13.6: Nanoscale Metal Particles
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Nanoscale metal particles have been the subject of intense research over the past 20 years, especially because of their unusual optical , magnetic , and catalytic properties. The synthesis of metal nanocrystals in various shapes has become increasingly sophisticated and rational, like the synthesis of semiconductor nanocrystals described above. By controlling the separate phases of nucleation and growth, and by using ligands that cap specific crystal faces during growth, it is possible to make metal nanocrystals of uniform size in a variety of interesting and useful shapes including cubes, truncated cubes, octahedra, triangular prisms, and high aspect ratio rods. By exploiting displacement reactions that replace one metal with another, complex hollow shapes such as nanocages (as shown at the left) can be made starting with other shapes. In this case, solid silver nanocubes are transformed to gold nanocages.
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Five-fold twinning in a gold nanoparticle |
The interesting optical properties of nanocrystalline Au, Ag, Cu, and a number of other metals, derive from the collective oscillation of their valence electrons, a phenomenon known as plasmon resonance . Remember that in these metals, the electron mean free path is long (about 100 times larger than the size of the atoms), so the valence electrons feel only the average positive charge of the atomic cores as they zoom around the crystal. Light impinging on the metal acts as an oscillating electric field, pushing and pulling on the valence electrons at the characteristic frequency of the light wave. The situation is very much like a pendulum or a weight on a spring. The electrons, pushed away from their equilibrium positions, feel a restoring force that is proportional to their displacement. Their motion can be described by Hooke's Law :
\[F = kx\]
where the spring constant k determines the "stiffness" of the spring. In the case of the plasmon resonance, k is proportional to the number density of valence electrons n, and the square of the electronic charge e:
\[k = \frac{ne^{2}}{\varepsilon_{0}}\]
The resonant frequency of the plasma oscillation is given by:
\[\omega_{p} = (\frac{k}{m})^{\frac{1}{2}} = (\frac{ne^{2}}{m_{e}\varepsilon_{0}}^{\frac{1}{2}}\]
where m e is the electron mass. For most metals, the plasmon resonance is in the ultraviolet part of the spectrum, but for a few metals like Au, Ag, and Cu it is in the visible.
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The Lycurgus cup (4th century Roman glass) derives its unique coloration from noble metal nanoparticles. The cup is red in transmitted light and green in scattered (reflected) light. |
For metal particles that are much smaller than the wavelength of light, this effect is called the localized surface plasmon resonance , or LSPR. There are three important consequences of the LSPR effect:
- The local electric field of the incoming light wave is greatly enhanced at the particle surface. This gives rise to huge enhancement factors in optical processes such as Raman scattering and fluorescence . Thus, certain analytical spectroscopic techniques are greatly enhanced by LSPR.
- Near the plasmon resonance frequency, metal nanocrystals absorb and scatter light very strongly. This makes them brightly reflective, and the strong light absorption can be exploited for light-induced local heating. These properties are being applied in medical diagnostics and therapy, e.g., for detection and photothermal destruction of cancer cells. By adjusting the size and shape of the gold nanoparticles, which are more stable than Ag and Cu in biological media, the plasmon frequency can be tuned to the tissue-transparent near-IR region of the spectrum between 700 and 900 nm. Small quantities of plasmonic Ag and Au particles also make brightly colored and strongly scattering pigments, e.g. in stained glass as shown above at the right.
- The plasmon frequency is sensitive to the refractive index of the particle's surroundings, i.e., its chemical environment. This makes metal nanoparticles of special interest for sensing and biosensing applications.
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The colors of plasmonic gold nanoparticles depend on their size and shape. |
Theory of light scattering and absorption by metal nanoparticles
The valence electrons in metal nanoparticles oscillate in the electric field of a light wave. While the nature of these oscillations is somewhat complex in metal particles that are non-spherical, the theory for spherical particles is relatively simple and in fact was worked out over 100 years ago by German physicist Gustav Mie.
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Mie considered the interaction of a spherical particle with a uniform electric field, E, oscillating at angular frequency ω (= 2π f). This is a good approximation when the particle diameter is much smaller than the wavelength of light, as shown on the left. The particle is embedded in a uniform, insulating material (e.g. a solvent) that has a dielectric constant ε diel . For insulators, ε diel is a positive real number.
The dielectric constant ε of a metal is actually a complex number:
\[\varepsilon = \varepsilon^{'} + i \varepsilon^{"}\]
Here the real part, ε', is related to the refraction of light, and the imaginary part, ε", is related to light absorption. Both ε' and ε" are dependent on the frequency of the light. For metals near the plasmon resonance frequency, ε' is typically a negative number.
The cross-section for absorption of the light wave by the particle is:
\[\sigma_{absorption} = \frac{9 \omega}{c} \epsilon^{\frac{3}{2}}_{diel} V \frac{\epsilon^{"}_{metal}}{(\epsilon^{'}_{metal} + 2 \epsilon_{diel})^{2} + (\epsilon^{"}_{metal})^{2}}\]
and the cross-section for scattering is:
\[ \sigma_{scattering} = \frac{3}{2\pi} (\frac{\omega^{4}}{c}) \epsilon^{2}_{diel} V^{2} \frac{(\epsilon^{'}_{metal} - \epsilon_{diel})^{2} + (\epsilon^{"}_{metal})^{2}}{(\epsilon^{'}_{metal} + 2 \epsilon_{diel})^{2} + (\epsilon^{"}_{metal})^{2}}\]
The sum of these two is the cross-section for extinction :
\[\sigma_{extinction} = \sigma_{absorption} + \sigma_{scattering}\]
These cross-sections become large when the (ε' metal + 2ε diel ) term in the denominator becomes small. This occurs when
\[\epsilon^{'}_{metal} \simeq -2\epsilon_{diel}\]
For 15 nm diameter gold nanoparticles in water, this happens at about 580 nm, resulting in the characteristic wine-red color of colloidal gold solutions. Changing the solution environment (e.g., by adsorbing a molecule onto the gold surface) changes ε diel and thus alters the color slightly.
It is important to note that the cross-section for scattering is proportional to the square of the volume of the particle, V 2 , whereas the absorption is proportional to V. This means that very small gold particles (< 5 nm) are strongly absorbing but not strongly scattering. Larger particles (>30 nm) scatter light very strongly. Depending on the application, therefore, we choose larger or smaller particles.
One of the key complementary properties of noble metal nanoparticles that is important to their use in biomedicine is the ease with which they can be covalently conjugated with polymers or small molecules, typically via thiol or amine bonds at their surface. This imparts biological recognition properties to the particles that enables them to bind to specific biomolecular targets. The figure at the left illustrates some of the functionality that can be imparted to nanoparticles through surface functionalization.
Functionalization of gold nanoparticles with thiol-terminated single-stranded DNA was the basis of one of the first nanoparticle sensors, developed by the Mirkin group at Northwestern University. DNA-coated nanoparticles have the characterstic wine-red plasmonic color of spherical nano-gold. However, when these particles are linked together by a complementary DNA strand, the resonance frequency shifs, resulting in a blue color. This color change, illustrated in the figure at the right, provides a "litmus test" for the presence of the target DNA sequence. [10] "Melting" of the DNA - heating it to the temperature at which double stranded DNA dissociates to make single strands - reverses the color change. The DNA hybridization/melting transition is highly cooperative because of the aggregation of many gold particles, so the transition temperature is very sharp. With proper temperature control, the color change can be sensitive to a single base mismatch in the target DNA that is detected by this method.
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Aggregation of Au nanoparticles (in this case by adding salt to a colloidal solution) causes a color change from wine red (left) to blue (right). Photo credit: George Lisensky, Beloit College |
Subsequent research has developed sophisticated diagnostic and therapeutic ("theranostic") applications for these spherical nucleic acid [11] particles. These particles easily penetrate cell membranes and can report on the chemistry happening inside living cells.
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General schematic of nanoflare-based detection. |
An important property of gold nanoparticles in these applications is their ability to quench the fluorescence of reporter molecules that are near their surface. Nucleic acid strands that contain a hairpin loop can position fluorescent molecules near the gold surface, where their fluorescence is turned off by nanoparticle quenching. Hybridization of these sequences to target RNA or DNA causes the fluorescence to turn on by moving the fluorescent molecule away from the nanoparticle surface. These so called "nanoflares" can thus signal the up- or down-regulation of specific genes inside cells. Nanoflares are the basis of the Verigene System, developed and commercialized by Nanosphere, Inc. to detect markers for infectious diseases and cancers.


