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| '''Sum frequency generation spectroscopy''' ('''SFG''') is a technique used to analyze surfaces and interfaces. This nonlinear laser spectroscopy method was developed in 1987 and rapidly applied to deduce the composition, orientation distributions, and some structural information of molecules at gas–solid, gas–liquid and liquid–solid interfaces. In a typical SFG setup, two laser beams mix at a surface and generate an output beam with a frequency equal to the sum of the two input frequencies. SFG has advantages in its ability to be monolayer surface sensitive, ability to be performed in situ (for example aqueous surfaces and in gases), and not causing much damage to the sample surface. SFG is comparable to [[second harmonic generation]] (SFG is a more general form) and [[Infrared spectroscopy|Infrared]] and [[Raman spectroscopy]].<ref name="shen"> Shen, Y.R.;"Surface properties probed by 2nd harmonic and sum frequency generation". ''Nature'', v 337, 1989, p 519-525.</ref>
| | Surely the second option would be more beneficial for any website. The next step is to visit your Word - Press blog dashboard. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. Word - Press also provides protection against spamming, as security is a measure issue. All this is very simple, and the best thing is that it is totally free, and you don't need a domain name or web hosting. <br><br>You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. If you loved this article and you would like to get much more details pertaining to [http://scridle.nl/wordpress_dropbox_backup_345579 wordpress backup] kindly go to our website. If a newbie missed a certain part of the video then they could always rewind. This plugin is a must have for anyone who is serious about using Word - Press. You can add new functionalities and edit the existing ones to suit your changing business needs. For a Wordpress website, you don't need a powerful web hosting account to host your site. <br><br>It is very easy to install Word - Press blog or website. But if you are not willing to choose cost to the detriment of quality, originality and higher returns, then go for a self-hosted wordpress blog and increase the presence of your business in this new digital age. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine. You or your web designer can customize it as per your specific needs. Socrates: (link to ) Originally developed for affiliate marketers, I've used this theme again and again to develop full-fledged web sites that include static pages, squeeze pages, and a blog. <br><br>Numerous bloggers are utilizing Word - Press and with good reason. php file in the Word - Press root folder and look for this line (line 73 in our example):. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. If you just want to share some picture and want to use it as a dairy, that you want to share with your friends and family members, then blogger would be an excellent choice. Word - Press offers constant updated services and products, that too, absolutely free of cost. <br><br>This advice is critical because you don't want to waste too expensive time establishing your Word - Press blog the exact method. By using Word - Press MLM websites or blogs, an online presence for you and your MLM company can be created swiftly and simply. Word - Press can also be quickly extended however improvement API is not as potent as Joomla's. Web developers and newbies alike will have the ability to extend your web site and fit other incredible functions with out having to spend more. Press CTRL and the numbers one to six to choose your option. |
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| == Theory ==
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| IR-visible sum frequency generation spectroscopy uses two laser beams that overlap at a surface of a material or the interface between two materials. An output beam is generated at a frequency of the sum of the two input beams. The two input beams have to be able to access the surface, and the output beam needs to be able to leave the surface to be picked up by a detector.<ref name="rangwalla">Rangwalla, H.; Dhinojwala, A; (2004) "Probing Hidden Polymeric Interfaces Using IR-Visible Sum-Frequency Generation Spectroscopy". ''The Journal of Adhesion'', v80, Issue 1 & 2, p 37 - 59, {{doi|10.1080/00218460490276768}}</ref> One of the beams is a visible wavelength laser held at a constant frequency and the other is a tunable infrared laser. By tuning the IR laser, the system can scan over resonances and obtain the vibrational spectrum of the interfacial region.<ref name="shen" />
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| As a nonlinear optical process, the polarization which generates the output depends on the electric fields of the two input beams.
