\in\mathbb{R}^n$ and $v\in\mathbb{R}^n$ define a linear functional $\frac{\partial}{\partial v}:C^\infty(\mathbb{R}^n)\rightarrow \mathbb{R}$ as $\frac{\partial}{\partial v}(f)=\frac{d}{dt}(f(\gamma(t)))_{t=0}$ where $\gamma:(-\epsilon,+\epsilon)\rightarrow\mathbb{R}^n$ is a smooth curve with $\gamma(0)=p$ and $\gamma'(0)=v$. Once you check this doesn't depends on the curve, this is intrinsic. –  matgaio May 1 '12 at 21:24
Do you imply that del operator will not change under any coordinate change? Even from an orthogonal one to an oblique one? –  Tim May 1 '12 at 21:33
The value that is returns when applyed to a function will not depend on the system of coordinates, once it can be calculated as the derivative of a composition. The expression in the coordinates you are using could change, but given $p$, $v$ and a function, the value $\frac{\partial}{\partial v}(f)$ in $p$ will not change –  matgaio May 1 '12 at 21:41
That's the first derivative. I still have doubts about higher derivative. Laplacian is second derivative. –  Tim May 1 '12 at 21:49

format: plain


text:
Open access peer-reviewed chapter - ONLINE FIRST

# Valorization of Native Nuts from Brazil and Their Coproducts

By Renan Danielski, Gabriela Polmann and Jane Mara Block

Submitted: May 22nd 2020Reviewed: November 17th 2020Published: December 2nd 2020

DOI: 10.5772/intechopen.95056

## Abstract

The consumption of nuts as part of a healthy diet and active lifestyle has long been associated with chronic disease prevention. Nuts and their coproducts such as oil, cake, plant-based milk substitutes, flour, and shell are rich in lipids, proteins, phenolics, and other bioactive compounds. Nut flour also presents interesting physical properties, such as water or oil holding capacity, foam properties, emulsifying activity, and emulsion stability. These biological and physical properties make these products commercially attractive as organic ingredients in several foods such as spreads, bakery products, and cereal bars. In this chapter, the nutritional and bioactive profiles, as well as the evidenced health-promoting effects of nuts originating from Brazil, will be discussed. The focus will be on commercial nuts such as cashews, pecan, and Brazil nuts, along with some underexplored and relatively unknown indigenous species, such as sapucaia, chichá, monguba, and pracaxi. The knowledge of these Brazilian native nuts and their coproducts is important for stimulating their consumption among the population and their large-scale commercialization.

### Keywords

• oilseeds
• biodiversity
• bioactive compounds
• lipids

## 1. Introduction

The consumption of nuts as part of a healthy diet and active lifestyle has long been associated with chronic disease prevention such as cardiovascular diseases, type 2 diabetes, cognitive function impairment, inflammatory disorders, among others. A closer look into the composition of nuts may help understand their health-promoting effects. They are rich in unsaturated acids such as oleic and linoleic, and have low concentrations of saturated fatty acids. In addition, the oil fraction presents significant amounts of tocopherols and phytosterols. The cake and shell, coproducts obtained from nuts, are rich in polyphenols. Besides the lipids and bioactive substances, nuts and their coproducts are also rich in other macronutrients (protein and fiber) and micronutrients (vitamins and minerals). The composition and concentration of bioactive compounds vary according to the type of nut and its coproducts [1].

Brazil has a great diversity of nut trees distributed in five of its six biomes Amazon, Cerrado, Atlantic Forest, Caatinga, Pampas, and Pantanal. Figure 1 presents the Brazilian biomes where the nuts discussed in this chapter are found.

Brazil nuts and cashew are commercial nuts native to Brazil. The cashew tree (Anacardium occidentale L.), which is well adapted in tropical and subtropical regions, is present in Cerrado, a biome known for long periods of drought. The nut, which is obtained from the cashew fruit, is composed of shell, skin, and almond. The largest producer of cashew nuts in 2018 was Vietnam (863,060 tons), followed by India (745,000 tons), Côte d’Ivoire (711,000 tons), Philippines (222,541 tons) and Brazil (141,418 tons) [2]. The Brazilian state of Ceará led the production with 61.9% of the planted area of cashew trees, followed by Rio Grande do Norte (15.4%), and Piauí (15.2%) [2].

Brazil nut tree (Bertholletia excelsa) is present in the Amazon, where it grows in well-drained soil along the Amazon River without the use of pesticides and herbicides. Brazil is the largest producer of Brazil nuts in the world (36,923 tons), followed by Bolivia, Ivory Coast, and Peru (25,749; 19,356; and 6042 tons, respectively) [2].

On the other hand, the pecan nut (Carya illinoinensis) is native to northern Mexico and southern United States. It was introduced in Brazil in 1866, and it is cultivated in the biomes Atlantic Forest, and mainly in the Pampas in the southeast and south regions. The tree is large-sized and can grow up to 20-40 m, and its fruit is technically classified as a drupe, characterized by a single pit surrounded by husk [3, 4].

