Refractometer Detector Detects Concentration of Which of the Following Range

Refractometer Detector Detects Concentration of Which of the Following Range

Differential Refractometer

When a differential refractometer is used equally a detector, instrumental broadening of the GPC chromatogram is compensated to some extent by another result due to the tendency for specific refractive indexes of polymer solutions to decrease with decreasing molecular weight in the low-molecular-weight range.

From: The Elements of Polymer Scientific discipline & Technology (Third Edition) , 2013

Chemical Analysis

Due west.Grand. Cummings , I. Verhappen , in Instrumentation Reference Book (Fourth Edition) , 2010

Detectors

Commercially available detectors used in HPLC are fluorimetric, conductiometric, heat of absorption detector, Christiansen effect detector, moving wire detector, ultraviolet absorption detector, and the refractive index detector. The last ii are the most popular.

Ultraviolet detection requires a UV-absorbing sample and a non-UV-absorbing mobile phase. Temperature regulation is not commonly required.

Differential refractometers are available for HPLC, merely refractive index measurements are temperature sensitive, and good temperature control is essential if high sensitivity is required. The main advantage of the refractive index detector is wide applicability.

HPLC has been applied successfully to analysis of petroleum and oil products, steroids, pesticides, analgesics, alkaloids, inorganic substances, nucleotides, flavors, pharmaceuticals, and environmental pollutants.

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Practical Aspects of Molecular Weight Measurements

Alfred Rudin , Phillip Choi , in The Elements of Polymer Science & Engineering (Third Edition) , 2013

three.4.iv Branched Polymers

Equation (3-66) links the intrinsic viscosity of a polymer sample to the radii of gyration r _g of its molecules while Eq. (iii-99) relates the hydrodynamic volume V of a solvated molecule to the production of its molecular weight and intrinsic viscosity. The separation process in GPC is on the footing of hydrodynamic volume, and the universal calibration described in Section three.four.3 is valid just if the relation between V and r _{one thousand} is the same for the calibration standards and the unknown samples.

Branched molecules of any polymer are more compact than linear molecules with the aforementioned molecular weight. They will have lower intrinsic viscosities (Department 3.3.seven) and smaller hydrodynamic volumes, in a given solvent, and will exit from the GPC columns at higher elution volumes. Universal calibration (preceding department) cannot be used to analyze polymers whose branching or limerick is not uniform through the whole sample. Generally useful techniques that apply to such materials, as well every bit to the linear homopolymers that are acquiescent to universal calibration, involve augmenting the concentration detector (which is ofttimes a differential refractometer, every bit mentioned) with detectors that measure the molecular weights to the polymers in the SEC eluant. These are continuous viscometers and light-scattering detectors. The former are used to measure the intrinsic viscosity of the eluting polymer at each GPC retentiveness fourth dimension. The universal calibration relation of Eq. (iii-94) or (iii-99) is equivalent to

(3-108) $\left[\eta \right]\mathrm{Thousand}={\left[\eta \right]}_{\mathrm{lin}}{M}_{\mathrm{lin}}$

where the unsubscripted values refer to the branched polymer and the subscript lin refers to its linear counterpart, which appears at the aforementioned elution book (or to the narrow distribution polystyrene or other polymer used as a standard for universal calibration). When [η] of each fraction is measured, the molecular weight of the branched polymer which elutes at any given retention volume is available from the relation of Eq. (three-108). This procedure is also applicable to copolymers, if the variable copolymer composition does non touch on the response of the concentration detector that is used along with the viscometer.

With a light-scattering photometer and a concentration detector such as a differential refractometer, the molecular weight distribution of the unknown polymer is obtained direct without demand for the universal scale process of the preceding section. This is by application of Eq. (three-53) to each successive "slice" of the GPC chromatogram. The virial coefficient terms in this equation are best gear up equal to zero, since their molecular weight dependence (Section three.i.4) is non known a priori. Various designs of light-scattering detectors are now bachelor, differing primarily in the number and magnitude of viewing angles used. Depression-angle low-cal scattering (using laser lite) eliminates the need for angular correction of the observed turbidity (Department 3.2.3), whereas photometers operating at right angles to the incident light axle are less sensitive to adventitious dust.