1.14.56: Properties: Equilibrium and Frozen
A given closed system having Gibbs energy \(\mathrm{G}\) at temperature \(\mathrm{T}\), pressure \(\mathrm{p}\), molecular composition (organization \(\xi\)) and affinity for spontaneous change \(\mathrm{A}\) is described by equation (a).
\[\mathrm{G}=\mathrm{G}[\mathrm{T}, \mathrm{p}, \xi] \nonumber \]
In the state defined by equation (a), there is an affinity for spontaneous chemical reaction \(\mathrm{A}\). Starting with the system in the state defined by equation (a) it is possible to change the pressure and perturb the system to a series of neighboring states for which affinity remains constant. The differential dependence of \(\mathrm{G}\) on pressure for the original state along the path at constant \(\mathrm{A}\) is given by \((\partial \mathrm{G} / \partial \mathrm{p})_{\mathrm{T}, \mathrm{A}}\). Returning to the original state characterized by \(\mathrm{T}\), \(\mathrm{p}\) and \(\xi\), we imagine that it is possible to perturb the system by a change in pressure in such a way that the system remains at fixed extent of reaction, \(\xi\). The differential dependence of \(\mathrm{G}\) on pressure for the original state along the path at constant \(\xi\) is given by \((\partial \mathrm{G} / \partial \mathrm{p})_{\mathrm{T}, \xi}\). We explore these dependences of \(\mathrm{G}\) on pressure at fixed temperature and at
- fixed composition, \(\xi\) and
- fixed affinity for spontaneous change, \(\mathrm{A}\).
The procedure for relating \((\partial \mathrm{G} / \partial \mathrm{p})_{\mathrm{T}, \mathrm{A}}\), and \((\partial \mathrm{G} / \partial \mathrm{p})_{\mathrm{T}, \xi}\) is a standard calculus operation. At fixed temperature,
\[\left[\frac{\partial \mathrm{G}}{\partial \mathrm{p}}\right]_{\mathrm{A}}=\left[\frac{\partial \mathrm{G}}{\partial \mathrm{p}}\right]_{\xi}-\left[\frac{\partial \mathrm{A}}{\partial \mathrm{p}}\right]_{\xi} \,\left[\frac{\partial \xi}{\partial \mathrm{A}}\right]_{\mathrm{p}} \,\left[\frac{\partial \mathrm{G}}{\partial \xi}\right]_{\mathrm{p}} \nonumber \]
This interesting equation shows that the differential dependence of Gibbs energy (at constant temperature) on pressure at constant affinity for spontaneous change does NOT equal the corresponding dependence at constant extent of chemical reaction. This inequality is not surprising. But our interest is drawn to the case where the system under discussion is, at fixed temperature and pressure, at thermodynamic equilibrium where \(\mathrm{A}\) is zero, \(\mathrm{d} \xi / \mathrm{dt}\) is zero, Gibbs energy is a minimum AND, significantly, \((\partial \mathrm{G} / \partial \xi)_{\mathrm{T}, \mathrm{p}}\) is zero. Hence
\[\mathrm{V}=\left[\frac{\partial \mathrm{G}}{\partial \mathrm{p}}\right]_{\mathrm{T}, \mathrm{A}=0}=\left[\frac{\partial \mathrm{G}}{\partial \mathrm{p}}\right]_{\mathrm{T}, \xi^{\mathrm{eq}}} \nonumber \]
The dependence of \(\mathrm{G}\) on pressure for differential displacements at constant ‘\(\mathrm{A} = 0\)’ and \(\xi^{\mathrm{eq}}\) are identical. We confirm that the volume \(\mathrm{V}\) of a system is a ‘strong’ state variable. These comments seem trivial but the point is made if we go on to consider the volume of a system as a function of temperature at constant pressure. We use a calculus operation to derive equation (d).
\[\left(\frac{\partial \mathrm{V}}{\partial \mathrm{T}}\right)_{\mathrm{A}}=\left(\frac{\partial \mathrm{V}}{\partial \mathrm{T}}\right)_{\xi}-\left(\frac{\partial \mathrm{A}}{\partial \mathrm{T}}\right)_{\xi} \,\left(\frac{\partial \xi}{\partial \mathrm{A}}\right)_{\mathrm{T}} \,\left(\frac{\partial \mathrm{V}}{\partial \xi}\right)_{\mathrm{T}} \nonumber \]
Again we are not surprised to discover that in general terms the differential dependence of \(\mathrm{V}\) on temperature at constant affinity does not equal the differential dependence of \(\mathrm{V}\) on temperature at constant composition/organization. Indeed, unlike the simplification we could use in connection with equation (b), {namely that at equilibrium \((\partial \mathrm{G} / \partial \xi)_{\mathrm{T}, \mathrm{p}}\) is zero} we cannot assume that the volume of reaction, \((\partial \mathrm{V} / \partial \xi)_{\mathrm{T}, \mathrm{p}}\) is zero at equilibrium. In other words for a closed system at thermodynamic equilibrium at fixed \(\mathrm{T}\) and fixed \(\mathrm{p}\) {when \(\mathrm{A}=0\), \(\xi = \xi^{\mathrm{eq}}\) and \(\mathrm{d} \xi^{\mathrm{eq}} / \mathrm{dt}=0\)}, there are two thermal expansions, at constant \(\mathrm{A}\) and at constant \(\xi\)ξ.
We consider a closed system in equilibrium state I defined by the set of variables,\(\left\{\mathrm{T}[\mathrm{I}], \mathrm{p}, \mathrm{A}=0, \xi^{\mathrm{eq}}[\mathrm{I}]\right\}\). The equilibrium composition is \(\xi^{\mathrm{eq}}[\mathrm{I}]\) at zero affinity for spontaneous change. This system is perturbed to two nearby states at constant pressure.
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State I is displaced to a nearby equilibrium state II defined by the set of variables, \(\left\{\mathrm{T}[\mathrm{I}]+\delta \mathrm{T}, \mathrm{p}, \mathrm{A}=0, \xi^{\mathrm{eq}}[\mathrm{II}]\right\}\). This equilibrium displacement is characterized by a volume change;
\[\Delta \mathrm{V}(\mathrm{A}=0)=\mathrm{V}[\mathrm{II}]-\mathrm{V}[\mathrm{I}] \nonumber \]
\[\mathrm{E}_{\mathrm{p}}(\mathrm{A}=0)=\left[\frac{\mathrm{V}[\mathrm{II}]-\mathrm{V}[\mathrm{I}]}{\Delta \mathrm{T}}\right]_{\mathrm{p}, \mathrm{A}=0} \nonumber \]
The equilibrium isobaric expansibility,
\[\alpha_{\mathrm{p}}(\mathrm{A}=0)=\mathrm{E}_{\mathrm{p}}(\mathrm{A}=0) / \mathrm{V} \nonumber \]
In order for the system to move from one equilibrium state, I with composition \(\xi^{\mathrm{eq}}[\mathrm{I}]\) to another equilibrium state, II with composition \(\xi^{\mathrm{eq}}[\mathrm{II}]\), the system changes by a change in chemical composition and/or molecular organization.
Hence we define the ‘frozen’ isobaric expansion, \(\mathrm{E}_{\mathrm{p}} (\xi = \text { fixed})\). An alternative name is the instantaneous expansion because, practically, we would have to change the temperature at a such a high rate that there is no change in molecular composition or organisation in the system.
\[\mathrm{E}_{\mathrm{p}}(\xi=\text { fixed })=\left(\frac{\partial \mathrm{V}}{\partial \mathrm{T}}\right)_{\mathrm{p}, \xi} \nonumber \]
Further
\[\alpha_{p}(\xi=\text { fixed })=\frac{1}{V} \,\left(\frac{\partial V}{\partial T}\right)_{p, \xi} \nonumber \]
Similar comments apply to isothermal compressibilities, \(\mathrm{K}_{\mathrm{T}}\); there are two limiting quantities \(\kappa_{\mathrm{T}}(\mathrm{A}=0)\) and \(\kappa_{\mathrm{T}}(\xi)\). In order to measure \(\kappa_{\mathrm{T}}(\xi)\) we have to change the pressure also in an infinitely short time.
The entropy \(\mathrm{S}\) is given by the partial differential, \(-(\partial \mathrm{G} / \partial \mathrm{T})_{\mathrm{p}, \xi}\). At equilibrium where \(\mathrm{A}=0, \mathrm{~S}=-(\partial \mathrm{G} / \partial \mathrm{T})_{\mathrm{p}, \mathrm{A}=0}\). We carry over the argument described in the previous section but now concerned with a change in temperature. We consider the two pathways, constant \(\mathrm{A}\) and constant \(\xi\).
\[\begin{aligned}
&(\partial \mathrm{G} / \partial \mathrm{T})_{\mathrm{p}, \mathrm{A}}= \\
&\quad(\partial \mathrm{G} / \partial \mathrm{T})_{\mathrm{p}, \xi}-(\partial \xi / \partial \mathrm{A})_{\mathrm{T}, \mathrm{p}} \,(\partial \mathrm{A} / \partial \mathrm{T})_{\mathrm{p}, \bar{\xi}} \,(\partial \mathrm{G} / \partial \xi)_{\mathrm{T}, \mathrm{p}}
\end{aligned} \nonumber \]
But at equilibrium, \(\mathrm{A}\) which equals \(-(\partial \mathrm{G} / \partial \xi)_{\mathrm{T}, \mathrm{p}}\) is zero, and so \(\mathrm{S}(\mathrm{A}=0)\) equals \(\mathrm{S}\left(\xi^{\mathrm{eq}}\right)\). Then just as for volumes, the entropy of a system is not a property concerned with pathways between states; entropy is a strong function of state. Another important link involving Gibbs energy and temperature is provided by the Gibbs-Helmholtz equation. We explore the relationship between changes in \((\mathrm{G} / \mathrm{T})\) at constant affinity \(\mathrm{A}\) and at fixed \(\xi\), following perturbation by a change in temperature.
\[\begin{aligned}
&{[\partial(\mathrm{G} / \mathrm{T}) / \partial \mathrm{T}]_{\mathrm{p}, \mathrm{A}}=} \\
&{[\partial(\mathrm{G} / \mathrm{T}) / \partial \mathrm{T}]_{\mathrm{p}, \xi}-(1 / \mathrm{T}) \,(\partial \xi / \partial \mathrm{A})_{\mathrm{T}, \mathrm{p}} \,(\partial \mathrm{A} / \partial \mathrm{T})_{\mathrm{p}, \xi} \,(\partial \mathrm{G} / \partial \xi)_{\mathrm{T}, \mathrm{p}}}
\end{aligned} \nonumber \]
But at equilibrium, \(\mathrm{A}\) which equals \(-(\partial \mathrm{G} / \partial \xi)_{\mathrm{T}, \mathrm{p}}\) is zero. Then \(\mathrm{H}(\mathrm{A}=0)=\mathrm{H}\left(\xi^{\mathrm{eq}}\right)\). In other words, the variable enthalpy is another strong function of state. This is not the case for isobaric heat capacities.
\[\begin{aligned}
&(\partial \mathrm{H} / \partial \mathrm{T})_{\mathrm{p}, \mathrm{A}}= \\
&(\partial \mathrm{H} / \partial \mathrm{T})_{\mathrm{p}, \xi}-(\partial \xi / \partial \mathrm{A})_{\mathrm{T}, \mathrm{p}} \,(\partial \mathrm{A} / \partial \mathrm{T})_{\mathrm{p}, \xi} \,(\partial \mathrm{H} / \partial \xi)_{\mathrm{T}, \mathrm{p}}
\end{aligned} \nonumber \]
We cannot assume that the triple product term in the latter equation is zero. Hence, there are two limiting isobaric heat capacities; the equilibrium isobaric heat capacity \(C_{p}(A=0)\) and the frozen isobaric heat capacity \(\mathrm{C}_{\mathrm{p}}(\xi \mathrm{eq})\). In other words, an isobaric heat capacity is not a strong function of state because it is concerned with a pathway between states. Unless otherwise stated, we use the symbol \(\mathrm{C}_{\mathrm{p}}\) to indicate an equilibrium transformation, \(\mathrm{C}_{\mathrm{p}}(\mathrm{A}=0)\).