These commercial or named conventional nuts in Brazil are usually consumed in a variety of ways such as raw, roasted and salted, caramelized, and coated. In addition, they can be incorporated into other food products, such as cereal bars, chocolates, bakery goods and spreads, among other foods. They can also be used for the extraction of specialty oils and for obtaining plant-based milk [1, 5, 6, 7].

However, the availability of nuts in Brazil is not limited to cashew, pecan, and Brazil nuts. A large variety of nut trees is available, especially in the Amazon region. These relatively unknown indigenous nuts represent a vast potential for the introduction into the diet of Brazilians and other consumers around the world. Sapucaia, chichá, monguba, and pracaxi are some of the nuts, which are not commercialized on a large scale and are usually consumed in their natural form by the local population. Therefore, data on their production is not found in the literature. A few reports showed that such nuts are also rich in macro and micronutrients, including phenolic compounds [8, 9, 10].

Sapucaia (Lecythis Pisonis) grows in the Atlantic Forest biome [9], while monguba (Prachira aquatica) and pracaxi (Pentaclethra macroloba (Wild.) Kuntze) can be found in the Amazon. The monguba tree is cultivated in different regions of the Amazon biome as an ornamental plant. Its fruits are oval-shaped, surrounded by a brown wooden peel where large-sized seeds are contained. The seeds are edible and can be consumed in a variety of ways, such as roasted, boiled, or fried [10]. The pracaxi tree produces a pod-shaped fruit containing edible seeds, from which phenolic-rich oils can be obtained [11]. Chichá (Sterculia striata), a nut tree originated from India and Malaysia, has thrived in the semi-arid conditions of the Cerrado, yielding nuts rich in phenolic compounds and lower lipid content [8].

This chapter presents the nutritional composition, phytochemical properties, and bioactive compounds of commercial (cashew, Brazil nuts, and pecan) and non-commercial (sapucaia, chichá, monguba, and pracaxi) nuts found in Brazil. The health benefits associated with their consumption, as well as novel products based on these nuts and their coproducts will be discussed with emphasis on their functional properties and nutritional profile.

## 2. Nutritional composition of native Brazilian nuts

Table 1 shows the macronutrient composition of conventional and non-conventional nuts native to Brazil. Brazil nuts present the highest lipid content and energy value. On the other hand, cashew nuts have higher protein content followed by chichá, which has the highest content of carbohydrates and the lower content of lipids. The sapucaia nut presents the highest fiber content among all nuts showed in Table 1.

Component (g/100 g)ConventionalNon-conventional
Brazil nuts [12, 13]Cashew [14]Pecan [15]Chichá [8, 16]Monguba [10, 17]Pracaxi [11]Sapucaia [18, 19]
Ashes3.32.8-4.11.83.0-3.22.3-2.71.92.9-3.5
Moisture3.1-3.22.7-8.43.38.2-11.45.3-8.34.04.1-4.2
Protein14.4-16.219.7-24.58.618.5-22.513.3-15.415.515.5-20.5
Lipids64.9-67.339.8-47.162.224.5-28.641.9-45.653.458.7-60.8
Total fiber7.5-8.02.5-4.210.94.6-5.84.7-6.116.5
Carbohydrate10.9-15.927.1-34.913.440.5-45.834.3-36.225.24.9-13.8
Energy value (kcal/100 g)659-715499-707633.9456-530557-677644616-665

### Table 1.

Composition of macronutrients of conventional and non-conventional nuts native from Brazil.

—: not presented.

Table 2 shows that the conventional and non-conventional nuts are rich in lipids considered beneficial to health, such as monounsaturated fatty acids (MUFAS) and polyunsaturated fatty acids (PUFAS). Pecan nut presents the highest content of the MUFA oleic acid (C18:1, ω9) followed by the cashew and pracaxi. Besides the nutritional benefits, another advantage of oleic acid is related to its higher oxidative stability compared to PUFAS. On the other hand, Brazil nuts show a high PUFA linoleic acid (C18:2, ω6) content (36-37%), which is an essential fatty acid. It also presents a balanced fatty acid composition containing significant concentrations of MUFAs and saturated fatty acids (SFAs). The main fatty acids present in Brazil nuts is oleic (C18:1, ω9), linoleic (C18:2, ω6), and palmitic (C16:0) acids. In addition, most of the nuts have a low concentration of saturated fatty acids. The exception is monguba, carrying 63% saturated fatty acid, with palmitic acid being the main fatty acid.