The iii SEC detector types in common apply at the time of writing—differential refractometer, continuous viscometer, and low-cal-handful photometer—differ in sensitivity. The differential refractometer betoken scales as the concentration, c, of the polymer solute. The viscometer signal is proportional to cM ^a (Section 3.three.ii), with the exponent a about equal to 0.7 for near polymer solutions used in this analysis. The light-scattering signal scales equally cM (Eq. 3-56). When all iii detectors are employed simultaneously, the light-handful device is most sensitive to big species and relatively insensitive to low-molecular-weight polymer, while the reverse selectivity applies to the differential refractometer. Electric current continuous viscometers are intermediate in performance and are the nearly more often than not useful detectors. The analytical technique should, even so, be tailored to the specific characteristics of the polymer of interest.

In a multidetector SEC apparatus, information technology is necessary to lucifer the output of the detector that senses eluant concentration with the signals of the detectors that sense molecular weight directly. To practise this, the annotator should match the unlike signals at equal hydrodynamic volumes in the different detectors [24].

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Footstep Polymerization

Dietrich Braun , Hans-Josef Ritzert , in Comprehensive Polymer Science and Supplements , 1989

36.5.i.i Gel permeation chromatography

Gel permeation chromatography (GPC) gives data on the composition and molecular weight distribution of UF- and MF-resins. ^99–105 Mostly DMF, DMSO or aqueous table salt solutions are used every bit eluents. The gel materials are crosslinked polystyrenes (Styragels), poly(vinyl acetate)s (Fractogel PVA OR) and saccharides (Sephadex). By and large, a differential refractometer (RI detector) is used as a detector. Effigy 3 shows a GPC of a typical UF-precondensate ¹⁰⁶ and Figure four that of an MF-resin. ¹⁰⁷

Figure iii. Typical GPC of a UF-precondensate as a office of reaction time: 1, urea; 2, mono(hydroxymethyl)urea; 3, di(hydroxymethyl)urea; 4, five, 6, dimers; 7, trimers; 8, tetramers; and 9, pentamers. Δn is difference in refractive alphabetize; 5 _e is elution volume (cts   =   counts, capricious units)

Effigy four. Typical GPC of a MF-precondensate: 1, mono-; ii, di-; 3, tri-; four, tetra-; 5, penta-; and half-dozen, hexa-(hydroxymethyl)melamine

In some cases it is useful to first prepare derivatives of the resins to eliminate the interactions of hydrogen bridge linkages. Silylation reactions are suitable for this. The hydroxymethyl groups and, in some cases, the NH groups tin can be substituted by several methods with trimethylsilyl groups; equation (11) shows the principle of this reaction. By this method it is also possible to separate the six different hydroxymethylmelamine compounds. ^108–111

(xi)

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The potential of natural composite materials in structural pattern

Ali Amiri , ... Chad Ulven , in Sustainable Composites for Aerospace Applications , 2018

13.three.i Characterization of double methacrylated epoxidized sucrose soyate resin

Label of MESS resin was presented in a previous report [43]. To characterize DMESS resin, Fourier Transform Infrared spectroscopy (FTIR) was performed with a Thermo Scientific Nicolet 8700 with a detector type of DTGS KBr nether nitrogen purge. Diluted sparse films of the samples were applied on a KBr plate, and the assimilation spectra were taken with 32 scans at a resolution of 4   cm^−one . The molecular weight of the resin was obtained using a gel permeation chromatography (GPC) organization (EcoSEC HLC-8320GPC, Tosoh Bioscience, Japan) with a differential refractometer (DRI) detector. Separations were performed using two TSKgel SuperH3000 6.00  mm ID×15   cm columns with an eluent flow rate of 0.35   mL/minutes. The columns and detectors were thermostated at 40°C. The eluent used was tetrahydrofuran (THF). Samples were prepared nominally at 1   mg/ml in an aliquot of the eluent, and immune to dissolve at ambient temperature for several hours; the injection book was xx   µL for each sample. Calibration was conducted using polystyrene standards (Agilent EasiVial PS-H 4   mL). Proton nuclear magnetic resonance spectroscopy (^oneH-NMR) was conducted with a Bruker arrangement, Arise 400   MHz magnet with an Avance III HD console (Bruker BioSpin Corporation, Billerica, Massachusetts, USA), using CDCl₃ equally the solvent. Acid number titration was carried out according to ASTM D664. The viscosity of the resins was measured at 25°C using an ARES Rheometer (TA Instruments) operating from 0.i   rad/seconds to 500   rad/seconds with 0.1% strain.