9: Least-Squares Approximation
The method of least-squares is commonly used to fit a parameterized curve to experimental data. In general, the fitting curve is not expected to pass through the data points, making this problem substantially different from the one of interpolation.
We consider here only the most common situation: the fitting of a straight line through data with the same experimental error for all the data points. We assume that the data to be fitted are given by \(\left(x_{i}, y_{i}\right)\) , with \(i=1\) to \(n\) .
We write for the fitting curve
\[y(x)=\alpha x+\beta . \nonumber \]
The distance \(r_{i}\) from the data point \(\left(x_{i}, y_{i}\right)\) and the fitting curve is given by
\[\begin{aligned} r_{i} &=y_{i}-y\left(x_{i}\right) \\ &=y_{i}-\left(\alpha x_{i}+\beta\right) . \end{aligned} \nonumber \]
A least-squares fit minimizes the sum of the squares of the \(r_{i}\) ’s. This minimum can be shown to result in the most probable values of \(\alpha\) and \(\beta\) .
We define
\[\begin{aligned} \rho &=\sum_{i=1}^{n} r_{i}^{2} \\ &=\sum_{i=1}^{n}\left(y_{i}-\left(\alpha x_{i}+\beta\right)\right)^{2} \end{aligned} \nonumber \]
To minimize \(\rho\) with respect to \(\alpha\) and \(\beta\) , we solve
\[\frac{\partial \rho}{\partial \alpha}=0, \quad \frac{\partial \rho}{\partial \beta}=0 \nonumber \]
Taking the partial derivatives, we have
\[\begin{aligned} &\frac{\partial \rho}{\partial \alpha}=\sum_{i=1}^{n} 2\left(-x_{i}\right)\left(y_{i}-\left(\alpha x_{i}+\beta\right)\right)=0 \\ &\frac{\partial \rho}{\partial \beta}=\sum_{i=1}^{n} 2(-1)\left(y_{i}-\left(\alpha x_{i}+\beta\right)\right)=0 \end{aligned} \nonumber \]
These equations form a system of two linear equations in the two unknowns \(\alpha\) and \(\beta\) , which is evident when rewritten in the form
\[\begin{aligned} \alpha \sum_{i=1}^{n} x_{i}^{2}+\beta \sum_{i=1}^{n} x_{i} &=\sum_{i=1}^{n} x_{i} y_{i} \\ \alpha \sum_{i=1}^{n} x_{i}+\beta n &=\sum_{i=1}^{n} y_{i} \end{aligned} \nonumber \]
These equations can be solved numerically, and MATLAB provides a built-in subroutine called polyfit.m. With the data in the vectors \(x\) and \(y\) , the MATLAB call
\[\mathrm{p}=\text { polyfit }(\mathrm{x}, \mathrm{y}, 1) \text {; } \nonumber \]
returns the values \(p(1)=\alpha\) and \(p(2)=\beta\) , which can then be used to draw the fitting line.


3.12: Chapter Review - Review Questions
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Review Questions
1 .
Which tab in the ribbon is the default tab that displays when you open a document file?
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the Insert tab
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the View tab
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the Layout tab
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the Home tab
2 .
What is one function of the Navigation pane?
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It helps the user locate web pages.
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It helps the user access help files.
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It helps the user find a specific word or phrase in their document.
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It helps the user find synonyms.
3 .
What is the purpose of the Page Setup command group?
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It is used to set page margins and the page size.
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It is used to wrap text and align text.
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It is used to insert object and pictures.
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It is used to insert WordArt or a signature line.
4 .
Where is the command for putting a section break located?
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on the Layout tab, in the Breaks drop-down menu
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on the Insert tab, in the Page Break drop-down menu
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on the Insert tab, in the Text Box drop-down menu
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on the Layout tab, in the Column drop-down menu
5 .
What is the difference between indenting a paragraph and aligning it?
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aligning a paragraph will center or position it left or right, whereas increasing the indent will add space in that selection
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increasing the indent will center and indent left or right, whereas aligning will add a tab space in that selection
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aligning a paragraph can increase the indent when you place it in the center or left or right
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indenting a paragraph can increase the alignment when you place it in the center or left or right
6 .
What is the default text wrapping when inserting a picture or an object?
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behind the text, at the point where the cursor is located
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in front of the text, at the point where the cursor is located
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in line with the text, at the point where the cursor is located
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square around the text
7 .
What can Track Changes do?
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see who made what changes to a document
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add comments to changes made
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search for changes to specific words
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use Smart Lookup to select text in a document
8 .
Where are the two places the Editor tool is located?
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on the Insert tab and on the View tab
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on the Review tab and on the References tab
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on the Home tab and on the Review tab
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on the Home tab and on the Design tab
9 .
A ________ is a cohesive set of fonts, colors, and line spacing that can be applied to an entire document.
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style
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watermark
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theme
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template
10 .
What is the main use of a watermark?
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to add a text or an image behind the body text of all pages
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to insert an image on top of the header on all papers
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to apply different font formatting throughout the document
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to delete the page background on every page
11 .
Word count is found in which menu in Docs?
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Edit
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File
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Tools
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Format
12 .
What do you need to do first before creating a new Doc?
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Create a template.
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Click the New plus sign.
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Go to the File menu.
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Log in to Drive.
13 .
How does the user apply a new font to an entire paragraph in Docs?
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Select all of the text, then either go to the Format menu or to the action bar to select a font type from the combo box.
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Place your cursor anywhere in the paragraph and choose the new font from the action bar.
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Navigate to the Format menu and select a new font.
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Select the entire paragraph and choose the font type from the Edit menu.
14 .
Where is the option to view section breaks in a Doc?
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on the action bar
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in the View menu
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in the Tools menu
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in the Format menu
15 .
Page setup is found in the ________ menu.
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Edit
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File
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Tools
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Format
16 .
What is the main purpose of Suggesting mode?
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to request comments from your coworkers
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to collect feedback on your products
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to gather voice messages in a chat like interface
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to keep track of added and edited text by different collaborators
17 .
What are the two ways to access version history in Docs?
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Go to the File menu, or click on the date link right beside the title bar.
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Go to the action bar and click on the Style combo box or click on the title bar.
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Go to the Explore icon on the bottom or click on insert equation on the View menu.
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Go to the Edit menu and click on Select All, or use Ctrl+A.
18 .
What is the purpose of naming versions?
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to have a record of the important changes in the progression of the document
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to download the file’s versions in order to have a hard copy on your computer
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to email each version to collaborators
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to have track changes recorded so that the team knows about the changes


3.2: Reflections from the Authors - Dahmitra Jackson
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- Susan Rahman, Prateek Sunder, and Dahmitra Jackson
- CC ECHO
Growing up in Marin County asa biracial woman is certainly a unique experience. As many biracial individuals describe, we don’t simply fit into any one group, and the expectation for us to pick a side is problematic. I grew up in over seven rental homes throughout Marin by the age of 17, which gave me another unique experience as I became extremely adaptable having to switch schools frequently. It was at a new school in 8th grade that I was called a racial slur. I later had to ask my mother for the meaning. In high school, it was not uncommon that police officers would be stationed out front, sometimes even detaining students. Another vivid remembrance from high school was that it was common knowledge amongst African American students that if we were in a certain Spanish teacher’s class, we would undoubtedly be assigned to sit in the front row. I didn’t believe it until it happened to me, 2nd period Spanish was a sight to see. With this brief introduction of a few of my early experiences with education, my goal is to remind you that there are still racial prejudices students face day to day. We should continue to ask, understand, hear, and really hear the lived experiences of all people of color if we truly want to do better.
Near the end of 2020 I decided to return to college and fulfill my dream of becoming the first in my family to graduate from college. I had been working at the same organization for 9 years and early in my career I experienced burnout, another gift from the pandemic. My first semester at College of Marin I enrolled in Dr. Susan Rahman’s Gender and Society course, and after completion she invited me to contribute to this piece. Her course was the first Zero Textbook Cost course I had taken, and I enjoyed every bit of it. One thing I am grateful for in returning to college as an adult is that I am more dedicated and have a stronger passion to learn. Going over each week’s material, I could tell how much effort was put into creating content that is relevant and inclusive. OERs and Zero Textbook Cost courses also give students an opportunity to learn about work created by people of color that may not have otherwise been featured in mainstream textbooks. Dr. Rahman has a talent for asking questions that get students thinking outside of our societal norms.
I joined this project later on, yet Dr. Rahman still provided me with spaces to have a voice. Throughout this work, I have gained experience, learned a great deal, and had the chance to work with an incredible team who share a vision. I want to give Dr. Rahman a huge shout out and thank you for challenging the academic system, pushing for us to create a better future,and shedding light on this topic. I am accustomed to being in environments dominated by whiteness, especially academically, and I often don’t question or feel comfortable in questioning certain ideas and teachings. In the past, when I thought I was in a safe space to share a few of the microaggressions thrown at me, I was told I was too sensitive, not believed,and my favorite, “it’s their generation, what are they going to do.” My hope with this book is that while we are pushing for more marginalized, underrepresented BIPOC to further their education and become future leaders, we can also provide them with inclusive material to learn from, and diverse, informed educators guiding them.


12.5J: Glossopharyngeal (IX) Nerve
The glossopharyngeal nerve (cranial nerve IX) serves many distinct functions, including providing sensory innervation to various head and neck structures.
- Describe the glossopharyngeal nerve (cranial nerve IX)
Key Points
- The glossopharyngeal nerve (cranial nerve IX) is responsible for swallowing and the gag reflex, along with other functions.
- The glossopharyngeal nerve receives input from the general and special sensory fibers in the back of the throat.
- The glossopharyngeal nerve has five components: branchial motor, visceral motor, visceral sensory, general sensory, and special sensory components.
Key Terms
- otic ganglion : A small parasympathetic ganglion located immediately below the foramen ovale in the infratemporal fossa that is associated with the glossopharyngeal nerve.
- medulla : The lower half of the brainstem that contains the cardiac, respiratory, vomiting, and vasomotor centers and is associated with autonomic, involuntary functions such as breathing, heart rate, and blood pressure.
- stylopharyngeus muscle : A muscle in the head that stretches between the temporal styloid process and the pharynx.
Structure
The glossopharyngeal nerve is the ninth of 12 pairs of cranial nerves. It exits the brainstem out from the sides of the upper medulla, just rostral (closer to the nose) to the vagus nerve.
Glossopharyngeal nerve : Image of head structures including the glossopharyngeal nerve.
The motor division of the glossopharyngeal nerve is derived from the basal plate of the embryonic medulla oblongata, while the sensory division originates from the cranial neural crest.
Function
There are a number of functions of the glossopharyngeal nerve. It controls muscles in the oral cavity and upper throat, as well as part of the sense of taste and the production of saliva.
Along with taste, the glossopharyngeal nerve relays general sensations from the pharyngeal walls. The various functions of the glossopharyngeal nerve are that:
- It receives general sensory fibers (ventral trigeminothalamic tract) from the tonsils, the pharynx, the middle ear, and the posterior 1/3 of the tongue.
- It receives special sensory fibers (taste) from the posterior 1/3 of the tongue.
- It receives visceral sensory fibers from the carotid bodies, carotid sinus.
- It supplies parasympathetic fibers to the parotid gland via the otic ganglion.
- It supplies motor fibers to the stylopharyngeus muscle.
- It contributes to the pharyngeal plexus.
Five Functional Components
The glossopharyngeal nerve consists of five components with distinct functions:
- Branchial motor (special visceral efferent): Supplies the stylopharyngeus muscle.
- Visceral motor (general visceral efferent): Provides parasympathetic innervation of the parotid gland.
- Visceral sensory (general visceral afferent): Carries visceral sensory information from the carotid sinus and body.
- General sensory (general somatic afferent): Provides general sensory information from the skin of the external ear, internal surface of the tympanic membrane, upper pharynx, and the posterior 1/3 of the tongue.
- Special sensory (special afferent): Provides taste sensation from the posterior 1/3 of the tongue.