Fatty acids (%)ConventionalNon-conventional
Brazil nuts [12, 13, 20]Cashew [21, 22]Pecan [4, 15]Chichá [8]Monguba [10]Pracaxi [11, 23]Sapucaia [18]
Miristic (C14:0)0-0.10.1
Palmitic (C16:0)14.9-16.710.35.426.560.91.4-1.512.9-15.2
Palmitoleic (C16:1 cis 9)0-0.40.32.40.2-0.3
Margaric (C17:0)0.10-0.1
Stearic (C18:0)9.9-11.99.81.44.01.82.5-2.77.7-8.4
Oleic (C18:1 cis 9)28.5-36.360.671.837.87.753.2-53.539.7-44.4
Linoleic (C18:2 cis 9,12)36-37.517.020.211.26.612.1-12.232.2-40.0
Linolenic (C18:3cis 9,12,15)0.1-0.20.20.80.30.10.3-0.4
Arachidic (C20:0)0-0.20.70.7
Gondoic (C20:1 cis 11)0-0.10.20.1
Behenic (C22:0)0.10.316.4-16.5
Lignoceric (C24:0)11.1-11.6
∑ Saturated24.9-28.921.37.031.562.733.3-33.621.5-23.3
∑Monounsaturated28.5-36.861.171.840.414.254.1-54.340.1-45.7
∑Polyunsaturated36.1-37.717.221.012.212.2-12.332.7-40.4
Tocopherol (μg/g)
α-Tocopherol72.578.41.716.6NDND11.2
β-Tocopherol1329.81.1NDNDND
γ-Tocopherol74.4300.326.888.55.1416.1285.0
δ-Tocopherol5.96.321.0ND7.82.8
Total152.81714.828.7127.05.1423.9299.0
Phytosterols (mg/100 g)
Brassicasterol1.5101.4NDND
β-Sitosterol39.57.8184.993.7
Campesterol4.018.68.6
Stigmasterol11.354.211.2
Sitostanol39.58.6
δ5-Avenasterol + δ7-stigmasterol6.7
Total47-148117.80.2-0.3257.7113.5

### Table 2.

Lipid composition of conventional and non-conventional nuts.

—: not presented.

Between the nuts shown in Table 2, cashew has the highest tocopherol content (1714.80 μg/g) followed by the pracaxi nuts (423 μg/g). The main tocopherols identified in the cashew nut were β-tocopherol > γ-tocopherol > α-tocopherol > δ-tocopherol. The chichá nut presents the highest content of phytosterols (257.7 mg/100 g), followed by the cashew nut (117 mg/100 g). β-sitosterol and brassicasterol were the main phytosterols found in these nuts. The bioactive composition of Brazilian nuts is presented in item 3 of this chapter.

Table 3 shows that Brazil and sapucaia nuts are a source of selenium. Considering the level of Se detected in Brazil (36.1 μg/g), and sapucaia (46.9 μg/g) nuts, a daily intake of more than one or two nuts can exceed the recommended daily dose of selenium for adults (55 μg/day) [18]. A selenium intake higher than 400 μg/day has been associated with toxic effects, including selenosis, which symptoms are hair loss, skin damage, and nervous system disorders [12]. Sapucaia nuts are also rich in magnesium (1572 μg/g) and calcium (1168 μg/g). Chichá is rich in potassium (8718 μg/g) and presents the highest concentration of zinc (24.2 μg/100 g). On the other hand, cashew is rich in potassium (K) and pecan in phosphorus (P).

Mineral (μg/g)ConventionalNon-conventional
Brazil nuts [25]Cashew [26]Pecan [27]Chichá [8, 16]Monguba [10, 17]Pracaxi [28]Sapucaia [18, 19]
Al6.21.7
Ca7432.8 ± 10.235.8 ± 0.770.0149.1558.98.9 ± 0.21168.0
Cd0.40.3
Cr1.3 ± 0.20.40.5
Cu59.4 ± 0.59.5 ± 0.27.57.516.9
Fe74.3 ± 0.526.1 ± 0.52.5218.24.41.7 ± 0.1
K1443.3 ± 26.24.18718.0
Mg9678.5 ± 68.5612.7 ± 13.2121.01327.0875.35.6 ± 0.21572.0
Mn3.4 ± 0.47.6 ± 0.24.532.12.041.4
Na148.5 ± 2.611.40.5
Ni0.6 ± 0.50.4
P277.018.1
Pb0.50.5
Se36.1 ± 0.40.2 ± 0.746.9
Sn16.611.1
Zn110.3 ± 1.328.9 ± 1.24.524.29.920.9

### Table 3.

Mineral composition of conventional and non-conventional nuts.

—: not presented.

Minerals play fundamental roles in several functions in the human body, acting as cofactors in enzymatic processes, structural elements, and participating in the regulation of acid–base balance, nerve impulse, and muscle activity [24]. The consumption of nuts as part of a balanced diet can contribute to a proper consumption of minerals, which play an important role in maintaining good health. On the other hand, an excessive consumption of Brazil and sapucaia nuts is not recommended due to the high levels of selenium.

## 3. Bioactive composition of Brazilian nuts

Tocopherols and tocotrienols are a group of eight compounds widely spread in nature. They are monophenols chemically characterized by a chromanol ring, in which a hydroxyl group is attached. The configuration of the side hydrocarbon chain determines whether the compound is either tocopherol or tocotrienol (saturated side chain or three double bonds, respectively). Both tocopherols and tocotrienols have four homologs each (α, β, γ, and δ), which are defined by the methylation pattern on the chromanol ring. These compounds can act as antioxidants by the donation of a hydrogen atom from the hydroxyl group to free radicals, stabilizing them and reducing oxidative stress. α-Tocopherol presents the highest in vivo antioxidant capacity and 100% of vitamin E activity. The activity of α-tocopherol is related to the transfer protein (α-TTP) in the liver, involved in the absorption of tocopherols [29].