The synthesis of DMESS is presented in Fig. 13.3. The DMESS was catalyzed by ATC-3, which likewise suppresses the hydroxyl–epoxy side reactions. The inhibitor, hydroquinone, was used in gild to forbid premature polymerization. The last resin was fully characterized via acid number titration, ^oneH-NMR, FTIR, GPC, and rheometry. A publication documenting the synthesis and characterization of a set of DMESS resins is forthcoming.

Figure thirteen.three. Synthetic route to double methacrylated epoxidized sucrose soyate.

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Low-cal Scattering

C. Wu , B. Chu , in Experimental Methods in Polymer Science , 2000

ane.5.5 DIFFERENTIAL REFRACTOMETER

1 of the most important parameters in static LLS is the specific refractive index increment dn/dC, which is defined as lim _{C →0}(∂n/∂C)_T,P,λ. Because this parameter is not an intrinsic holding of the polymer, the weather of fixing temperature T, pressure level P, and wavelength of lite in vacuum λ are needed in its definition. Notation that, according to Eqs. (7) and (32), an error of E% in dn/dC volition lead to an error of 2 E% in the derived M _w.

The refractive index increase Δn of a polymer solution is unremarkably measured by using either a differential refractometer or an interferometer. In the former, the light beam is refracted at the boundary betwixt the sample and a reference liquid. Commonly, the beam displacement is direct measured and then converted to Δ n later multiplying a calibrated constant, which is normally obtained past using a solution with an accurately known refractive index difference Δn [81, 82]. This method is non an accented 1 because the constant has to be calibrated at the same conditions every bit in the light-scattering measurements. In these measurements, two light beams with identical geometrical paths traverse two unlike optical paths. I passes through the sample and the other through the reference liquid. This method relies on the interference of the two beams. Its details can be found elsewhere [83, 84]. In a high-temperature LLS measurement, the conventional divided differential refractometer cuvette had to be replaced by a plain-featured cylindrical light-handful cell in which the go out laser beam is refracted past the solution–air interface [66].

Figure 1.19a schematically shows a novel differential refractometer that was starting time designed by Wu et al. [85] and subsequently commercialized by ALV GmbH, Langen, Germany. A small pinhole (P) with a diameter of 400 μm is illuminated with a laser light. The illuminated pinhole is imaged to a position-sensitive detector (PD) (Hamamatsu Due south 3932) by a lens (L) located at an equal distance from the pinhole and the detector, where the altitude is 4 times the focal length (f = 100 mm) of the lens. Thus, this novel refractometer uses a (2f-2f) design instead of the conventional (1f) pattern, which uses parallel incident light beams and makes the distance between the detector and the lens equal to merely one focal length. A temperature-controlled refractometer cuvette (C) (Hellma 590.049-QS) is placed just in front of the lens. It is a flow prison cell and has a volume of ≈20 mL, which is divided past a glass plate at ≈45° into two compartments. The pinhole, the cuvette, the lens, and the detector are rigidly mounted on a pocket-size optical rail. The refractometer has dimensions of but twoscore cm in length, 15 cm in width, and 10 cm in height, and the length can hands be reduced to twenty cm with another lens if necessary. The output voltage (–10 to 10 volts) from the position-sensitive detector is proportional to the deportation of the light spot from the center of the detector and tin can exist measured by a digital voltmeter or an analog-to-digital data acquisition organisation and a personal figurer.

Effigy 1.nineteen. (a) Schematic view of a novel differential refractometer (commercialized past ALV GmbH, Langen, Deutschland), which consists of a pinhole (P), a differential refractometer cuvette (C), a lens (L, f = ten cm), and a position-sensitive detector (PD). All components are rigidly mounted on a 40-cm-long optical rail, (b) Lite path in which 1 compartment of the cuvette contains a solvent with refractive index n and the other contains a solution with slightly different refractive alphabetize n = due north ₀ + Δnorth. The cuvette and angles θ'', θ″ and θ″ (really very pocket-sized, ≈0.01 radian) are enlarged to make the lite path distinct.