What you’ll learn to do: explain changes and advances in cognitive development during middle childhood
Children in middle childhood are beginning a new experience—that of formal education. In the United States, formal education begins at a time when children are beginning to think in new and more sophisticated ways. According to Piaget, the child is entering a new stage of cognitive development where they are improving their logical skills. During middle childhood, children also make improvements in short term and long term memory.
Contributors and Attributions
CC licensed content, Original
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Introduction to Cognitive Development in Middle Childhood.
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5.1: Introduction
Astronomy Laboratory 5 – Scaling the Solar System
Module Introduction
The size of our Universe is hard for one to fathom. In order to get an idea of the size and scale, you will lay out the Solar System — in miniature and to scale. The model will highlight distances and planet sizes.
You will also model how eclipses occur, both solar eclipses and lunar eclipses, as well as partial and total eclipses. Along with phases of the moon and seasons, this concept is one of the most misunderstood in astronomy. (1)
Objectives
At the end of this module, students will be able to:
- Model the scale of the solar system
- Model solar and lunar eclipses (1)
Outcomes
The material in this module includes content designed to meet the following course outcomes:
- Explain and apply major concepts in astronomy including planets, satellites, stars, meteors, galaxies, and theories of the universe.
- Communicate scientific ideas through oral or written assignments.
- Demonstrate the ability to think critically. (1)
Assigned Readings
Learning Unit 5
Assignments
- Scaling the Solar System Activity
- Eclipses Activity
- Lab 5 Quiz (1)
- Authored by : Florida State College at Jacksonville. License : CC BY: Attribution


14.8: Summary
14.1 Meteors
When a fragment of interplanetary dust strikes Earth’s atmosphere, it burns up to create a meteor. Streams of dust particles traveling through space together produce meteor showers, in which we see meteors diverging from a spot in the sky called the radiant of the shower. Many meteor showers recur each year and are associated with particular comets that have left dust behind as they come close to the Sun and their ices evaporate (or have broken up into smaller pieces).
14.2 Meteorites: Stones from Heaven
Meteorites are the debris from space (mostly asteroid fragments) that survive to reach the surface of Earth. Meteorites are called finds or falls according to how they are discovered; the most productive source today is the Antarctic ice cap. Meteorites are classified as irons, stony-irons, or stones accordingly to their composition. Most stones are primitive objects, dated to the origin of the solar system 4.5 billion years ago. The most primitive are the carbonaceous meteorites, such as Murchison and Allende. These can contain a number of organic (carbon-rich) molecules.
14.3 Formation of the Solar System
A viable theory of solar system formation must take into account motion constraints, chemical constraints, and age constraints. Meteorites, comets, and asteroids are survivors of the solar nebula out of which the solar system formed. This nebula was the result of the collapse of an interstellar cloud of gas and dust, which contracted (conserving its angular momentum) to form our star, the Sun, surrounded by a thin, spinning disk of dust and vapor. Condensation in the disk led to the formation of planetesimals, which became the building blocks of the planets. Accretion of infalling materials heated the planets, leading to their differentiation. The giant planets were also able to attract and hold gas from the solar nebula. After a few million years of violent impacts, most of the debris was swept up or ejected, leaving only the asteroids and cometary remnants surviving to the present.
14.4 Comparison with Other Planetary Systems
The first planet circling a distant solar-type star was announced in 1995. Twenty years later, thousands of exoplanets have been identified, including planets with sizes and masses between Earth’s and Neptune’s, which we don’t have in our own solar system. A few percent of exoplanet systems have “hot Jupiters,” massive planets that orbit close to their stars, and many exoplanets are also in eccentric orbits. These two characteristics are fundamentally different from the attributes of gas giant planets in our own solar system and suggest that giant planets can migrate inward from their place of formation where it is cold enough for ice to form. Current data indicate that small (terrestrial type) rocky planets are common in our Galaxy; indeed, there must be tens of billions of such earthlike planets.
14.5 Planetary Evolution
After their common beginning, each of the planets evolved on its own path. Different possible outcomes are illustrated by comparison of the terrestrial planets (Earth, Venus, Mars, Mercury, and the Moon). All are rocky, differentiated objects. The level of geological activity is proportional to mass: greatest for Earth and Venus, less for Mars, and absent for the Moon and Mercury. However, tides from another nearby world can also generate heat to drive geological activity, as shown by Io, Europa, and Enceladus. Pluto is also active, to the surprise of planetary scientists. On the surfaces of solid worlds, mountains can result from impacts, volcanism, or uplift. Whatever their origin, higher mountains can be supported on smaller planets that have less surface gravity. The atmospheres of the terrestrial planets may have acquired volatile materials from comet impacts. The Moon and Mercury lost their atmospheres; most volatiles on Mars are frozen due to its greater distance from the Sun and its thinner atmosphere; and Venus retained CO 2 but lost H 2 O when it developed a massive greenhouse effect. Only Earth still has liquid water on its surface and hence can support life.


6: Multicellularity, the Cell Cycle and the Life Cycle
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- 6.1: Mitosis and the Cell Cycle
- Mitosis is a process of equal cell division, where each of the new cells receives the same number of chromosomes as the original cell. Mitosis does not change the cells’ genotype. The goal of mitosis is to distribute pre-combined genetic material equally. Actually, mitosis is a kind of karyokinesis, or splitting of the nucleus, as opposed to cytokinesis, which is the splitting of the whole cell. Karyokinesis and cytokinesis are parts of the cell cycle.
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- 6.2: Syngamy and Meiosis
- A sexual process is important to the survival of a species. First, it makes the population more diverse, which allows more flexibility to adapt via natural selection. Natural selection means that all organisms are different, but if environmental conditions change, only most adapted will survive. If the population is uniform, it has less chance of survival. Second, it prevents lethal mutations from being transferred to the offspring, because those with the mutations will die and not pass on genes
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- 6.3: Life Cycle of the Unicellular Eukaryote
- The life cycle of a unicellular organism begins with syngamy: one cell unites with cell having different genotype. The life cycle has all three possible ways of reproduction: sexual (ploidy doubles: syngamy), asexual (ploidy reduces: meiosis of zygote) and vegetative (ploidy does not change: mitotic divisions)
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- 6.4: Life Cycle of the Multicellular Eukaryote
- Cells do not always part after mitosis, but sometimes stay together to form multicellular organisms. Cells in the multicellular body are not connected forever. Sometimes, one or few cells escape and start a new body. This body will be exact copy (clone) of the previous one (vegetative reproduction). It is also possible that when these “escaped cells” go the different route: they become “sex delegates”, gametes.
Thumbnail: Principal scheme of meiosis. Only one of two telophase I variants is shown.


2.6: Central Electric Heat
Click play on the following audio player to listen along as you read this section.
A central electric furnace is comprised of a large bank of resistive heating coils, and a blower motor that pushes air across them. Most furnaces allow for the installation of air filters to help purify the air as it circulates through the building.
Control of the furnace comes from a low-voltage thermostat installed in a central location of the house. This room thermostat energizes a 24V solenoid contactor, which in turn energizes the 240V heating elements. As the temperature in the plenum chamber rises, eventually the blower motor thermostat engages and begins to push heated air throughout the building.
The furnace houses the relays which control the heating elements. These are normally switched on and off in increments of 5 kW or less. This helps reduce the strain on the line due the heavy currents drawn when large heating loads are all switched on simultaneously. This helps reduce the flickering of lights and other under voltage concerns in parallel circuits.
The furnace will also contain a high temperature safety cut-out switch that will disconnect all power to the heating elements if the temperature rises above a pre-set safety threshold. This can happen if the blower fan fails to engage and drive the heated air through the house, and thus draw cool air into the plenum chamber.
Electric furnaces are sized according to their power consumption and can generally range anywhere from 5 kW to 40 kW, and be supplied with either single-phase voltage for household use, or three-phase voltage for industrial and commercial heaters, depending upon the availability at the point of installation.