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| :<math>P = \epsilon_0(\chi^{(1)}:E + \chi^{(2)}:EE + \chi^{(3)}:EEE + \dots)</math>
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| As a second-order nonlinear process, SFG is dependent on the 2nd order susceptibility χ<sup>(2)</sup>. The fact that the 2nd order susceptibility, a third rank tensor, becomes zero in [[centrosymmetric]] media, limits what samples are accessible for SFG. Centrosymmetric media include the bulk of gases, liquids, and most solids under the assumption of the electric-dipole approximation, which neglects the signal generated by multipoles and magnetic moments.<ref name="rangwalla" /> At an interface between two different materials or two centrosymmetric media, the inversion symmetry is broken and an SFG signal can be generated. This suggests that the resulting spectra represent a thin layer of molecules. A signal is found when there is a net polar orientation.<ref name="rangwalla" /><ref name="schultz">Schultz, D.S.; (2005), ''Interrogating the Electrochemical Interface Using Sum Frequency Generation Spectroscopy".</ref>
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| === SFG intensity ===
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| The output beam is collected by a detector and its intensity is measured. The intensity of the beam is given by
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| :<math>I(\omega)\propto|\chi^{(2)}|^2I_1(\omega_1)I_2(\omega_2)</math>
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| Here, intensity is directly proportional to the susceptibility squared and the product of the intensities of the incoming beams.<ref name="chen"> Chen, Z.; Shen, Y.R.; Samorjai, G.A.; (2002) "Studies of polymer surfaces by sum frequency generation vibrational spectroscopy". ''Annual Review of Physical Chemistry'', v 53, 2002, p 437-465.</ref><ref name="rangwalla" /> The IR frequency is given as ω<sub>2</sub> and the visible frequency is given as ω<sub>1</sub>. The constant of proportionality varies across literature, many of them including the product of the square of the output frequency, ω<sup>2</sup> and the squared secant of the reflection angle, sec<sup>2</sup>β. Other factors include index of refractions for the three beams.<ref name="shen" />
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| The second order susceptibility has two contributions
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| :<math>\chi {{=}} \chi_{nr} + \chi_r</math>
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| where χ<sub>nr</sub> is the non-resonating contribution and χ<sub>r</sub> is the resonating contribution. The non-resonating contribution is assumed to be from electronic responses. Although this contribution has often been considered to be constant over the spectrum, because it is generated simultaneously with the resonant response, the two responses must compete for intensity. This competition shapes the nonresonant contribution in the presence of resonant features by resonant attenuation.<ref>{{cite journal|last=Curtis|first=Alexander D.|coauthors=Burt, Scott R., Calchera, Angela R., Patterson, James E.|title=Limitations in the Analysis of Vibrational Sum-Frequency Spectra Arising from the Nonresonant Contribution|journal=The Journal of Physical Chemistry C|date=19 May 2011|pages=110519094237033|doi=10.1021/jp200915z}}</ref> Because it is not currently known how to adequately correct for nonresonant interferences, it is very important to experimentally isolate the resonant contributions from any nonresonant interference, often done using the technique of nonresonant suppression.<ref>{{cite journal|last=Lagutchev|first=A.|coauthors=Hambir, S.A., Dlott, D.D.|title=Nonresonant Background Suppression in Broadband Vibrational Sum-Frequency Generation Spectroscopy|journal=Journal of Physical Chemistry C|date=20 September 2007|volume=111|issue=37|pages=13645–13647|doi=10.1021/jp075391j}}</ref>
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| The resonating contribution is from the vibrational modes and shows changes in resonance. It can be expressed as a sum of a series of Lorentz oscillators
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| :<math>\sum_q \frac{A_q}{\omega_2-\omega_q+i\Gamma_q}</math> | |
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| where A is the strength or amplitude, ω is the frequency or energy, Γ is the damping or linewidth coefficient, and each q is a resonance mode. The amplitude is a product of μ, the induced dipole moment, and α, the polarizability.<ref name="rangwalla" /><ref name="schultz" /> Together, this indicates that the transition must be both IR and Raman active.<ref name="shen" />
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| The above equations can be combined to form
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| :<math>\chi = \chi_{nr}e^{i\phi} + \sum_q \frac{A_q}{\omega_2-\omega_q+i\Gamma_q}</math>