Figure i.19b shows the basic principle and the light path of the refractometer, where θ' θ'', θ″' and the cuvette are drawn enlarged to make the details clearer. If both compartments are filled with a solvent (i.e., northward = n ₀), the illuminated pinhole volition exist imaged at point O. Notwithstanding, if the solvent in one of the compartments is replaced by a dilute polymer solution with a slightly different refractive index (i.east., n = n ₀ + Δn), the light will be bent showtime by the glass plate, then past the cuvette wall, and finally by the lens. The image is shifted away from the signal O past a distance of Y. Figure ane.19b shows that

(106) $Y=Y_1+Y_2+Y_{\mathrm{iii}}=c\text{tan}(\theta )+(\mathrm{ii}f-X-c)\text{tan}({\theta }^{\prime })+2f\text{tan}(\theta ″)$

and

(107) $f\text{tan}({\theta }^{\prime })=f\text{tan}(\theta ″)+c\text{tan}(\theta )+(2f-X-c)\text{tan}({\theta }^{\prime })$

where c, X, and θ are constants. Snell'southward police force gives

(108) $n_{0}sin(90-\mathrm{\theta })=(n_0+{\Delta }_n)sin(90°-\theta -\theta )$

and

(109) $({\mathrm{northward}}_0+{\Delta }_{\mathrm{northward}})\text{sin}(\theta )=\text{sin}({\theta }^{\prime })$

where θ, θ′ and θ″ are actually so pocket-sized considering An is on the gild of 10⁻⁴ refractive index units that nosotros may set sin(θ) = θ, sin(θ') = θ', tan(θ) = θ, tan(θ') = θ'. and tan(θ") = θ". Combining Eqs. (106-109) leads to

(110) $Y=k\Delta n$

where Yard = [X + c″(fifty − ane /n ₀)] tan(xc° – θ). For a given optical setup and solvent, X, c, θ, n ₀, and hence K are constants. Equation (110) shows that the signal is proportional to An, and the larger the value of X, the higher the sensitivity (Y/ Δn) is. This means that the cuvette should exist placed as close as possible to the lens in the experimental setup.

In the 2f-2f pattern, the detector and the pinhole (interim equally a light source) are placed at the exact imaging positions along the optical axis of the lens. This configuration is optically equivalent to placing the detector directly behind the pinhole so that the light amplification by stimulated emission of radiation beam drift is eliminated. In comparison with the conventional differential refractometer, this novel design has made the measurement of An much easier and provides reliable and accurate values for dn/dC because it is stable and the results tin can be recorded and averaged on a computer. Figure i.20 shows the concentration dependence of Δnorthward for a 13% PET–PCL copolymer in three different solvents. The lines represent the least-square fits to the data points.

Figure 1.20. Concentration dependence of the refractive index difference (Δn) between the polymer solution and solvent for a 13% PET-PCL copolymer. The lines represent the least-square fits to the measured data.

The refractometer with its nowadays dimensions can hands be installed into any existing laser lite-handful spectrometer together with the light amplification by stimulated emission of radiation source, the thermostat, and the estimator, as exemplified in Figure 1.21. The optical glass plate placed in the laser low-cal path at 45° reflects laser lite past about four%, and the reflected low-cal is used every bit the light source. With this blueprint, the calorie-free scattering and the refractive index increase can simultaneously be measured under identical experimental conditions of wavelength and temperature. The details of this novel spectrometer have been described elsewhere [85].

Figure 1.21. Possible arrangement of the novel differential refractometer with an existing laser calorie-free-handful spectrometer.

In summary, this chapter has shown that static and dynamic laser light scattering (LLS) combined provide a very powerful method for polymer characterization. LLS has advantages over other polymer characterization methods, which include ultracentrifugation and chromatography, in such features as speed, nonper-turbation, and farthermost dissolution conditions (loftier temperature or stiff acrid). The most important factor is that the calibration is contained of a particular LLS musical instrument used. Even so, the LLS method for the determination of mass distributions described in this affiliate has its limitations in that its resolution is not as high every bit the fractionation methods, particularly for samples whose mass distributions take closely packed peaks. The LLS method should play a useful part when polymers intractable by conventional characterization methods have to be treated. Finally, dynamic LLS tin can be used with other characterization methods that take reward of the dependence of the hydrodynamic book on molar mass.

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Polymer Label

Peter Thousand. Budd , in Comprehensive Polymer Scientific discipline and Supplements , 1989

eleven.iii.7.2 Polyelectrolyte with added salt

In general, addition of a salt leads to increasingly high elution volumes for polyelectrolytes, as charges are shielded and the polyion chain contracts. At moderate table salt concentrations elution occurs in order of decreasing size, as for a nonionic polymer. If too much salt is added, still, adsorption of the polyion on to the packing tin be pregnant, and there is then no longer a size-based separation. The salt concentration in the eluant thus has to be carefully optimized. Depending on the natures of the polymer and the packing, information technology may too be desirable to buffer the eluant at a particular pH or to add a surfactant to reduce adsorption. ⁹⁵

When a table salt is present in the eluant and a detector is used which responds to changes in common salt concentration, such as a differential refractometer, a 'Donnan' peak appears at loftier elution volumes due to salt excluded from the sample region. Provided that the polymer peak is separated from the Donnan peak, information technology is possible to determine the Donnan parameter Γ. ^{50, 51} Under the weather condition of an SEC experiment on a polyelectrolyte PX _Z in the presence of a table salt XY ⁵¹

(21)

where Q _ex is the number of moles of salt excluded and Q _u is the number of moles of equivalent units (per charge) of polyelectrolyte.

