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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>
| | It involves expertise and knowledge of various tools and technologies used for creating websites. It is thus, on these grounds that compel various web service provider companies to integrate the same in their packages too. Should you go with simple HTML or use a platform like Wordpress. Keep reading for some great Word - Press ideas you can start using today. You can easily customize the titles of the posts in Word - Press blog in a way that only title comes in the new post link and not the date or category of posts. <br><br>As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. The higher your blog ranks on search engines, the more likely people will find your online marketing site. You are able to set them within your theme options and so they aid the search engine to get a suitable title and description for the pages that get indexed by Google. These four plugins will make this effort easier and the sites run effectively as well as make other widgets added to a site easier to configure. Many times the camera is following Mia, taking in her point of view in almost every frame. <br><br>Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source. Note: at a first glance WP Mobile Pro themes do not appear to be glamorous or fancy. I've applied numerous Search engine optimization-ready Word - Press themes and I can say from knowledge that I consider the Genesis Search engine marketing panel one particular of the simplest to use. The first thing you need to do is to choose the right web hosting plan. Search engine optimization pleasant picture and solution links suggest you will have a much better adjust at gaining considerable natural site visitors. <br><br>You can add keywords but it is best to leave this alone. I have compiled a few tips on how you can start a food blog and hopefully the following information and tips can help you to get started on your food blogging creative journey. Some examples of its additional features include; code inserter (for use with adding Google Analytics, Adsense section targeting etc) Webmaster verification assistant, Link Mask Generator, Robots. It supports backup scheduling and allows you to either download the backup file or email it to you. Make sure you have the latest versions of all your plugins are updated. <br><br>In the event you cherished this information and also you would like to get more details regarding [http://GET7.pw/wordpress_backup_770878 wordpress backup] generously check out our web site. Under Settings —> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. 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. Verify whether your company has a team of developers or programmers having hands-on experience and knowledge about all Word - Press concepts. |
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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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As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. The higher your blog ranks on search engines, the more likely people will find your online marketing site. You are able to set them within your theme options and so they aid the search engine to get a suitable title and description for the pages that get indexed by Google. These four plugins will make this effort easier and the sites run effectively as well as make other widgets added to a site easier to configure. Many times the camera is following Mia, taking in her point of view in almost every frame.
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