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| which used to model the SFG output over a range of wavenumbers. When the SFG system scans over a vibrational mode of the surface molecule, the output intensity is resonantly enhanced.<ref name="shen" /><ref name="schultz" /> In a graphical analysis of the output intensity versus wave number, this is represented by peaks. Depending on the system, inhomogeneous broadening and interference between peaks may occur. The Lorentz profile can be convoluted with a Gaussian intensity distribution to better fit the intensity distribution. <ref name="richmond">Richmond, G.L.; (2002) "Molecular Bonding and Interactions at Aqueous Surfaces as Probed by Vibrational Sum Frequency Spectroscopy", ''Chemical Reviews'', v102, n8, August, 2002, p 2693-2724.</ref>
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| === Orientation information ===
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| From the second order susceptibility, it is possible to ascertain information about the orientation of molecules at the surface. χ<sup>(2)</sup> describes how the molecules at the interface respond to the input beam. A change in the net orientation of the polar molecules results in a change of sign of χ<sup>(2)</sup>. As a rank 3 tensor, the individual elements provide information about the orientation. For a surface that has azimuthal symmetry, only four of the twenty seven tensor elements are nonzero:
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| :<big>χ<sub>zzz</sub>, χ<sub>xxz</sub> = χ<sub>yyz</sub>, χ<sub>xzx</sub> = χ<sub>yzy</sub>, and χ<sub>zxx</sub> = χ<sub>zyy</sub></big>.
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| The tensor elements can be determined by using two different polarizers, one for the electric field vector perpendicular to the plane of incidence, labeled S, and one for the electric field vector parallel to the plane of incidence, labeled P. Four combinations are sufficient: PPP, SSP, SPS, PSS, with the letters listed in decreasing frequency, so the first is for the sum frequency, the second is for the visible beam, and the last is for the infrared beam. The four combinations give rise to four different intensities:
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| :<math>I_{PPP}=|f'_zf_zf_z\chi_{zzz}^{(2)}+f'_zf_if_i\chi_{zii}^{(2)}+f'_if_zf_i\chi_{zii}^{(2)}+f'_if_if_z\chi_{iiz}^{(2)}|^2</math>
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| :<math>I_{SSP}=|f'_if_if_z\chi_{iiz}^{(2)}|^2</math>
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| :<math>I_{SPS}=|f'_if_zf_i\chi_{zii}^{(2)}|^2</math>
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| :<math>I_{PSS}=|f'_zf_if_i\chi_{zii}^{(2)}|^2</math>
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| where indice i is of the interfacial xy-plane, and f and f’ are the linear and nonlinear Fresnel factors.
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| By taking the tensor elements and applying the correct transformations, the orientation of the molecules on the surface can be found.<ref name="shen" /><ref name="schultz" /><ref name="richmond" />
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| == Experimental setup ==
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| Since SFG is a higher order function, one of the main concerns in the experimental setup is being able to generate a signal strong enough to detect, with discernible peaks and narrow bandwidths. Pico-second and femto-second pulse width lasers are used due to being pulsed lasers with high peak fields. [[Nd:YAG|Nd:YAG lasers]] are commonly used. However, the bandwidth is increased with shorter pulses, forming a tradeoff for desired properties.
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| Another limitation is the tunable range of the IR laser. This has been augmented by optical parametric generation (OPG), [[Optical parametric oscillator|optical parametric oscillation]] (OPO), and [[Optical parametric amplifier|optical parametric amplification]] (OPA) systems.<ref name="richmond" />
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| Signal strength can be improved by using special geometries, such as a [[total internal reflection]] setup which uses a prism to change the angles so they are close to the critical angles, allowing the SFG signal to be generated at its critical angle, enhancing the signal. <ref name="richmond" />
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| Common detector setups utilize a [[monochromator]] and a [[photomultiplier]] for filtering and detecting.<ref name="rangwalla" />
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| == References ==
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| {{reflist}}
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| [[Category:Spectroscopy]]
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