3.5: Triangle with the given sides
Consider the triangle \(ABC\). Set
\(a = BC\), \(b = CA\), \(c = AB.\)
Without loss of generality, we may assume that
\(a \le b \le c.\)
Then all three triangle inequalities for \(\triangle ABC\) hold if and only if
\(c \le a + b\).
The following theorem states that this is the only restriction on \(a\), \(b\), and \(c\).
Assume that \(0 < a \le b \le c \le a + b\). Then there is a triangle with sides \(a, b\), and \(c\); that is, there is \(\triangle ABC\) such that \(a = BC\), \(b = CA\), and \(c = AB\).
- Proof
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Fix the points \(A\) and \(B\) such that \(AB = c\). Given \(\beta \in [0, \pi]\), suppose that \(C_{\beta}\) denotes the point in the plane such that \(BC_{\beta} = a\) and \(\measuredangle ABC = \beta\).
According the Corollary \(\PageIndex{1}\), the map \(\beta \mapsto C_{\beta}\) is continuous. Therefore, the function \(b(\beta) = AC_{\beta}\)is continous (formally, it follows from Exercise 1.9.1 and Exercise 1.9.2 ).
Note that \(b(0) = c - a\) and \(b (\pi) = c + a\). Since \(c - a \le b \le c + a\), by the intermediate value theorem ( Theorem 3.2.1 ) there is \(\beta_0 \in [0, \pi]\) such that \(b(\beta_0) = b\), hence the result.
Assume \(r > 0\) and \(\pi > \beta > 0\). Consider the triangle \(ABC\) such that \(AB = BC = r\) and \(\measuredangle ABC = \beta\). The existence of such a triangle follows from Axiom IIIa and Proposition 2.2.2 .
Note that according to Axiom IV , the values \(\beta\) and \(r\) define the triangle \(ABC\) up to the congruence. In particular, the distance \(AC\) depends only on \(\beta\) and \(r\).
\[s(\beta, r):= AC.\]
Given \(r > 0\) and \(\varepsilon > 0\), there is \(\delta > 0\) such that
\(0 < \beta < \delta \Rightarrow s(r, \beta) < \varepsilon.\)
- Proof
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Fix two points \(A\) and \(B\) such that \(AB = r\).
Choose a point \(X\) such that \(AY = \dfrac{\varepsilon}{2}\); it exists by Proposition 2.2.2 .
Note that \(X\) and \(Y\) lie on the same side of \((AB)\); therefore, \(\angle ABY\) is positive. Set \(\delta = \measuredangle ABY\).
Suppose \(0 < \beta < \delta\); by Axiom IIIa , we can choose \(B\) so that \(\measuredangle ABC = \beta\) and \(BC = r\). Further we can choose a half-line \([BZ)\) such that \(\measuredangle ABZ = \dfrac{1}{2} \cdot \beta\).
Note that \(A\) and \(Y\) lie on opposite sides of \((BZ)\) and moreover \(\measuredangle ABZ \equiv - \measuredangle CBZ\). In particular, \((BZ)\) intersects \([AY]\); denote by \(D\) the point of intersection.
Since \(D\) lies between \(A\) and \(Y\), we have that \(AD < AY\).
Since \(D\) lies on \((BZ)\) we have that \(\measuredangle ABD \equiv \measuredangle CBD\). By Axiom IV , \(\triangle ABD \cong \triangle CBD\). It follows that
\[\begin{array} {rcl} {s(r, \beta)} & = & {AC \le} \\ {} & \le & {AD + DC =} \\ {} & = & {2 \cdot AD <} \\ {} & < & {2 \cdot AY =} \\ {} & = & {\varepsilon} \end{array}\]
Fix a real number \(r > 0\) and two distinct points \(A\) and \(B\). Then for any real number \(\beta \in [0, \pi]\), there is a unique point \(C_{\beta}\) such that \(BC_{\beta} = r\) and \(\measuredangle ABC_{\beta} = \beta\). Moreover, \(\beta \mapsto C_{\beta}\) is a continuous map from \([0, \pi]\) to the plane.
- Proof
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The existence and uniqueness of \(C_{\beta}\) follows from Axiom IIIa and Proposition 2.2.2 .
Note taht if \(\beta_1 \ne \beta_2\), then
\[C_{\beta_1} C_{\beta_2} = s(r, |\beta_1 - \beta_2|).\]
By Proposition \(\PageIndex{1}\), the map \(\beta \mapsto C_{\beta}\) is continuous.
Given a positive real number \(r\) and a pint \(O\), the set \(\Gamma\) of all points on distance \(r\) from \(O\) is called a circle with radius \(r\) and center \(O\).
Exercise \(\PageIndex{1}\)
Show that two circles intersect if and only if
\[|R - r| \le d \le R + r,\]
where \(R\) and \(r\) denote their radiuses, and \(d\) — the distance between their centers.
- Hint
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The "only-if" part follows from the triangle inequality. To prove "if" part, observe that Theorem \(\PageIndex{1}\) implies existence of a triangle with sides \(r_1\), \(r_2\), and \(d\). Use this triangle to show that there is a point \(X\) such that \(O_1X = r_1\) and \(O_2X = r_2\), where \(O_1\) and \(O_2\) are the centers of the corresponding circles.


1: Success Skills Last updated Save as PDF Page ID 58171 Lumen Learning Lumen Learning 1.1: Why It Matters- Success Skills 1.2: Introduction to Habits for Success 1.3: Habits for Success 1.4: Utilizing Your Support Network 1.5: Introduction to Time Management 1.6: Time Management and Scheduling 1.7: Avoiding Procrastination 1.8: Introduction to Communication and Professionalism 1.9: Communication and Context 1.10: Writing in College 1.11: Introduction to Using Technology in Writing 1.12: Word-Processing Skills 1.13: Discussion Boards 1.14: Social Media 1.15: Introduction to Critical Thinking and Reflection 1.16: Critical Thinking 1.17: What is Reflective Thinking? 1.18: Reflective Writing 1.19: Putting It Together- Habits for Success 1.20: Discussion- What is Success? 1.21: Assignment- College Reflection


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14: Yoga and Buddhism as Personality Development Paths
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14.1: Chapter Introduction
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14.2: Zen Buddhism in America
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14.3: Historical Description of Yoga
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14.4: The Yoga Sutras of Patanjali
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14.5: The Bhagavad Gita
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14.6: Pathways to Personal Growth - Schools of Yoga
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In her discourse accompanying the translation of Patanjali’s Yoga Sutras, Bailey refers to four types of Yoga that developed as humanity developed (1927). In chronological order they are Hatha-Yoga, Laya-Yoga, Bhakti-Yoga, and Raja-Yoga (also known as Kriya-Yoga). Feuerstein adds three more to what he describes as the seven major branches of the tree of Hindu Yoga: Jnana-Yoga, Karma-Yoga, and Mantra-Yoga.
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14.7: Obstacles to Personal Growth- Patanjali's Five Hindrances
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14.8: Yoga in America- The Self-Realization Fellowship and Transcendental Meditation
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14.9: Historical Description of Buddhism
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14.10: The Four Noble Truths of Human Life
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Following his enlightenment, the Buddha began to teach what he had realized. In his first lesson, he described the Four Noble Truths: 1) suffering is an unavoidable reality in human life; 2) the source of suffering is craving or desire, and the bad karma it creates; 3) the craving that leads to suffering can be destroyed; 4) the Middle Way is the path to eliminate craving and suffering (Suzuki, 1960; World’s Great Religions, 1957; Wilkins, 1967).
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14.11: Obstacles to Personal Growth- The Three Poisons of Buddhism
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14.S: Chapter Summary
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4.7: The DX Cooling Cycle
Click play on the following audio player to listen along as you read this section.
A step-by-step analysis of the forces acting upon the refrigerant as it passes through each of the four main components of a DX cooling system will help in our understanding of the process.
The Compressor
This is the component which drives the refrigerant throughout the system. It receives a low pressure, room temperature gas , and pumps the refrigerant through a valve into a much narrower diameter pipe and this restriction in volume, combined with the increased pressure of the refrigerant causes its temperature to rise rapidly. The refrigerant is a high temperature, high pressure gas as it is exiting the compressor valve.
The Condenser
As the refrigerant enters the condenser coil it is a high temperature , high pressure gas . The condenser coil has a large surface area that is exposed to the air. It will often be attached to a large metal grill to increase its available surface area, dissipating heat through conduction as well as convection. The refrigerant dissipates the thermal energy and condenses into a liquid as it moves through the coil. Most of the heat energy is dissipated at this stage, utilizing the Second Law of Thermodynamics to transfer heat from the refrigerant to the surrounding air. A fan can be incorporated into the cooling system to help circulate air across the condenser coils and take heat away from the system. Condenser units are often installed outdoors on rooftops for convenient heat dissipation.
The Expansion Valve
This component regulates the flow of refrigerant from the high pressure/temperature side of the system and the low pressure/temperature side. As the refrigerant enters the expansion valve it is a high pressure, room temperature liquid , and as it expands into the larger area beyond the valve, its pressure, and thus its temperature drops dramatically. This is when the refrigerant is at its coldest, as a low pressure, low temperature liquid . The amount of refrigerant that the valve lets through is controlled by a diaphragm, which is connected to a capillary type thermal sensor filled with a separate refrigerant. The sensing bulb is attached to the exit line of the evaporator . By sensing the temperature of the refrigerant as it leaves the evaporator, the expansion valve can let in more or less refrigerant at a given moment, thus raising or lowering the temperature of the refrigerant as it enters the evaporator.
The Evaporator
The evaporator coils are similar in design to the condenser coils but with the purpose of drawing heat from the surrounding air into the refrigerant. Again a large surface area helps to conduct heat from the air to the refrigerant. Fans can be used circulate the air and replace cooled air with warmer air. As the low pressure, low temperature liquid enters the evaporator coil and starts to absorb heat, it rapidly evaporates from a liquid to a gas. This phase shift draws energy from the surrounding air in the form of heat, and carries it away as the low pressure, room temperature gas is suctioned towards the compressor, where energy is added to drive the cycle again.