There take been a number of attempts to apply the 'universal calibration' concept to polyelectrolytes. For some systems it has been reported that, provided the common salt concentration is sufficiently high, polyelectrolytes and nonionic polymers obey the same relationship between [η]M and elution book; ^97–102 on decreasing the salt concentration, even so, in that location is generally an increasing deviation from the universal calibration plot. For other systems, failure of the universal scale concept at all table salt concentrations has been reported. ^{103, 104}

It is possible to avoid the demand for calibration altogether past employing a low-angle laser light-scattering detector, together with a concentration detector, to provide an accented molecular weight distribution, ¹⁰⁵ although there are some bug with this approach in exercise.

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Chain Polymerization II

Thomas C. Kendrick , ... James W. White , in Comprehensive Polymer Science and Supplements , 1989

25.5.3.1 Measurement of the Molecular Weights and Molecular Weight Distributions of Siloxane Copolymers

The molecular weight distribution (MWD) and the different molecular weights (Grand _n, M _westward, Grand _z) are nearly ofttimes determined by the size exclusion chromatography (SEC) technique (see Volume 1, Chapter 12) also known as gel permeation chromatography (GPC). ^98,99,100 For homopolysiloxanes, the concentration of the eluted polymer fraction is measured with a differential refractometer. This type of detector is suitable for linear or branched homopolymers. However, a calibration curve must be synthetic in gild to convert the elution volume into molecular weight and the chromatogram into the MWD. ⁹⁸ This is done with standard polymers, viz. monodisperse polystyrenes or poly(dimethylsiloxane)southward. The calibration procedure is very of import for accuracy in the determination of the MWD and there is still considerable effort in the literature to find improve scale methods. ^101–105 Universal calibration curves are based on the assumption that the solvodynamic volume is a function just of molecular size. Although this is true for homopolymers when concentration furnishings are absent, ^106–108 it is not necessarily valid for copolymers, since the solvodynamic volume and SEC retention volume may be a function of the polymer composition besides every bit of its molecular weight. In the case of copolymers, when the composition is invariant with molecular weight, the universal calibration procedure tin can be applied. ¹⁰⁹ Still, when information technology changes with molecular weight, measurements of the MWD presents additional problems. The dependency of elution volume of the different species on the molecular composition and structure is one such problem. Some other trouble arises from the fact that specific organic groups take different refractive indices. If the copolymer composition changes with the degree of polymerization, ¹¹⁰ then the measured differential refractive index is not directly related to the amount of copolymer being eluted. Finally the introduction of groups such as hydroxyls, amines, etc. will increase the potential for intermolecular clan, which will influence the elution time. Large discrepancies accept been observed between number boilerplate molecular weight K _n determined by SEC and past ²⁹Si NMR, which have been attributed to differential spreading of the chromatogram by various disiloxanol species. ¹¹¹

These item problems have not been solved and efforts to exercise so are still beingness pursued. The breakthrough will be the possibility of specifically detecting the different eluting copolymer molecules. The development and combination of new techniques of detection have recently been proposed that overcome these problems. ¹¹⁰ An evaporative detector (ED), a differential refractive index detector (DRI) and a low-angle laser light-scattering detector (LALLS) are simultaneously used to monitor the refractive index difference betwixt the solvent and the solution, the concentration of the eluting species and the molecular weight of the eluting species. This latter development has been applied to organic copolymers.