Nuts, seeds, and vegetable oils are good sources for tocopherols, and α-tocopherol is the most abundant one in photosynthetic tissues. On the other hand, seeds accumulate about 10–20 times more γ-tocopherol. Tocopherols can be found in considerable amounts in Brazil nuts, where they are concentrated in the oil fraction due to their lipophilic character, as reported by Costa et al. [20]. The authors reported a total tocopherol content of 152.80 μg/g for Brazil nuts, composed of α-tocopherol (72.55 μg/g), γ-tocopherol (74.35 μg/g), and δ-tocopherol (5.90 μg/g). This profile may change according to the region where the nuts are grown. Funasaki et al. [30] reported the tocopherol composition of Brazil nuts from seven different Amazon rainforest areas. α-Tocopherol content ranged from 37.92 μg/g (Manicoré 2-AM) to 74.48 μg/g (Manicoré 1-AM) and γ-tocopherol levels varied between 106.88 μg/g (Manicoré 2-AM) and 171.80 μg/g (Xapuri – AC). The differences in the tocopherol content can be related to climate variations and post-harvest handling.

As natural antioxidants, tocopherols play a role in the protection of nuts against oxidation. Zajdenwerg et al. [31] showed a correlation between the decrease in tocopherol concentration and the appearance of secondary oxidation products in Brazil nuts after a period of storage of 16 days at 80°C γ-tocopherol was depleted by 50%, and α-tocopherol was completely consumed, while aldehydes started to build up from hydroperoxide breakdown. The authors suggested that α-tocopherol acted as a primary antioxidant, which would explain why this homolog was depleted first. α-Tocopherol is less polar than γ-tocopherol due to the presence of three methyl groups on its chromanol ring, which gives it higher antioxidant efficiency in non-polar systems [31].

Cashew nuts, on the other hand, present a lower concentration of tocopherols when compared with Brazil nuts. Ryan et al. [32] reported α-tocopherol and γ-tocopherol contents of 3.6 mg/g and 57.2 mg/g, respectively, for cashew oil. Meanwhile, Brazil nut oil was composed of 82.9 mg/g of α-tocopherol and 116.2 mg/g of γ-tocopherol. However, according to the same study, cashew oil is richer in other bioactive compounds than Brazil nut oil, namely some types of phytosterols, such as β-sitosterol (1768 mg/g against 1325 mg/g from Brazil nut) and campesterol (105.3 mg/g against 26.9 mg/g for Brazil nut). Nevertheless, stigmasterol is more concentrated in Brazil nuts oil (577.5 mg/g) than cashew oil (116.7 mg/g). The consumption of phytosterols has been associated with a decrease in LDL-cholesterol levels. The reason behind this bioactivity relies on the higher hydrophobicity of phytosterols compared with cholesterol, which would give them an advantage in being transported by micelles and later exerted once humans do not absorb them. This would prevent cholesterol from accumulating in the enterocytes and further reaching the bloodstream [32]. Pecan nut is rich in γ-tocopherol, with 23.8-38.1 mg/100 g [4].

The bioactive composition of cashew, Brazil and pecan nuts goes beyond the presence of tocopherols and phytosterols in their oil fraction. Both are also rich sources of polyphenols, an extensive class of secondary plant metabolites with antioxidant properties. Polyphenols primarily act by donating a hydrogen atom to free radicals in order to interrupt oxidation reaction chains. As a minor antioxidant mechanism, phenolics also can chelate transition metals, preventing these prooxidant agents from initiating the reaction chain that originates from the oxidative process. Based on structural differences, this large group can be further divided into subgroups, with the main ones being flavonoids, hydroxycinnamic and hydroxybenzoic acids, hydrolysable tannins, and proanthocyanidins. In nuts, phenolics can be present as free soluble compounds, esterified to fatty acids (soluble esters), or insoluble-bound to macromolecules (e.g., cellulose, structural protein, pectin) [1].

John et al. [1] reported the phenolic composition and antioxidant activity of Brazil nut. Soluble phenolics (free plus esterified) were found to be the predominant state present in the whole nut (519.11 mg/100 g), as well as the kernel (406.83 mg/100 g) and the brown skin (1236.07 mg/100 g). However, a significant amount (352.48 mg/100 g) of insoluble-bound phenolics were detected in the brown skin of Brazil nuts. Gallocatechin, protocatechuic acid, catechin, and vanillic acid were the main phenolics identified in the bound fraction. Insoluble-bound polyphenols are related to beneficial effects on gut health, once they are associated with a decrease in the colonic pH, preventing the growth of harmful microorganisms [33]. The study of John et al. [1] also demonstrated that the brown skin extract of Brazil nuts showed the highest in vitro antioxidant activity, measured by DPPH, hydroxyl radical scavenging activity, reducing power and ORAC assay. The brown skin showed the highest amount of soluble and insoluble-bound polyphenols and this coproduct of Brazil nuts can be considered an economical source of natural antioxidants.

