differential refractometer

The refractive index increment,$\backslash frac\{dn\}\{dC\}$, often expressed as mL/g,{{Cite web |title=Differential Index of Refraction, dn/dc |url=https://www.appliedpolymertechnology.org/uploads/1/0/8/8/108867241/dndc.pdf}} is the change in a solutions' refractive index vs concentration. A differential refractometer facilitates determining this term.{{Cite book |url=https://link.springer.com/book/10.1007/978-3-540-71951-9 |title=Light Scattering from Polymer Solutions and Nanoparticle Dispersions |series=Springer Laboratory |date=2007 |language=en |doi=10.1007/978-3-540-71951-9|isbn=978-3-540-71950-2 }} Typical light sources include Helium–neon laser, Argon-ion laser, and Sodium-vapor lamp.{{Cite web |title=Waters 2410 Differential Refractometer Operator's Guide |url=http://www.marshallscientific.com/v/vspfiles/files/manuals/2410%20waters%20hplc.pdf}} There are two compartments or flow cells, one for the sample and the other for the reference solution.{{Cite web |title=Differential Index of Refraction, dn/dc |url=https://www.appliedpolymertechnology.org/uploads/1/0/8/8/108867241/dndc.pdf}}

The optical wedge or prism sits after the cells and separates the light coming from the flow cells. The difference in refractive index causes the light paths to reflect at different angles.{{Cite web |last=Barron |first=John |title=Refractive Index (RI) and Brix Standards – Theory and Application |url=https://knowledge.reagecon.com/wp-content/uploads/2021/03/Refractive-Index-and-Brix-Standards-Paper.pdf}}{{Cite journal |last=Kőrösy |first=F. |date=August 1954 |title=A Modified Differential Refractometer |url=https://www.nature.com/articles/174269b0 |journal=Nature |language=en |volume=174 |issue=4423 |pages=269 |doi=10.1038/174269b0 |issn=1476-4687}} This difference is magnified by the optical wedge/prism.{{Citation |last1=de Angelis |first1=M. |title=Optical Instruments |date=2005-01-01 |encyclopedia=Encyclopedia of Condensed Matter Physics |pages=159–175 |editor-last=Bassani |editor-first=Franco |url=https://linkinghub.elsevier.com/retrieve/pii/B0123694019004927 |access-date=2024-11-18 |place=Oxford |publisher=Elsevier |doi=10.1016/b0-12-369401-9/00492-7 |isbn=978-0-12-369401-0 |last2=Tino |first2=G. M. |editor2-last=Liedl |editor2-first=Gerald L. |editor3-last=Wyder |editor3-first=Peter}}

A detector that can measure of range of wavelengths, usually a Photodiode array, measures the position of the two light paths. The detector quantifies the angle of refraction, which is proportional to the refractive index.

There exist various brands of differential refractometers. Popular models include:

• Waters 2414 Refractive Index Detector {{Cite web |title=2414 Refractive Index (RI) Detector |url=https://www.waters.com/nextgen/ca/en/products/chromatography/chromatography-detectors/2414-refractive-index-ri-detector.html |access-date=November 4, 2024 |website=Waters}}
• Agilent 1290 Infinity II Refractive Index Detector{{Cite web |title=1260 Infinity II Refractive Index Detector |url=https://www.agilent.com/en/product/liquid-chromatography/hplc-components-accessories/hplc-detectors/1260-refractive-index-detector |access-date=November 4, 2024 |website=Agilent}}
• Thermo Scientific RefractoMax521 Refractive Index Detector{{Cite web |title=RefractoMax 521 Refractive Index Detector |url=https://www.thermofisher.com/order/catalog/product/5060.0050 |access-date=November 4, 2024 |website=ThermoFisher Scientific}}

All refractive index detectors require calibration upon first setting up the instrument as well as periodic quality control. Most manufacturer's recommend calibration with pure water and a sucrose calibration solution of a known refractive index.{{Cite journal |last1=Klongratog |first1=B. |last2=Suesut |first2=T. |last3=Nunak |first3=N. |date=2013 |title=The Uncertainty in Sugar Solution Concentration Measurement Based on Density Approach |url=https://www.scientific.net/AMR.811.358 |journal=Advanced Materials Research |language=en |volume=811 |pages=358–364 |doi=10.4028/www.scientific.net/AMR.811.358 |issn=1662-8985}} Once the instrument is in calibration mode, the pure water acts as a zero baseline reading, while the sucrose solution compares its known RI to the output, and the machine is adjusted accordingly.{{Cite journal |last1=Charles |first1=D. F. |last2=Meads |first2=P. F. |date=1955-03-01 |title=Measurement of Refractometric Dry Substance of Sucrose Solutions |url=https://pubs.acs.org/doi/abs/10.1021/ac60099a013 |journal=Analytical Chemistry |language=en |volume=27 |issue=3 |pages=373–379 |doi=10.1021/ac60099a013 |issn=0003-2700}}

After the pump has not been used for a while, it is necessary to purge the tubes of any contaminant air that has diffused into the channels. This is typically accomplished with isopropyl alcohol.