3.3: Other Aromatic Substitutions
After completing this section, you should be able to
- write a balanced equation for the halogenation (F, Cl, Br, I) of benzene in the presence of a suitable catalyst or promoter.
- draw the resonance contributors for the carbocation which is formed during the reaction of chlorine or bromine with benzene.
- write the equation for the nitration and sulfonation of benzene.
- write the detailed mechanism for the nitration and sulfonation of benzene.
- write the equation for the reduction of an aromatic nitro compound to an amine.
- identify aromatic sulfonation as being a reversible process, and describe the conditions under which the forward and reverse reactions are favoured.
- write the equation for the desulfonation of an aromatic sulfonic acid.
- identify aromatic sulfonic acids as being key intermediates in the manufacture of sulfa drugs.
There are many other kinds of electrophilic aromatic substitutions besides bromination, and all occur by the same general mechanism. Let’s look at some of these other reactions briefly.
Aromatic Halogenation
Aromatic rings react with Cl 2 in the presence of FeCl 3 catalyst to yield chlorobenzenes, just as they react with Br 2 and FeBr 3 . This kind of reaction is used in the synthesis of numerous pharmaceutical agents, including the antiallergy medication loratadine, marketed as Claritin.
Lewis Acidic Catalysts
Halogens need the help and aid of Lewis Acidic Catalysts to activate and become very strong electrophiles as they polarize the Br-Br bond. An A ctivated halogen, X + , where X= Br or Cl, reacts with benzene as it is a much better electrophile than X 2 alone.
Examples of Lewis Acidic Catalysts are Ferric halides (FeX 3 ) and Aluminum Halides (AlX 3 ) where X= Br or Cl. We had covered the activation of the halogens using Ferric halides (FeX 3 ); now, let's observe the activation using Aluminum Halides (AlX3).
In the example of bromine, in order to make bromine electrophillic enough to react with benzene, we use the aid of an aluminum halide such as aluminum bromide.
With aluminum bromide as a Lewis acid, Br 2 reacts with AlBr 3 to form a complex structure for Br + . The presence of this complex for Br + is a much better electrophile than Br 2 alone.
As the bromine has now become more electrophillic after activation of a catalyst, an electrophillic attack by the benzene occurs at the terminal bromine of Br-Br-AlBr 3 . The mechanism continues as presented in the previous section. Since the by-product aluminum tetrabromide is a strong nucleophile, it pulls of a proton from the Hydrogen on the same carbon as bromine. In the end, the catalyst regenartes as it is not consumed during the reaction.
Dissociation Energies of Halogens and its Effect on Halogenation of Benzenes
The electrophillic bromination of benzenes is an exothermic reaction. Considering the exothermic rates of aromatic halogenation decreasing down the periodic table in the Halogen family. Fluoridation is the most exothermic, and Iodination is the least. Being so exothermic, a reaction of flourine with benzene is explosive! For iodine, electrophillic iodination is generally endothermic, hence a reaction is often not possible. Similar to bromide, chlorination would require the aid of an activating presence such as Alumnium Chloride or Ferric Chloride. The mechanism of this reaction is the same as with Bromination of benzene.
Iodine and Fluorine need specific reagents
Iodine and fluorine cannot be introduced into an aromatic ring by the method used for bromine and chlorine. On its own, iodine is unreactive with aromatic rings. Still, one method for aromatic iodination is treatment in the presence of a copper salt such as copper(II)chloride, where I 2 is oxidized to a more powerful electrophilic species that reacts as if it were I + .
In contrast, fluorine is too reactive, so it cannot be used directly for aromatic monofluorination. However, fluorinating agents like 1-(chloromethyl)-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane ditetrafluoroborate (also known as F-TEDA-BF 4 ) sold commercially as Sectfluor® offer convenient sources of “F + ” for this type of reaction.
Electrophilic aromatic halogenations also occur in the biosynthesis of many naturally occurring molecules, particularly those produced by marine organisms. In humans, the best-known example occurs in the thyroid gland during the biosynthesis of thyroxine, a hormone involved in regulating growth and metabolism. The amino acid tyrosine is first iodinated by thyroid peroxidase, and two of the iodinated tyrosine molecules then couple. The electrophilic iodinating agent is an I + species, perhaps hypoiodous acid (HIO), that is formed from iodide ion by oxidation with H 2 O 2 .
More than 20% of all pharmaceutical agents sold contain fluorine, including 30% of the top 100 drugs sold. Sitagliptin (Januvia), used to treat type 2 diabetes, fluoxetine (Prozac), an antidepressant, and atorvastatin (Lipitor), a statin used to lower cholesterol, are examples.
Aromatic Nitration
Aromatic rings are nitrated by reaction with a mixture of concentrated nitric and sulfuric acids.
Sulfuric Acid Activation of Nitric Acid
The first step in the nitration of benzene is to activate HNO 3 with sulfuric acid to produce a stronger electrophile, the nitronium ion. The formation of the nitronium ion is through the protonation of nitric acid by sulfuric acid, which causes the loss of a water molecule and formation of a nitronium ion.
Because the nitronium ion is a good electrophile, it is attacked by benzene to produce Nitrobenzene.
Mechanism
(Resonance forms of the intermediate can be seen in the generalized electrophilic aromatic substitution)
Electrophilic nitration of an aromatic ring does not occur in nature but is particularly important in the laboratory because the nitro-substituted product can be reduced by reagents such as iron, tin, or SnCl 2 to yield the corresponding arylamine, ArNH 2 . Attachment of an amino group (–NH 2 ) to an aromatic ring by the two-step nitration/reduction sequence is a key part of the industrial synthesis of many dyes and pharmaceutical agents. We’ll discuss more reactions of aromatic nitrogen compounds in Chapter 10.
Aromatic Sulfonation
Aromatic rings can be sulfonated by reaction with so-called fuming sulfuric acid, a mixture of \(\ce{H2SO4}\) and \(\ce{SO3}\). The reactive electrophile is either \(\ce{HSO3^{+}}\) or neutral \(\ce{SO3}\), depending on reaction conditions, and substitution occurs by the same two-step mechanism seen previously for bromination and nitration (Figure \(\PageIndex{2}\)). Note, however, that the sulfonation reaction is readily reversible. It can occur either forward or backward, depending on the reaction conditions. Sulfonation is favored in strong acid, but desulfonation (benzenesulfonic acid to produce benzene) is favored in hot, dilute aqueous acid.
Mechanism
To produce benzenesulfonic acid from benzene, fuming sulfuric acid and sulfur trioxide are added. Fuming sulfuric acid is a concentrated solution of dissolved sulfur trioxide in sulfuric acid. The sulfur in sulfur trioxide is electrophilic because the oxygens pull electrons away from it because oxygen is very electronegative. The benzene attacks the sulfur (and subsequent proton transfers occur) to produce benzenesulfonic acid.
Reverse Sulfonation
Sulfonation of benzene is a reversible reaction. Sulfur trioxide readily reacts with water to produce sulfuric acid and heat. Therefore, by adding heat to benzenesulfonic acid in diluted aqueous sulfuric acid the reaction is reversed.
Because sulfonation is a reversible reaction, it can also be used in further substitution reactions in the form of a directing blocking group because it can be easily removed. The sulfonic group blocks the carbon from being attacked by other substituents and after the reaction is completed it can be removed by reverse sulfonation.
Aromatic sulfonation does not occur naturally but is widely used in the preparation of detergents, dyes, and pharmaceutical agents. For example, the sulfa drugs, such as sulfanilamide, were among the first clinically useful antibiotics. Although largely replaced today by more effective agents, sulfa drugs are still used in the treatment of meningitis and urinary tract infections. Another example is Bezenesulfonyl Chloride, which is a precursor to sulfonamides, which are used in chemotherapy. These drugs are prepared commercially by a process that involves aromatic sulfonation as its key step.
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Bezenesulfonyl Chloride |
Sulfanilamide |
Feeling Curious? https://en.wikipedia.org/wiki/Sulfanilamide
Exercises
1. What is/are the required reagent(s)for the following reaction:
- Answer
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SO 3 and H 2 SO 4 (fuming)
What is the product of the following reaction:
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Why is it important that the nitration of benzene by nitric acid occurs in sulfuric acid?
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Sulfuric acid is needed in order for a good electrophile to form. Sulfuric acid protonates nitric acid to form the nitronium ion (water molecule is lost). The nitronium ion is a very good electrophile and is open to attack by benzene. Without sulfuric acid the reaction would not occur.
Write a detailed mechanism for the sulfonation of benzene, including all resonance forms.
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Draw an energy diagram for the nitration of benzene. Draw the intermediates, starting materials, and products. Label the transition states.
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In each case, how many products would be possible for the bromination of p -xylene, o -xylene, and m -xylene?
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If toluene is treated with D 2 SO 4 all the hydrogen’s are replaced with deuterium. Explain.
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The deuterium is added to the ring. When the ring “re-aromatizes” the base scavenges the hydrogen before the deuterium and therefore is left on the ring. Continues for the rest of the hydrogen on the ring.
Make certain that you can define, and use in context, the key term below.
- nitronium ion, (NO +2 )
References
- Laali, Kenneth K., and Volkar J. Gettwert. “Electrophilic Nitration of Aromatics in Ionic Liquid Solvents.” The Journal of Organic Chemistry 66 (Dec. 2000): 35-40. American Chemical Society.
- Malhotra, Ripudaman, Subhash C. Narang, and George A. Olah. Nitration: Methods and Mechanisms. New York: VCH Publishers, Inc., 1989.
- Sauls, Thomas W., Walter H. Rueggeberg, and Samuel L. Norwood. “On the Mechanism of Sulfonation of the Aromatic Nucleus and Sulfone Formation.” The Journal of Organic Chemistry 66 (1955): 455-465. American Chemical Society.
- Vollhardt, Peter. Organic Chemistry : Structure and Function. 5th ed. Boston: W. H. Freeman & Company, 2007.


11.2: Reading- Benefits of Value-Based Pricing
The Customer and the Pricing Decision
We have discussed common company objectives that affect pricing and the competitive impact on pricing. The most important perspective in the pricing process is the customer’s. Value-based pricing brings the voice of the customer into the pricing process. It bases prices primarily on the value to the customer rather than on the cost of the product or historical prices determined by competitors.
If we consider the three approaches to setting price, cost-based pricing is focused entirely on the perspective of the company, with very little concern for the customer; demand-based pricing is focused on the customer, but only as a predictor of sales; and value-based pricing focuses entirely on the customer as the determiner of the total price/value package. Marketers who employ value-based pricing might describe it this way: “Price is what you think your product is worth to that customer at that time.” This approach regards the following as marketing/price truths:
- To the customer, price is the only unpleasant part of buying.
- Price is the easiest marketing tool to copy.
- Price represents everything about the product.
Still, value-based pricing is not altruistic. It asks and answers two questions:
- What is the highest price I can charge and still make the sale?
- Am I willing to sell at that price?
In order to answer these questions we need to consider both customer- and competitor-related factors. In answering the second question, we would also want to use the break-even analysis that we discussed in the previous section, as well as other financial and strategic analyses.
Customer-Related Factors
Several customer-related factors are important in value-based pricing; one of them is understanding the customer buying process. For a convenience good, customers often spend little time, planning, or effort in the buying process, and purchases are more often made on impulse. With a shopping product, the consumer is more likely to compare a number of options when evaluating quality, cost, and features; as a result, he or she will require a better understanding of price in order to assess value.
Another issue is that different groups or segments of customers view price differently. Buyer personas can be instrumental to a marketer’s grasp of those differences and the role price plays in the decision-making process. Some buyers will weight convenience or quality over price, for instance, while others will be highly price sensitive.
The marketer must understand what the customer values, what the customer expects, and how the customer evaluates price in the value equation.
Competitor-Related Factors
A second factor influencing value-based pricing is competitors. We asserted above that the primary driver of value-based pricing is the customer’s estimation of value—not costs or historical competitor prices. Still, competitors do influence the customer’s view of value. The marketing mix of competitive products have an impact on customer expectations because they an important part of the decision-making context. Customers are shopping across products and brands and take price differences into account when evaluating the quality and benefits of competitive products. These direct comparisons have tremendous impact on the customer’s perceptions of value.
In value-based pricing, the marketer must also consider indirect competitors that consumers may use as a basis for price comparisons. For example, one might use the price of a vacation as a basis for buying vacation clothes. The cost of eating out is frequently compared to the cost of groceries.
Ultimately, value-based pricing offers the following three tactical recommendations:
- Employ a segmented approach toward price that considers how each group of customers assesses value.
- Establish the highest possible price level and justify it with comparable value.
- Use price as one component in the marketing mix, building compelling value across all elements of the offering.
Contributors and Attributions
- Benefits of Value-Based Pricing. Provided by : Lumen Learning. License : CC BY: Attribution
- Hot Soup Charitable Elephants. Authored by : Julian Partridge. Located at : www.flickr.com/photos/julianpartridge/11512394244/. License : CC BY-SA: Attribution-ShareAlike
- Choices. Authored by : Darwin Bell. Located at : https://www.flickr.com/photos/darwinbell/3340033037/ . License : CC BY-NC: Attribution-NonCommercial