Yang et al. [34] compared the phenolic content and antiproliferative activities of Brazil nuts and cashew. Cashew showed a higher concentration of both soluble (86.7 mg/100 g) and insoluble-bound (229.7 mg/100 g) phenolics when compared to Brazil nuts (46.2 mg/100 g of soluble and 123.1 mg/100 g of insoluble-bound). Brazil nuts did not display antiproliferative activity against HepG2 (human liver cancer cells) at the doses tested in the study (from 1 to 200 mg/mL). On the other hand, cashew displayed the effect at high doses (100-200 mg/mL). In addition, neither of them showed inhibition for human colon cancer cells (Caco-2) proliferation.

The roasting, which is a common process in nut preparation, has shown evidence to impact the phenolic composition of cashew and Brazil nuts in different ways. Özcan et al. [35] reported that the total phenolic content of Brazil nuts significantly decreased from 68.97 mg/100 (raw nut) to 66.47 mg/100 g when oven-roasted (130°C for 20 min). The microwave-roasted (720 W for 5 min) showed the highest impact on the phenolic compounds, decreasing from 68.97 mg/100 to 25.88 mg/100 g. The DPPH radical scavenging capacity of the phenolic extracts also declined from 81.77% in the raw nut to 40.66% in the oven-roasted nut and 34.60% in the microwave-roasted nut. On the other hand, Chandrasekara and Shahidi [21] demonstrated that oven-roasting cashew at 130°C for 33 min increased the total phenolic content (both soluble and insoluble-bound) of the whole nut, as well as the kernel and the testa. At the same time, the levels of proanthocyanidins decreased, except for soluble phenolic extract from the kernel. In particular, the concentrations of the flavonoids (+)-catechin, (−)-epicatechin, and epigallocatechin were enhanced after the roasting process, which also positively affected the antioxidant capacity of such extracts. According to the authors, these findings could be owed to the release of phenolics because of temperature, making them readily soluble in the extraction solvent. Although relatively high, the temperature was applied for a short period, which prevented an extensive degradation of polyphenols.

Pecan nutshell, a coproduct, have demonstrated great potential due to its rich phenolic composition and high antioxidant capacity. According to Hilbig et al. [36], extracts from this coproduct obtained under optimum conditions yielded total phenolic contents of 426.15-581.9 mg GAE/g, resulting in antioxidant activities of 2574.32-2573 μmol TEAC/g and 1268.03-1287.08 μmol TEAC/g measured by ABTS and DPPH assays, respectively. The extracts showed a variety of 29 different phenolic compounds, with gallic acid as the predominant one.

Demoliner et al. [9, 18] investigated the nutritional and phytochemical composition of sapucaia nut. The oil extracted from the nuts presented a considerable amount of total tocopherols (21.8-29.9 mg/100 g), with γ-tocopherol identified as the primary homolog (19.2-28.5 mg/100 g). α- and δ-Tocopherols were also identified in smaller quantities. Mounting evidence has shown that γ-Tocopherol excels in scavenging reactive oxygen species, which play an essential role in the development of chronic diseases [37, 38, 39]. Sapucaia nut oil also showed a significant concentration of phytosterols, namely β-sitosterol (92.8-193.9 mg/100 g), stigmasterol (9.92-13.2 mg/100 g), and campesterol (8.42-9.63 mg/100 g) [9].

Demoliner et al. [9] extracted the phenolic compounds from sapucaia nut and shell and used LC-ESI-MS/MS to identify and quantify the individual polyphenols present. The nut extracts were composed of 14 compounds, mainly phenolic acids, and flavonoids, with myricetin, vanillic, ferulic, and ellagic acid showing the highest amounts. Interestingly, shell extracts demonstrated to carry a greater variety of phenolics, with 22 compounds identified, with high levels of phenolic acids (gallic, protocatechuic, vanillic, ferulic, and ellagic) and flavonoids (epigallocatechin, catechin, epicatechin, taxifolin, myricetin, and vanillin). Shell extracts were also superior to the nut extracts in terms of in vitro antioxidant activity, measured by DPPH, FRAP, and ABTS. These outcomes highlight the potential for using nuts coproducts as sources of natural antioxidants.

Similar to sapucaia, the coproducts of chichá, namely the pellicle (26.26 mg GAE/g) and the shell (21.42 mg GAE/g), have been reported to be richer in total phenolic compounds than the nut (16.85 mg GAE/g). The extracts presented a wide variety of phenolic acids, such as ellagic, ferulic, salicylic, protocatechuic, and rosmarinic acid [8].

It has been reported that monguba oil is source of γ-tocopherol (513.5 mg/kg). In addition, ten phenolic compounds have been identified, mainly phenolic acids and flavonoids. The majority of phenolics (74.58%) were in the esterified form, followed by the glycosylated (13.02%), free (8.22%), and insoluble bound (4.18%) forms. Caffeic acid Monguba was the main phenolic compound found in this raw material (57.5%) [10].

Teixeira et al. [11] reported total phenolic contents ranging from 31.92 to 54.05 mg GAE/kg for pracaxi oil extracted by supercritical CO2 extraction. The highest phenolic content and in vitro antioxidant activity of the extracts was obtained using 200 bar at 40-60°C. The oils obtained under low pressure demonstrated high antioxidant capacity measure by the CUPRAC method, indicating a significant content of both hydrophilic (phenolics) and lipophilic (carotenoids and tocopherols) antioxidants. The presence of natural antioxidants may also have positively affected the stability oxidative index (OSI of 11.38 h at 110°C and 10.83 at 120°C), which suggests a prolonged shelf life for the oil [11].