The number average degree of polymerization, DP, is the other parameter which is very important in the characterization of polymers. Any analytical technique that tin can quantitate the cease grouping concentration provides absolute values of DP and M _n. Spectroscopic methods such as FT–IR and FT–NMR are preferred to chemical titrations of reactive groups since the spectroscopic techniques are more rapid, specific, precise and accurate. ¹¹² Furthermore chemically non-reactive groups such equally the trimethylsilyl group can exist determined. The importance of MWD, Thou _n and DP on the performance of the polymer and its chemical reactivity has been emphasized. ¹¹³

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Polymer Label

John 5. Dawkins , in Comprehensive Polymer Science and Supplements , 1989

12.5.iii Detectors

In SEC the concentration by weight of polymer in the eluting solvent may be monitored continuously with a detector measuring refractive alphabetize, UV absorption or IR absorption. The resulting chromatogram is therefore a weight distribution of the polymer as a office of V _R. When the molecular weight of the polymer in the eluting solvent is measured experimentally with a low angle laser light-handful detector (LALLS), and then the dependence of west(M) on M can be established straight. Alternatively, if universal calibration is valid, equally shown in Figures 5 to 8, and so at a given Five _R the relation

(25)

will apply. Here, subscript p refers to a polymer requiring characterization and subscript ps to polymer standards, which will be polystyrene standards for organic eluents and poly(ethylene oxide) and/or polysaccharide standards for aqueous eluents. Equation (25) permits the determination of the M _p calibration curve when the dependence of [η]_p and [η]_ps on Five _R have been established, which may exist achieved past measuring [η] with an on-line viscometer detector. This universal calibration arroyo is an of import component of the characterization procedure for branched polymers and copolymers.

The experimental SEC atmospheric condition crave highly sensitive concentration detectors giving a detector response which is linearly related to polymer concentration. The most common detector for monitoring polymer concentration in the eluent is the differential refractometer. Except for very low polymers, the response of the detector to polymer concentration does not depend on polymer molecular weight. The most sensitive detector is the differential UV photometer, which is appropriate for a polymer with a significant UV absorbance at a convenient wavelength with a nonabsorbing eluent. This detector is non affected appreciably by menstruum pulsations, menses charge per unit changes and temperature fluctuations. In the characterization of copolymers it is necessary to have two detectors in serial, e.g. a refractometer with either a UV detector or an IR detector. An IR detector is preferred for the detection of polyalkenes at elevated temperatures, considering baseline noise and migrate are much less than for the refractometer detector.

In LALLS the intensity of scattering from the polymer is expressed in terms of the excess Rayleigh factor R _θ defined as the scattering intensity of the polymer solution minus the scattering intensity of the solvent at a given bending θ normalized with respect to the intensity of the incident beam and the handful volume. The value of R _θ will be a part of the handful angle, the polymer concentration and the polymer molecular weight. When measurements are performed at low angles with respect to the incident beam, the equation

(26)

is applicative where c is the polymer concentration, A ₂ is the second virial coefficient and K is an optical constant defined as

(27)

where north is the refractive alphabetize of the solvent, λ is the wavelength of the incident axle and the dn/dc is the specific refractive alphabetize increase of the polymer solution. In order to apply equations (26) and (27) to an eluting polymer, concentration and LALLS detectors must be attached on-line to the column system, and separate measurements must exist performed to establish calibration values of dn/dc and A _ii. M̄_w, M̄_n and west(M) may and then be computed for a polymer. Although calorie-free scattering gives good handful intensities for polymers having high M, there may exist little or no LALLS detector sensitivity with M  <   10⁴. For a polydisperse polymer, experimental measurement of M for the chromatogram at high V _R may not be authentic. Information technology follows that when average molecular weights are computed from the distribution w(One thousand) derived from information obtained with concentration and molecular weight detectors, the value of M̄_w is likely to be more reliable than M̄_n, which could be essentially in error. ^102–105

Various viscometric detectors have been reported. The polymer concentration must exist known in an elution volume increment, and the viscometric and concentration detectors must exist attached online to the cavalcade system in guild to constitute the intrinsic viscosity [η] of the polymer in whatever increment of eluting solution. ^106–110

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Analysis of Substances in the Gaseous Phase

In Comprehensive Analytical Chemical science , 1991

9.2.1 Basic Relationships

The refractive alphabetize of a substance is defined as the ratio of the velocity of lite in a vacuum to the velocity in the substance. Consequently, these indices accept values greater than unity for real media. The refractive indices of gases are much lower than those of liquids or solids. As examples, the refractive indices of water in various states are given in Tabular array nine.4, and those for a number of gases are given in Table 9.5.