Differential refractometers are often used for the analysis of polymer samples in size exclusion chromatography. Other types of information that can be gathered from differential refractometers are:

Since the molecular weight (or extent of polymerization) of a solute will correspond to a specific refractive index increment, the relationship between increasing solute weight and refractive index increment can be plotted to determine the exact molecular weight of an unknown solute.{{Cite journal |last1=Han |first1=Ying |last2=Li |first2=Dejie |last3=Li |first3=Deqiang |last4=Chen |first4=Wenwen |last5=Mu |first5=Shu’e |last6=Chen |first6=Yuqin |last7=Chai |first7=Jinling |date=2020-02-05 |title=Impact of refractive index increment on the determination of molecular weight of hyaluronic acid by muti-angle laser light-scattering technique |journal=Scientific Reports |language=en |volume=10 |issue=1 |pages=1858 |doi=10.1038/s41598-020-58992-7 |issn=2045-2322 |pmc=7002679 |pmid=32024914}}

Increasing addition of solute will alter the solvent's viscosity and polarizability, which cannot be measured by instruments that rely on low viscosity. Since differential refractometer is an external tool,{{Cite web |title=Differential Index of Refraction, dn/dc |url=https://www.appliedpolymertechnology.org/uploads/1/0/8/8/108867241/dndc.pdf}}{{Cite web |title=Waters 2410 Differential Refractometer Operator's Guide |url=http://www.marshallscientific.com/v/vspfiles/files/manuals/2410%20waters%20hplc.pdf}} the solvent viscosity does not pose a physical barrier to measurement, making them universal detectors.{{Cite web |title=Refractive Index Detection (RID) |url=https://www.shimadzu.com/an/service-support/technical-support/analysis-basics/basic/refractive_index_detection.html |access-date=2024-11-18 |website=www.shimadzu.com |language=en}}

The shape of a solute will influence its induced dipole.{{Cite web |title=Induced Dipole Forces |url=https://www.chem.purdue.edu/gchelp/liquids/inddip.html |access-date=2024-11-18 |website=www.chem.purdue.edu}} This will affect the solvent polarizability, which affects the refractive index.{{Cite journal |last1=Pachucki |first1=Krzysztof |last2=Puchalski |first2=Mariusz |date=2019-04-30 |title=Refractive index and generalized polarizability |url=https://link.aps.org/doi/10.1103/PhysRevA.99.041803 |journal=Physical Review A |language=en |volume=99 |issue=4 |page=041803 |doi=10.1103/PhysRevA.99.041803 |arxiv=1902.05725 |issn=2469-9926}}

There are many practical factors that can affect the accuracy of a differential refractometer.

When solutes are added to a solvent, they change the solution's optical density. The size,{{Cite journal |last1=Zhao |first1=Huaying |last2=Brown |first2=Patrick H. |last3=Schuck |first3=Peter |date=May 2011 |title=On the Distribution of Protein Refractive Index Increments |journal=Biophysical Journal |volume=100 |issue=9 |pages=2309–2317 |doi=10.1016/j.bpj.2011.03.004 |issn=0006-3495 |pmc=3149238 |pmid=21539801}} polarizability and shape and molecular structure of a solute all have effects on the refractive index of a solution. Generally, a Gaussian distribution is observed, although deviations occur.

A controlled temperature is needed to ensure accurate measurements, as temperature affects many properties of a solution.{{Citation |last1=Lu |first1=Jue Xi |title=Biochemistry, Dissolution and Solubility |date=2024 |work=StatPearls |url=https://www.ncbi.nlm.nih.gov/books/NBK431100/ |access-date=2024-11-18 |place=Treasure Island (FL) |publisher=StatPearls Publishing |pmid=28613752 |last2=Tupper |first2=Connor |last3=Gutierrez |first3=Alejandra V. |last4=Murray |first4=John}} If the temperature changes between measurements, this variance will be reflected in the measured refractive index.{{Cite web |last=Held |first=Daniela |date=December 5, 2017 |title=Tips & Tricks GPC/SEC: How to Treat Your RI Detector |url=https://www.chromatographyonline.com/view/tips-tricks-gpcsec-how-treat-your-ri-detector-0}}

Cauchy's equation and Sellmeier equation describe the effect of wavelength on refractive index of medium.