## 4. Bioavailability and health-promoting benefits

The nutritional profile and bioactive compounds present in Brazilian nuts are certainly a positive characteristic of these raw materials. However, the presence of these nutrients and minor compounds do not guarantee their conversion into health-promoting benefits. They need to be efficiently released from the food matrix and be absorbed in sufficient amounts to be converted into biologically active metabolites for having and positive impact on human health. In addition, the potentially toxic compounds should be assessed to ensure its safety. That is especially true when considering expanding the commercialization of relatively unknown nuts, like the ones we have been presenting throughout this chapter.

Moreda-Piñeiro et al. [40] assessed the in vitro bioavailability of essential and toxic metals in several nuts and seeds, including Brazil nuts and cashew. Essential metals (Ba, Ca, Cd, Co, Cu, K, Li, Mg, Mn, Mo, P, Pb, Se, Sr., Tl, and Zn) consistently presented moderate bioavailability (dialyzability of 2.1-40.7%) among the samples. The exception was iron, which presented a low dialyzability (0.70-3.7%). On the other hand, toxic metals (Al, Ba, Cd, and Hg) demonstrated poor bioavailability (dialyzability ratios between 0.35-16.8%). The results suggest that the consumption of these nuts can be considered as safe and beneficial because of the high bioavailability of the essential metals. The authors also found a positive correlation between carbohydrate content and dialyzability ratio, meaning that the higher the carbohydrate concentration, the greater the bioavailability. On the other hand, nuts with high-fat content were found to present lower mineral bioavailability.

Nascimento et al. [41] reported the in vitro bioavailability of Cu and Fe in cashew nuts using simulated gastric and intestinal fluids as well as dialysis procedures. The results showed that 83% of Cu and 78% of Fe were recovered during the experiment, indicating a high level of bioavailability for these minerals in cashew nuts. These two minerals are essential for a variety of physiological and metabolic processes. Cu deficiency can lead to high blood pressure and infertility, while Fe deficiency can cause anemia.

Using an in vitro dialyzability approach, Herbello-Hermelo et al. [42] evaluated the bioavailability of the polyphenol fraction of selected nuts and seeds. Brazil nuts and cashew were among the samples with the highest recovery of phenolics in the digested extracts (81 and 89%, respectively). The authors also showed that polyphenol bioavailability was dependent on Cu content. This can be explained by the strong binding ability between Cu+ and phenolics, with the latter being reported to reduce Cu2+ to Cu+, even though the mechanism by which this happens is not entirely understood yet.

Brazil nuts are one of the main sources of Se in nature, which are constituents of selenoproteins (e.g., glutathione peroxidases – GSH-Px), enzymes that are part of the endogenous antioxidant defenses system. A high blood concentration of such enzymes is associated with a lower risk of cardiovascular diseases. Stockler-Pinto et al. [43] conducted a human trial on the supplementation of Brazil nuts to patients on hemodialysis, which produces a large amount of reactive oxygen species. The administration of one nut per day for three months increased the subjects’ GSH-Px activity. Before the supplementation, 11% of the patients presented GSH-Px levels below the normal range. After the supplementation, all subjects showed results within the normal range.

Inflammation processes are essential biological responses when the organism needs to fight intrusive agents. However, inflammatory disorders are extremely damaging and can lead to conditions such as cancer, type 1 diabetes, and rheumatoid arthritis, among others [44]. Colpo et al. [45] monitored the activity of inflammation markers upon the intake of different portions of Brazil nuts (from 0 to 50 g) by healthy individuals. The trial revealed that the consumption of 20 or 50 g of Brazil nuts was responsible for a decrease in serum levels of inflammation markers (IL-1, IL-6, TNF-α, and INF-γ).

Nanoemulsions prepared from cashew nut shell liquid showed cytotoxicity against human breast cancer cell line MCF-7. The cells treated with the nanoemulsion presented reduced viability, primarily through apoptosis or necrosis [46]. Cashew nut has also demonstrated a positive impact on cholesterol levels and systolic blood pressure. In a trial conducted with 300 type 2 diabetic adult patients, the administration of 30 g of cashew nuts daily for 12 weeks could reduce the subjects’ blood pressure while the concentration of plasma HDL cholesterol increased.

Müller et al. [47] reported a potential biological effect of pecan nutshell extracts in vivo and in vitro studies. The phenolic-rich extracts from pecan nutshell demonstrated protection against liver damage induced by ethanol in rats by increasing the levels of endogenous antioxidant defenses, such as glutathione (by 33%), superoxide dismutase (by 47%) and catalase (by 47-73%). Hilbig et al. [48] showed that aqueous extracts from pecan nutshell were able to reduce the viability of MCF-7 breast cancer cells. The effect was attributed to the high abundance of phenolic compounds in the extract, such as gallic, ellagic, and chlorogenic acid, as well as catechin, epicatechin, epigallocatechin, among others.