Tabular array 9.iv. Refractive index of various forms of h2o

	Refractive alphabetize
Ice at 0°C	1.3049
H2o at 25°C	one.33287
Steam	i.000249

Tabular array 9.5. Refractive indices of some gases and vapours

Gas or vapour	Refractive index
Acetone	one.001078
Ammonia	i.000373
Argon	1.000281
Benzene	i.001700
Nitrogen	1.000296
Helium	ane.000036
Chlorine	1.000773
Chloroform	one.001436
Oxygen	1.000271
Methyl hydride	1.000444
Nitrogen oxide	one.000297
Dinitrogen oxide	1.000516
Carbon monoxide	ane.000335
Carbon dioxide	1.000448
Sulphur dioxide	1.000686
Carbon disulphide	1.001478
Hydrogen sulphide	1.000644
Hydrogen	1.000132
Air	i.0002926

Commercial refractometers which mensurate the refractive indices of solids and liquids tin can exist used for values in the range from 1.3000 to 1.84000. It can exist seen from Table 9.5 that these cannot exist used for determinations of gases, as the maximal measuring precision is simply ± 0.0001 refractive index units.

The refractive alphabetize depends on the temperature of the substance, wavelength of calorie-free used, and on all factors that tin can touch the concentration of the substance in the cuvette. Imprecision resulting from changes in the temperature, density, force per unit area, instrumental characteristics, etc., can be eliminated past differential measurement. The refractive indices of substances with known and unknown refractive alphabetize values are measured under identical conditions, yielding a departure from which the value for the unknown sample can exist calculated. Differential measurements endure from a narrow measuring range but, on the other hand, small differences in the refractive alphabetize (0.0001 units) tin be determined with relatively high precision. Consequently, differential refractometers are used more than often; these instruments are also called interference refractometers or interferometers.

The principle of the interferometer was discovered by Immature in 1802, in an experiment to demonstrate the wave nature of light. It follows from wave theory that, when two lite waves are in phase and have the aforementioned amplitude and direction, the resultant amplitude is equal to the sum of the two amplitudes and the intensity of the calorie-free ray, which is proportional to the square of the amplitude, is 4 times greater than that of the elementary moving ridge. If the waves are in opposite phases, the resultant amplitude and intensity of the beam are equal to aught.

Young's experiment is depicted in Fig. 9.6. The calorie-free from source S passes through ii narrow slits S_i and Due south₂, which are very close together and class 2 new coherent sources. If a screen D is placed behind these slits, a number of night and light lines can exist seen parallel to the slits. These lines disappear when one of the slits is covered. The distance between the night and light lines is directly proportional to the wavelength of the lite used, and indirectly proportional to the distance between the slits. When white lite is used, then the cardinal line A is white and the subsequent lines have slightly red and blue edges. When monochromatic low-cal is used, all the lines are the same colour.

Fig. nine.six. The Young experiment. S = Light source, S_i, Southward₂ = slits, D = shield, A = fundamental strip.

Arago later carried out an experiment in which an optical medium with refractive alphabetize north _a was replaced by a medium with alphabetize northward _b for abiding beam path length; when northward _a > n _b, and so the fix of lines is shifted towards the substance with index n _a. The number of lines, h, respective to the shift from the fundamental line, A, yields the deviation in the refractive indices of the substances co-ordinate to the equation

(ix.26) $n={\mathrm{northward}}_{\text{a}}-{\mathrm{north}}_{\text{b}}=\frac{h\lambda }{L}$

where λ is the wavelength of the calorie-free employed, and Fifty is the pathlength of the light axle in the medium with refractive index north _a. If monochromatic low-cal is employed, the shift in the interference spectrum cannot be determined because all the lines are the same colour. Consequently, white light is used, where merely the central line is white.

The analytical awarding of interferometric measurements is based on the validity of the Biot-Arago constabulary, which expresses the human relationship between the refractive index of a mixture and the indices of the individual components:

(9.27) $\mathrm{northward}=\frac{{\mathrm{ten}}_{\mathrm{i}}}{100}{\mathrm{northward}}_{\mathrm{ane}}+\frac{x_{\mathrm{ii}}}{100}{n}_{\mathrm{two}}+\cdots$

where north is the total alphabetize of the mixture, x ₁ and x _two are the mole fractions of the gas components in the mixture and n _ane and due north₂ are the refractive indices of the individual components. Instead of the refractive index, the value R = (n−1)·10^six, i.e. the refractivity is oftentimes used, avoiding the necessity of list values with many figures afterward the decimal point.