9.4: Lenz's Law
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Learning Objectives
By the end of this section, you will be able to:
- Use Lenz’s law to determine the direction of induced emf whenever a magnetic flux changes
- Use Faraday’s law with Lenz’s law to determine the induced emf in a coil and in a solenoid
The direction in which the induced emf drives current around a wire loop can be found through the negative sign. However, it is usually easier to determine this direction with Lenz’s law, named in honor of its discoverer, Heinrich Lenz (1804–1865). (Faraday also discovered this law, independently of Lenz.) We state Lenz’s law as follows:
Lenz's Law
The direction of the induced emf drives current around a wire loop to always oppose the change in magnetic flux that causes the emf.
Lenz’s law can also be considered in terms of conservation of energy. If pushing a magnet into a coil causes current, the energy in that current must have come from somewhere. If the induced current causes a magnetic field opposing the increase in field of the magnet we pushed in, then the situation is clear. We pushed a magnet against a field and did work on the system, and that showed up as current. If it were not the case that the induced field opposes the change in the flux, the magnet would be pulled in produce a current without anything having done work. Electric potential energy would have been created, violating the conservation of energy.
To determine an induced emf \(\epsilon\), you first calculate the magnetic flux \(\Phi_m\) and then obtain \(d\Phi_m/dt\). The magnitude of \(\epsilon\) is given by
\[\epsilon = \left|\dfrac{d\Phi_m}{dt}\right|. \nonumber \]
Finally, you can apply Lenz’s law to determine the sense of \(\epsilon\). This will be developed through examples that illustrate the following problem-solving strategy.
Problem-Solving Strategy: Lenz’s Law
To use Lenz’s law to determine the directions of induced magnetic fields, currents, and emfs:
- Make a sketch of the situation for use in visualizing and recording directions.
- Determine the direction of the applied magnetic field \(\vec{B}\).
- Determine whether its magnetic flux is increasing or decreasing.
- Now determine the direction of the induced magnetic field \(\vec{B}\). The induced magnetic field tries to reinforce a magnetic flux that is decreasing or opposes a magnetic flux that is increasing. Therefore, the induced magnetic field adds or subtracts to the applied magnetic field, depending on the change in magnetic flux.
- Use right-hand rule 2 (RHR-2; see Magnetic Forces and Fields ) to determine the direction of the induced current I that is responsible for the induced magnetic field \(\vec{B}\).
- The direction (or polarity) of the induced emf can now drive a conventional current in this direction.
Let’s apply Lenz’s law to the system of Figure \(\PageIndex{1a}\). We designate the “front” of the closed conducting loop as the region containing the approaching bar magnet, and the “back” of the loop as the other region. As the north pole of the magnet moves toward the loop, the flux through the loop due to the field of the magnet increases because the strength of field lines directed from the front to the back of the loop is increasing. A current is therefore induced in the loop. By Lenz’s law, the direction of the induced current must be such that its own magnetic field is directed in a way to oppose the changing flux caused by the field of the approaching magnet. Hence, the induced current circulates so that its magnetic field lines through the loop are directed from the back to the front of the loop. By RHR-2, place your thumb pointing against the magnetic field lines, which is toward the bar magnet. Your fingers wrap in a counterclockwise direction as viewed from the bar magnet. Alternatively, we can determine the direction of the induced current by treating the current loop as an electromagnet that opposes the approach of the north pole of the bar magnet. This occurs when the induced current flows as shown, for then the face of the loop nearer the approaching magnet is also a north pole.
Part (b) of the figure shows the south pole of a magnet moving toward a conducting loop. In this case, the flux through the loop due to the field of the magnet increases because the number of field lines directed from the back to the front of the loop is increasing. To oppose this change, a current is induced in the loop whose field lines through the loop are directed from the front to the back. Equivalently, we can say that the current flows in a direction so that the face of the loop nearer the approaching magnet is a south pole, which then repels the approaching south pole of the magnet. By RHR-2, your thumb points away from the bar magnet. Your fingers wrap in a clockwise fashion, which is the direction of the induced current.
Another example illustrating the use of Lenz’s law is shown in Figure \(\PageIndex{2}\). When the switch is opened, the decrease in current through the solenoid causes a decrease in magnetic flux through its coils, which induces an emf in the solenoid. This emf must oppose the change (the termination of the current) causing it. Consequently, the induced emf has the polarity shown and drives in the direction of the original current. This may generate an arc across the terminals of the switch as it is opened.
Exercise \(\PageIndex{1A}\)
Find the direction of the induced current in the wire loop shown below as the magnet enters, passes through, and leaves the loop.
Solution
To the observer shown, the current flows clockwise as the magnet approaches, decreases to zero when the magnet is centered in the plane of the coil, and then flows counterclockwise as the magnet leaves the coil.
Example \(\PageIndex{1A}\): A Circular Coil in a Changing Magnetic Field
A magnetic field \(\vec{B}\) is directed outward perpendicular to the plane of a circular coil of radius \(r = 0.50 \, m\) (Figure \(\PageIndex{3}\)). The field is cylindrically symmetrical with respect to the center of the coil, and its magnitude decays exponentially according to \(B = (1.5T)e^{(5.0s^{-1})t}\), where B is in teslas and t is in seconds.
- Calculate the emf induced in the coil at the times \(t_1 = 0\), \(t_2 = 5.0 \times 10^{-2}s\), and \(t_3 = 1.0 \, s\).
- Determine the current in the coil at these three times if its resistance is \(10 \, \Omega\).
Strategy
Since the magnetic field is perpendicular to the plane of the coil and constant over each spot in the coil, the dot product of the magnetic field \(\vec{B}\) and normal to the area unit vector \(\hat{n}\) turns into a multiplication. The magnetic field can be pulled out of the integration, leaving the flux as the product of the magnetic field times area. We need to take the time derivative of the exponential function to calculate the emf using Faraday’s law. Then we use Ohm’s law to calculate the current.
Solution
- Since \(\vec{B}\) is perpendicular to the plane of the coil, the magnetic flux is given by \[\Phi_m = B\pi r^2 = (1.5 e^{-5.0 t}T)\pi (0.50 \, m)^2 \nonumber \]\[= 1.2 e^{-(5.0 s^{-1})t} Wb. \nonumber \] From Faraday’s law, the magnitude of the induced emf is \[\epsilon = \left|\frac{d\Phi_m}{dt}\right| = \left|\frac{d}{dt} (1.2 e^{-(5.0s^{-1})t} Wb)\right| = 6.0 e^{-(5.0s^{-1})t}V. \nonumber \] Since \(\vec{B}\) is directed out of the page and is decreasing, the induced current must flow counterclockwise when viewed from above so that the magnetic field it produces through the coil also points out of the page. For all three times, the sense of ε is counterclockwise; its magnitudes are \[\epsilon (t_1) = 6.0 V; \, \epsilon (t_2) = 4.7 \, V; \, \epsilon (t_3) = 0040 \, V. \nonumber \]
- From Ohm’s law, the respective currents are \[I(t_1) = \frac{\epsilon (t_1)}{R} = \frac{6.0 \, V}{10 \, \Omega} = 0.60 \, A; \nonumber \]\[I(t_2) = \frac{4.7 \, V}{10 \, \Omega} = 0.47 \, A; \nonumber \] and \[I(t_3) = \frac{0.040 \, V}{10 \, \Omega} = 4.0 \times 10^{-3} \, A. \nonumber \]
Significance
An emf voltage is created by a changing magnetic flux over time. If we know how the magnetic field varies with time over a constant area, we can take its time derivative to calculate the induced emf.
Example \(\PageIndex{1B}\): Changing Magnetic Field Inside a Solenoid
The current through the windings of a solenoid with \(n = 2000\) turns per meter is changing at a rate \(dI/dt = 3.0 \, A/s\). (See Sources of Magnetic Fields for a discussion of solenoids.) The solenoid is 50-cm long and has a cross-sectional diameter of 3.0 cm. A small coil consisting of \(N = 20\) closely wound turns wrapped in a circle of diameter 1.0 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assuming that the infinite-solenoid approximation is valid at the location of the small coil, determine the magnitude of the emf induced in the coil.
Strategy
The magnetic field in the middle of the solenoid is a uniform value of \(\mu_0 nI\). This field is producing a maximum magnetic flux through the coil as it is directed along the length of the solenoid. Therefore, the magnetic flux through the coil is the product of the solenoid’s magnetic field times the area of the coil. Faraday’s law involves a time derivative of the magnetic flux. The only quantity varying in time is the current, the rest can be pulled out of the time derivative. Lastly, we include the number of turns in the coil to determine the induced emf in the coil.
Solution
Since the field of the solenoid is given by \(B = \mu_0 nI\), the flux through each turn of the small coil is
\[\Phi_m = \mu_0 nI\left(\frac{\pi d^2}{4}\right), \nonumber \]
where \(d\) is the diameter of the coil. Now from Faraday’s law , the magnitude of the emf induced in the coil is
\[ \begin{align*} \epsilon &= \left|N\frac{d\Phi_m}{dt}\right| \\[4pt] &= \left|N\mu_0 n\frac{\pi d^2}{4} \frac{dI}{dt}\right| \\[4pt] &= 20 (4\pi \times 10^{-7} T \cdot m/s)(2000 \, m^{-1}) \frac{\pi(0.010 \, m)^2}{4} (3.0 \, A/s) \\[4pt] &= 1.2 \times 10^{-5} \, V. \end{align*} \nonumber \]
Significance
When the current is turned on in a vertical solenoid, as shown in Figure \(\PageIndex{4}\), the ring has an induced emf from the solenoid’s changing magnetic flux that opposes the change. The result is that the ring is fired vertically into the air.
Note
A demonstration of the jumping ring from MIT.