## 5. Nut-based products

Nuts are usually consumed as a snack, in their natural form, as well as toasted, salted, or caramelized. The Brazil nuts, cashew and pecan and are used as ingredients in several industrialized food products such as bakery goods, sweets, chocolates and ice creams, among others. The underexplored nuts, such as chichá, monguba, pracaxi, and sapucaia, although not reaching the same level of commercialization, have shown to be potentially suitable for these types of application.

### 5.1 Nut oil

Nut oils are usually obtained by pressing, and since they are not refined, they are classified as extra virgin. The main steps involved in the processing of an extra virgin nut oil are harvesting, pre-drying, peeling, drying, oil extraction, and centrifugation. Because of the appreciable sensorial attributes and elevated price compared with other vegetable oils, the nut oils are considered gourmet oils. The price will differ according to the nut type, its availability, and the processing used.

Brazil nut, pecan and cashew nut oils are usually found in specialized stores of natural products, in pharmacies (for use as cosmetics) and are available for online purchase, where their price ranges from 8 US $to 17 US$. The pracaxi oil can be found for commercialization, mainly as a cosmetic, due to its emollient properties. On the other hand, chichá, sapucaia and monguba oils have not been commercially produced yet. However, studies show that these oils are rich in monounsaturated fatty acids and possess high oxidative stability, thus showing great potential for commercialization [8, 18]. Monguba oil, which is rich in palmitic acid, has a great potential for food applications as a substitute for cocoa butter [10].

### 5.2 Cereal bars

Cereal bars are consumed mainly as a diet substitute for sugar-dense snacks, as well as an energy and protein source for athletes. In the formulation of cereal bars, it is important to take into account the cereal choice (oats, wheat, rice, barley, maize). In addition, the selection of the appropriate carbohydrate to maintain a balance between taste and shelf life, the nutrient profile, the dietary fiber, and the processing stability [49] are also important. Cereal bars made with nuts are widely accepted by consumers. Besides their nutritional and sensory quality, they remain stable during product storage. Currently, we can easily find cereal bars containing Brazil nuts and cashew as ingredients.

### 5.3 Nut flour

Nuts can be ground into flour for use in bakery goods. Cake, the residue left after nut oil extraction, can be used as raw material to produce defatted nut flour. This is considered a sustainable process since it adds value to a coproduct, reducing waste generation [50]. Nut flour is rich in dietary fiber, protein, vitamins, minerals, and bioactive compounds. The application of partially defatted nut flour has been reported to improved consumer acceptance of gluten-free bakery products [50]. The combination of rich nutritional composition with appreciable physical properties makes these flours suitable for bakery products, such as cookies, bread, cakes, sweets, among others.

Physical properties, such as water or oil retention capacity, foam properties, emulsifying activity, and emulsion stability, are very important for the incorporation of flour into bakery products. Sanchez et al. [51] reported that pistachio and cashew nut flours with thermal trapping in autoclave showed interesting emulsifying and water rectifying properties for application in bakery products. In another study, Teixeira et al. [19] reported functional properties of defatted sapucaia flour. The parameters of emulsion formation and stability indicated that it could be applied as an ingredient in emulsified products such as cakes, creams, sauces and sausages, among others.

### 5.4 Nut-based milk alternative

Plant-based milk alternatives are beverages obtained from crushing a specific feedstock homogenized in water. The resulting particle size distribution should be between 5 and 20 μm to mimic cow’s milk in appearance and consistency. Sethi et al. [5] reported that the vegetable-based milks can be divided in five categories according to the raw material used: cereals (oats, rice, corn, spelled), vegetables (soy, peanuts, lupines, cowpea), nuts (almonds, coconut, hazelnuts, pistachios, walnuts), oilseeds (sesame, flax, hemp, sunflower), and pseudo-cereals (quinoa, teff, amaranth).

The improved diagnosis of conditions related to cow’s milk consumption, such as milk protein allergy and lactose intolerance, increased the demand for non-dairy milk alternatives. Besides, vegans also prefer these beverages, and it is being considered a continuously growing niche [5]. Nuts, such as walnuts, chestnuts, and almonds, are used to produce plant-based milk alternatives, mainly due to their functionality and better sensory characteristics [5]. The allergenic potential and high cost are some of the limiting factors presented by the nut-based milks.

The addition of Brazil nuts extract in a soybean-based drink positively influenced the sensory characteristics of the product [52]. On the other hand, prebiotic drinks based on cashew nuts and fruit juice have proved to be a viable alternative for the development of functional products [53]. Bruno et al. [6] reported that cashew nut-based milk alternative was a good matrix for the development of probiotics. They showed that Bifidobacterium animalis, Lactobacillus acidophilus and L. plantarum remained viable during 30 days at 4°C. The probiotic drink based on cashew nuts also achieved a good sensory acceptance, without significant changes in whiteness and microbiological quality.

Plant-based milk of sapucaia nut cake using block freeze concentration, which was done in five consecutive stages, allowed the concentration of the phenolic compounds (gallic, vanillic, ferulic, sinapic and salicylic acids, catechin, taxifolin and sinapaldehyde) and minerals in all the five fractions [54]. Studies with different raw materials and formulations, especially non-conventional nuts, are still scarce. The knowledge about such products should contribute to encouraging their consumption.