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Polymer Label

Marker G. Styring , Archie E. Hamielec , in Comprehensive Polymer Scientific discipline and Supplements , 1989

13.ii.2 Practice

13.2.2.1 Sample preparation

The experimental procedure is very straightforward. Eluants and suspensions for injection into the instrument are usually filtered before use. Eluant flow rates are typically 0.five to 2.0   cm³ min⁻ⁱ. Owing to the high sensitivity of UV detectors only very pocket-sized amounts of sample are required; 0.ane   cm³ of sample at 0.005% solids concentration was sufficient according to Small, ^v whereas a tenfold increase in amount was required for the arrangement described by Coll and Fague ²⁹ where a differential refractometer detector was used. Such an increase might lead to earlier plugging of the columns with deposited sample than might otherwise be the example. A UV-absorbing 'mark' species of low molecular weight, commonly sodium dichromate at approx. 0.02% concentration, is also incorporated in the sample. This tin can admission the unabridged interstitial volume in the column and elutes at the end of the chromatographic process. A typical chromatogram obtained for a single colloidal species plus marker is shown in Figure ii.

Figure 2. Typical chromatogram obtained by injection of a single colloidal species plus mark. Chromatographic parameters used in evaluating resolution are indicated

13.ii.2.two Quantification

By convention the rate of colloid migration through the column is expressed as a dimensionless quantity, the R _F number, which is contained of the flow charge per unit and is simply the ratio of the rate of migration of the colloid to the rate of eluant menses in the interstices. The latter is assumed equal to the rate of migration of the mark and then in terms of the parameters introduced in Figure 2 we have

(i)

13.two.2.3 Colloid deposition and column maintenance

It is well known that colloidal stability is the issue of a frail balance of electrostatic and steric forces nowadays in aqueous solutions which are critically dependent upon such parameters equally ionic strength and surface charge. ³¹ Colloids have a tendency to adhere themselves to one another and to other surfaces with which they come in contact, due east.g. the HDC packing materials. Larger particles tend to eolith more readily than smaller ones. This, together with the pocket-sized size of the flow channels in packed columns, means that at that place is an constructive maximum size of colloid which can pass through an HDC column. The verbal cutting-off bore varies from column to column and with eluant ionic strength, but mostly particles larger than approx. 5000   Å will be retained to some extent. This has been amply demonstrated in several particle-recovery studies. ^17,23,32 One implication of this phenomenon is that HDC will non yield the true PSD of a polydisperse latex sample which contains particles larger than about 5000   Å. However, at that place are several ways of circumventing the difficulty. Secchi et al. ²³ and Rudin and Frick ³² reported the necessity of injecting several samples of 'sacrificial' latex at the start of each working day earlier a abiding recovery was obtained. The latter authors also found it useful to keep eluant flowing continuously through the appliance. These expediencies yielded a size scale which was reportedly stable for weeks. In addition, the use of larger column packings resulted in macerated loss of larger particles, though at the price of poorer resolution. ^23,32 Increasing the surfactant concentration (to around the cmc) also improved recoveries. ^23,32

Another effect of degradation is a gradual deterioration in column performance manifested as a shift in the R _F vs. particle-diameter calibration and eventual column plugging. McGowan and Longhorst ^10a reported a typical useful cavalcade lifetime of ∼ 6 months, i.due east. ∼ 2000 injections, but that the packing materials could hands be cleaned and re-used.

13.2.2.four Precision and accurateness

Owing to the reliability of modern chromatographic equipment, peculiarly the pumps and detectors, the precision of the technique is very proficient. An uncertainty in top position for a given latex after xv injections over 2 days of   ±   0.03% has been reported. ^10a Precision in terms of PSD is more difficult to quantify since it depends on having a proper calibration for the instrument and upon the method of data processing. Accuracy, also, depends entirely on the reliability of the calibration of the instrument (for both peak separation and broadening), which is achieved by chromatographing a series of latex standards, usually polystyrenes, having very narrow PSDs. Their diameters demand to be previously determined, normally by some absolute technique such as transmission electron microscopy (TEM). At this stage nosotros quote results from ref. 10a in which a standard polystyrene latex was chromatographed and found to take a diameter of 2504   Å by HDC (based on a calibration established using other polystyrene standards), compared with 2423   Å by TEM: a difference of ∼ 3%. This compares with a figure of 5–vii% error in the TEM technique itself as applied to monodisperse latices. ³³ We reserve further comments about the all-important calibrations until some farther experimental observations and the mechanism and resolution of the technique have been discussed.

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Refractometer Detector Detects Concentration of Which of the Following Range

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