1.3: Moments
A moment (also sometimes called a torque) is defined as the "tendency of a force to rotate a body". Where forces cause linear accelerations, moments cause angular accelerations . In this way moments, can be thought of as twisting forces.
The Vector Representation of a Moment:
Moments, like forces, can be represented as vectors and have a magnitude, a direction, and a "point of application". For moments however a better name for the point of application is the axis of rotation . This will be the point or axis about which we will determine all the moments.
Magnitude:
The magnitude of a moment is the degree to which the moment will cause angular acceleration in the body it is acting on. It is represented by a scalar (a single number). The magnitude of the moment can be thought of as the strength of the twisting force exerted on the body. When a moment is represented as a vector, the magnitude of the moment is usually explicitly labeled. though the length of the moment vector also often corresponds to the relative magnitude of the moment.
The magnitude of the moment is measured in units of force times distance. The standard metric units for the magnitude of moments are Newton-meters, and the standard English units for a moment are foot-pounds.
\[ M = F * d \]
\[ \text{Metric:} \,\, N * m \]
\[ \text{English:} \,\, lb * ft \]
Direction:
In a two-dimensional problem, the direction can be thought of as a scalar quantity corresponding to the direction of rotation the moment would cause. A moment that would cause a counterclockwise rotation is a positive moment, and a moment that would cause a clockwise rotation is a negative moment.
In a three-dimensional problem, however, a body can rotate about an axis in any direction. If this is the case, we need a vector to represent the direction of the moment. The direction of the moment vector will line up with the axis of rotation that moment would cause, but to determine which of the two directions we can use along that axis we have available we use the right hand rule. To use the right hand rule, align your right hand as shown in Figure \(\PageIndex{2}\) so that your thumb lines up with the axis of rotation for the moment and your curled fingers point in the direction of rotation for your moment. If you do this, your thumb will be pointing in the direction of the moment vector.
If we look back to two-dimensional problems, all rotations occur about an axis pointing directly into or out of the page (the \(z\)-axis). Using the right hand rule, counterclockwise rotations are represented by a vector in the positive \(z\) direction and clockwise rotations are represented by a vector in the negative \(z\) direction.
Axis of Rotation:
In engineering statics problems we can choose any point/axis as the axis of rotation. However, the choice of this point will affect the magnitude and direction of the resulting moment, and the moment is only valid about that point.
Though we can take the moment about any point in a statics problem, if we are adding together the moments from multiple forces, all the moments must be taken about a common axis of rotation . Moments taken about different points cannot be added together to find a "net moment."
Additionally, if we move into the subject of dynamics, where bodies are moving, we will want to relate moments to angular accelerations. For this to work, either we will need to take the moments about a single point that does not move (such as the hinge on a door) or we will need to take the moments about the center of mass of the body. Summing moments about other axes of rotation will not result in valid calculations.
Calculating Moments:
To calculate the moment that a force exerts on a body, we will have two main options: scalar methods and vector methods . Scalar methods are generally faster for two-dimensional problems where a body can only rotate clockwise or counterclockwise, while vector methods are generally faster for three-dimensional problems where the axis of rotation is more complex.


1.3: Defining Communication
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Learning Objectives
By the end of this section, you will be able to:
- Define the term “communication” and explain the primary types of communication.
- Define the term “communication competence” and explain attributes of communication competence.
- Identify differences between linear and transactional communication models.
- Identify the components of interpersonal communication.
Now that you know how to define communication study, are you able to develop a simple definition of communication? Try to write a one-sentence definition of communication!
We’re guessing it’s more difficult than you think. Don’t be discouraged. For decades communication professionals have had difficulty coming to any consensus about how to define the term communication (Hovland; Morris; Nilsen; Sapir; Schramm; Stevens). Even today, there is no single agreed-upon definition of communication. In 1970 and 1984 Frank Dance looked at 126 published definitions of communication in our literature and said that the task of trying to develop a single definition of communication that everyone likes is like trying to nail jello to a wall.
Communication Study Then
Aristotle The Communication Researcher
Aristotle said, “Rhetoric falls into three divisions, determined by the three classes of listeners to speeches. For of the three elements in speech-making — speaker, subject, and person addressed — it is the last one, the hearer, that determines the speech’s end and object.”
For Aristotle it was the “to whom” that determined if communication occurred and how effective it was. Aristotle, in his study of “who says what, through what channels, to whom, and what will be the results” focused on persuasion and its effect on the audience. Aristotle thought is was extremely important to focus on the audience in communication exchanges.
What is interesting is that when we think of communication we are often, “more concerned about ourselves as the communication’s source, about our message, and even the channel we are going to use. Too often, the listener, viewer, reader fails to get any consideration at all (Lee).
Aristotle’s statement above demonstrates that humans who have been studying communication have had solid ideas about how to communicate effectively for a very long time. Even though people have been formally studying communication for a long time, it is still necessary to continue studying communication in order to improve it.
Lee, Dick. Developing Effective Communications. University of Missouri Extension. 31 March 2008. Web. Dec. 2014.
We recognize that there are countless good definitions of communication, but we feel it’s important to provide you with our definition so that you understand how we approach each chapter in this book. We are not arguing that this definition of communication is the only one you should consider viable, but you will understand the content of this text better if you understand how we have come to define communication. For the purpose of this text we define communication as the process of using symbols to exchange meaning .
Let’s examine two models of communication to help you further grasp this definition. Shannon and Weaver proposed a Mathematical Model of Communication (often called the Linear Model) that serves as a basic model of communication. This model suggests that communication is simply the transmission of a message from one source to another. Watching YouTube videos serves as an example of this. You act as the receiver when you watch videos, receiving messages from the source (the YouTube video). To better understand this, let’s break down each part of this model.
The Linear Model of Communication is a model that suggests communication moves only in one direction. The Sender encodes a Message , then uses a certain Channel (verbal/nonverbal communication) to send it to a Receiver who decodes (interprets) the message. Noise is anything that interferes with, or changes, the original encoded message.
• A sender is someone who encodes and sends a message to a receiver through a particular channel . The sender is the initiator of communication. For example, when you text a friend, ask a teacher a question, or wave to someone you are the sender of a message.
• A receiver is the recipient of a message . Receivers must decode (interpret) messages in ways that are meaningful for them. For example, if you see your friend make eye contact, smile, wave, and say “hello” as you pass, you are receiving a message intended for you. When this happens you must decode the verbal and nonverbal communication in ways that are meaningful to you.
• A message is the particular meaning or content the sender wishes the receiver to understand . The message can be intentional or unintentional, written or spoken, verbal or nonverbal, or any combination of these. For example, as you walk across campus you may see a friend walking toward you. When you make eye contact, wave, smile, and say “hello,” you are offering a message that is intentional, spoken, verbal and nonverbal.
• A channel is the method a sender uses to send a message to a receiver . The most common channels humans use are verbal and nonverbal communication which we will discuss in detail in Chapters 2 and 3. Verbal communication relies on language and includes speaking, writing, and sign language. Nonverbal communication includes gestures, facial expressions, paralanguage, and touch. We also use communication channels that are mediated (such as television or the computer) which may utilize both verbal and nonverbal communication. Using the greeting example above, the channels of communication include both verbal and nonverbal communication.
• Noise is anything that interferes with the sending or receiving of a message . Noise is external (a jack hammer outside your apartment window or loud music in a nightclub), and internal (physical pain, psychological stress, or nervousness about an upcoming test). External and internal noise make encoding and decoding messages more difficult. Using our ongoing example, if you are on your way to lunch and listening to music on your phone when your friend greets you, you may not hear your friend say “hello,” and you may not wish to chat because you are hungry. In this case, both internal and external noise influenced the communication exchange. Noise is in every communication context, and therefore, NO message is received exactly as it is transmitted by a sender because noise distorts it in one way or another.
A major criticism of the Linear Model of Communication is that it suggests communication only occurs in one direction. It also does not show how context, or our personal experiences, impact communication. Television serves as a good example of the linear model. Have you ever talked back to your television while you were watching it? Maybe you were watching a sporting event or a dramatic show and you talked at the people in the television. Did they respond to you? We’re sure they did not. Television works in one direction. No matter how much you talk to the television it will not respond to you. Now apply this idea to the communication in your relationships. It seems ridiculous to think that this is how we would communicate with each other on a regular basis. This example shows the limits of the linear model for understanding communication, particularly human to human communication.
Given the limitations of the Linear Model, Barnlund adapted the model to more fully represent what occurs in most human communication exchanges. The Transactional Model demonstrates that communication participants act as senders AND receivers simultaneously, creating reality through their interactions. Communication is not a simple one-way transmission of a message: The personal filters and experiences of the participants impact each communication exchange. The Transactional Model demonstrates that we are simultaneously senders and receivers, and that noise and personal filters always influence the outcomes of every communication exchange.
The Transactional Model of Communication adds to the Linear Model by suggesting that both parties in a communication exchange act as both sender and receiver simultaneously, encoding and decoding messages to and from each other at the same time .
While these models are overly simplistic representations of communication, they illustrate some of the complexities of defining and studying communication. Going back to Smith, Lasswell, and Casey, as Communication scholars we may choose to focus on one, all, or a combination of the following: senders of communication, receivers of communication, channels of communication, messages, noise, context, and/or the outcome of communication. We hope you recognize that studying communication is simultaneously detail-oriented (looking at small parts of human communication), and far-reaching (examining a broad range of communication exchanges).
Contributions and Affiliations
- Survey of Communication Study. Authored by : Scott T Paynton and Linda K Hahn. Provided by : Humboldt State University. Located at : https://en.wikibooks.org/wiki/Survey_of_Communication_Study . License : CC BY-SA: Attribution-ShareAlike
- Image of linear model of communication. Authored by : Andy Schmitz. Located at : commons.wikimedia.org/wiki/File:Linearmodel.jpg. License : CC BY-SA: Attribution-ShareAlike
- Image of transactional model of communication. Authored by : Andy Schmitz. Located at : commons.wikimedia.org/wiki/File:Transactionalmodel.jpg. License : CC BY-SA: Attribution-ShareAlike
- Image of Aristotle. Authored by : Jastrow. Located at : commons.wikimedia.org/wiki/File:Aristotle_Altemps_Inv8575.jpg. License : Public Domain: No Known Copyright