## 6. Nuts shell and cake

Industrial nut processing results in a large amount of shells, a coproduct that can represent approximately 40-50% of the original total mass. The reuse of these coproducts, which are usually discarded, should be encouraged for reducing waste disposal, preserving the environment and adding value to the raw materials.

Some nutshells, such as pecan, are sold in pieces to make tea [4]. The ethnopharmacological use of nutshell tea includes the prevention and treatment of various diseases, such as type 2 diabetes, obesity, hypertension, hypercholesterolemia, cancer and, inflammatory diseases [24]. The therapeutic effects of the tea made with pecan nutshell have been associated with the presence of several phenolic compounds, such as phenolic acids, flavonoids, and proanthocyanidins. The antioxidant, antimicrobial, and antitumor activity of pecan peel extract have been reported [4, 50]. Other nutshells may have health benefits due to their bioactive composition.

Cashew nut is covered with a thin antioxidant-rich layer of reddish-brown color, known as testa. This fraction is an excellent source of hydrolysable tannins and polymeric proanthocyanidins. It comprises of phenolic acids like syringic acid, gallic acid, and p-coumaric acid as the major components. The concentration of catechin and epicatechin were found as 5.70 and 4.46 g/kg of dry matter, respectively [55].

The process of mechanical oil extraction generates a partially defatted by-product known as cake. The agro-industrial use of the defatted nut cake has great nutritional value, based on its high lipid and protein contents and the functional aspect present in this material, adding value to food products. The nuts cake can be used in bakery (as presented in item 5.3), but also in sweets. In the study by Lima et al. [56], the cashew nut cake was used to replace peanuts in the production of a sweet known as paçoca, made by mixing ground peanuts with other ingredients, such as corn flour, sugar, honey, and oil. The product showed physicochemical and microbiological stability, as well as good sensory acceptance. In addition, the nut cake presents bioactive compounds. For instance, Maciel et al. [57] demonstrated that pecan nut cake is rich in phenolic compounds with antioxidant activity.

## 7. Future perspectives

Commercial and non-commercial Brazilian nuts are nutritionally rich in macronutrients and bioactive compounds, with considerable amounts of natural antioxidants. Such substances are related to a myriad of health benefits since they are able to reduce oxidative stress. A significant number of studies have investigated the bioavailability of these bioactive compounds of Brazil nuts and cashew with promising results. The effect of the nuts on health using human trials had positive outcomes. However, relatively unknown Brazilian nuts, such as sapucaia, chichá, pracaxi, and monguba remain an underexplored topic. Information about their bioavailability aspects and their impact on human health is still necessary. Therefore, more studies should be done in order to stimulate large-scale commercialization.

Finally, nuts are incredibly versatile with great economic potential. The incorporation of the coproducts, which are rich in nutrients and bioactive compounds, is an opportunity to enrich food formulation with these cost-effective ingredients, diminishing the waste generated by nut processing.

## Acknowledgments

The authors are grateful to National Council for Scientific and Technological Development (CNPq) for the scientific productivity fellowship of Jane Mara Block (process 311070/2018-3), and to Coordination for the Improvement of Higher Education Personnel (CAPES) for the doctoral scholarship of Gabriela Polmann (process 88882.344944/2019-2101).

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Renan Danielski, Gabriela Polmann and Jane Mara Block (December 2nd 2020). Valorization of Native Nuts from Brazil and Their Coproducts [Online First], IntechOpen, DOI: 10.5772/intechopen.95056. Available from:


text:
# Distribution function for divisors of an Integer

For a fixed $n$, let $D_n(x) = \{ d|n : d \leq x \}$ . We assume here $p \leq x \leq n/p$, where $p$ is the smallest prime factor of $n$.

For example if $n = p^i$ for some prime $p$ then $D_n(x) \sim \log x/ \log p$.

What are the other 'nice' distribution function of divisors that are satisfied by an infinite family of integers ( like $\log x/ \log p$ for $\{p^i, i \in \mathbb{N}\}$ ).

Here 'nice', means it is easy to do calculus (integrate or differentiate) with such functions.

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The distribution of divisors on 'average' is known (so to say giving the behavior of a 'typical'integer).

Set $F_n(u) = d(n)^{-1} D_n(n^u)$ where $d(n)$ is the total number of divisors of $n$, then

$$x^{-1} \sum_{n\le x} F_n(u) = \frac{2}{\pi} \arcsin \sqrt{u} + O((\log x)^{-1/2})$$ uniformly for $x\ge 2$ and $u \in [0,1]$. This is due to Deshouillers, Dress, Tennenbaum (1979) and can be found for example in Tennenbaum's Introduction to Analytic and Probabilistic Number Theory (see Thm 7 in II.6).

Roughly this means, there are many small divisors.

A lot of information on this type of question, and I assume also this result but could not check, is in Hall and Tennenbaum's book 'Divisors'.

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Thank you for the answer. – Kamalakshya Dec 7 '12 at 13:12


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