The use of and results from differential refractometers are valuable in numerous fields of science, with its theory and function applied in various research directions, including drug analysis{{Cite journal |last1=Al-Sanea |first1=Mohammad M. |last2=Gamal |first2=Mohammed |date=2022-07-01 |title=Critical analytical review: Rare and recent applications of refractive index detector in HPLC chromatographic drug analysis |url=https://www.sciencedirect.com/science/article/abs/pii/S0026265X22001679 |journal=Microchemical Journal |volume=178 |pages=107339 |doi=10.1016/j.microc.2022.107339 |issn=0026-265X}} and nanoparticle tracking.{{Cite journal |last1=van der Pol |first1=Edwin |last2=Coumans |first2=Frank A. W. |last3=Sturk |first3=Auguste |last4=Nieuwland |first4=Rienk |last5=van Leeuwen |first5=Ton G. |date=2014-11-12 |title=Refractive Index Determination of Nanoparticles in Suspension Using Nanoparticle Tracking Analysis |url=https://pubs.acs.org/doi/10.1021/nl503371p |journal=Nano Letters |language=en |volume=14 |issue=11 |pages=6195–6201 |doi=10.1021/nl503371p |pmid=25256919 |issn=1530-6984}}

The nature of refractive indexes allows RIDs to be used in conjunction with additional analytical chemistry instruments. Following the use of other machines, differential refractometers can immediately (further) characterize compounds eluting from chromatographers, spectrometers, and detectors, including:

• High Performance Liquid Chromatography (HPLC){{Citation |last1=Bruno |first1=Alfredo E. |title=Chapter 11 On-Column Refractive Index Detection of Carbohydrates Separated by HPLC and CE |date=1995-01-01 |work=Journal of Chromatography Library |volume=58 |pages=431–446 |editor-last=El Rassi |editor-first=Ziad |url=https://www.sciencedirect.com/science/article/abs/pii/S0301477008605163 |access-date=2024-11-08 |series=Carbohydrate Analysis |publisher=Elsevier |last2=Krattiger |first2=Beat|doi=10.1016/S0301-4770(08)60516-3 |isbn=978-0-444-89981-1 }}{{Citation |last=LaCourse |first=William R. |title=HPLC Instrumentation |date=2017-01-01 |work=Reference Module in Chemistry, Molecular Sciences and Chemical Engineering |url=https://www.sciencedirect.com/science/article/abs/pii/B9780124095472111230 |access-date=2024-11-08 |publisher=Elsevier |isbn=978-0-12-409547-2}}
• Ultraviolet-Visible Spectroscopy{{Cite journal |last1=Antony |first1=Airin |last2=Mitra |first2=J. |date=2021-03-08 |title=Refractive index-assisted UV/Vis spectrophotometry to overcome spectral interference by impurities |url=https://www.sciencedirect.com/science/article/abs/pii/S0003267020312691 |journal=Analytica Chimica Acta |volume=1149 |pages=238186 |doi=10.1016/j.aca.2020.12.061 |pmid=33551061 |issn=0003-2670}}
• Mass Spectrometry{{Cite journal |last1=Endo |first1=Yasushi |last2=Tagiri-Endo |first2=Misako |last3=Seo |first3=Hwan-Sook |last4=Fujimoto |first4=Kenshiro |date=2001-03-09 |title=Identification and quantification of molecular species of diacyl glyceryl ether by reversed-phase high-performance liquid chromatography with refractive index detection and mass spectrometry |url=https://www.sciencedirect.com/science/article/abs/pii/S0021967300012401 |journal=Journal of Chromatography A |volume=911 |issue=1 |pages=39–45 |doi=10.1016/S0021-9673(00)01240-1 |pmid=11269594 |issn=0021-9673}}
• Evaporative Light Scattering Detection (ELSD){{Cite journal |last1=Clement |first1=A. |last2=Yong |first2=D. |last3=Brechet |first3=C. |date=April 1992 |title=Simultaneous Identification of Sugars by HPLC Using Evaporative Light Scattering Detection (ELSD) and Refractive Index Detection (RI). Application to Plant Tissues |url=http://www.tandfonline.com/doi/abs/10.1080/10826079208018836 |journal=Journal of Liquid Chromatography |language=en |volume=15 |issue=5 |pages=805–817 |doi=10.1080/10826079208018836 |issn=0148-3919}}

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Category:Measuring instruments