Calibration curves universal

An interesting outgrowth of these considerations is the idea that In r versus K or Vj should describe a universal calibration curve in a particular column for random coil polymers. This conclusion is justified by examining Eq. (9.55), in which the product [i ]M is seen to be proportional to (rg ), with r = a(rg 0 ) - This suggests that In rg in the theoretical calibration curve can be replaced by ln[r ]M. The product [r ]M is called the hydrodynamic volume, and Fig. 9.17 shows that the calibration curves for a variety of polymer types merge into a single curve when the product [r ]M, rather than M alone, is used as the basis for the cafibration. 

PMMA, on the unmodified porous glass and silica gel, and the universal calibration curves for polystyrenes and poly(methyl methacrylates) did not coincide (10,12,19). 

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

FIGURE 20.3 Universal calibration curve for TSK-PW columns with an aqueous mobile phase of 0.10 N sodium nitrate. 

FIGURE 20.1 I Universal calibration curve of PVP using CATSEC columns in an aqueous mobile phase of 0.20 N sodium nitrate/0.1 % trifluoroacetic acid. 

The most widely used molecular weight characterization method has been GPC, which separates compounds based on hydrodynamic volume. State-of-the-art GPC instruments are equipped with a concentration detector (e.g., differential refractometer, UV, and/or IR) in combination with viscosity or light scattering. A viscosity detector provides in-line solution viscosity data at each elution volume, which in combination with a concentration measurement can be converted to specific viscosity. Since the polymer concentration at each elution volume is quite dilute, the specific viscosity is considered a reasonable approximation for the dilute solution s intrinsic viscosity. The plot of log[r]]M versus elution volume (where [) ] is the intrinsic viscosity) provides a universal calibration curve from which absolute molecular weights of a variety of polymers can be obtained. Unfortunately, many reported analyses for phenolic oligomers and resins are simply based on polystyrene standards and only provide relative molecular weights instead of absolute numbers. 

From this it follows that plotting a graph of log M[7]] against elution volume should give a straight line for all polymer-solvent combinations. This was shown by Benoit et al to be true for a large number of systems and is referred to as the universal calibration curve. It is illustrated in Figure 6.6. 

In reality, the universal calibration curve is not quite universal. Certain exceptions exist, such as polymers with very rigid backbones. However, the... 

Figure 3, HDC universal calibration curve (eluant ionic strength L29rriM. AM A monodisperse lattices (O) polystyrene polyvinyl chloride ( ) poly (styrene-...

Once a value for M[ is assumed, this leaves one unknown b which can be determined from the SEC chromatogram and the measured whole polymer intrinsic viscosity in the following manner. First, one estimates a value for b, and calculates M CV) and [n](V) across the chromatogram using the universal calibration curve and equation (3). Then the whole polymer intrinsic viscosity is obtained from... 

Figure 12 were superimposable on those for detector 2. Therefore, when the plot shown in Figure 14 is linear over the range of compositions involved in the sample, then (according to equations (1-4) ) the composition of the sample is the same at each retention volume. If the variation with retention volume is negligible the copolymer can then possibly be treated as is a homopolymer in GPC interpretation. In particular, intrinsic viscosity measurements could then lead to estimates of molecular weight via the universal calibration curve. 

Figure 19. Universal calibration curves for GPC 1 and GPC 2 based on hydrodynamic volume in GPC 1 (Vthf) (J) 100% THF (B3, Table I) obtained by sampling narrow standards infected into GPC 1 (A3, Table I) (2) 57% n-heptane in THF (B4, Table 1) (obtained as in 1 above) (3) 57% n-heptane in THF (B4, Table 1), obtained by direct injection into GPC 2 (4) 62% n-heptane in THF (B5, Table 1) (obtained as in 3 above) (5) 100% THF (A3, Table I), obtained by sampling GPC 1 (NBS706, 0.375 and 0.750 mg into GPC 1 and...

Figure 19 shows the Universal Calibration Curve obtained for the coupled GPCs in terms of the hydrodynamic volume in THF (Ref Table II). The addition of the n-Heptane caused a dramatic shift downstream of the polystyrene standards. 

This analytical method, based on TXRF, enables a large number of trace elements to be determined simultaneously. The range is suitable for different areas of the sea. The motivation to use TXRF resulted mainly from the characteristic features of the method its high detection power, its universal calibration curve, which eliminates the need for matrix-dependent standard samples or standard-addition procedures, the simple preparation of the sample films, and of course the possibility of multielement determination. 

Novolac molecular weights were measured in THF at 35°C by high pressure size exclusion chromatography using a Waters Model 510 pump (flow rate=1.0 ml/min), 401 differential viscometer detector and a set of Dupont PSM 60 silanized columns. A universal calibration curve was obtained with a kit of 10 narrow molecular weight distribution, linear polystyrene standards from Toya Soda Company. Data acquisition and analysis were performed on an AT T 6312 computer using ASYST Unical 3.02 software supplied with the Viscotek instrument. 

Other analysis methods dependent on multiple detectors can be implemented using this automated system. Two methods under development are the use of a continuous viscometer detector with a refractive index detector to yield absolute molecular weight and branching, utilizing the universal calibration curve concept (4), and the use of a UV or IR detector with the refractive index detector to measure compositional distribution as a function of molecular weight. 

Consequently, a relatively low molecular weight polymer (MM=1.39x 10 ) has an intrinsic viscosity (25.6 dl/g) equivalent to a PS or PDMS more than lOx higher in MW. (Earlier GPC work on PBIC (9) and PHIC (7) had shown no deviations from the universal calibration curve for GPC at high molecular weights). The primary role of chain flexibility in GPC degradation rather than simple molecular hydrodynamic volume is conclusively shown by these results. 

From the primary calibration curve based on polystyrene standards and the Mark-Houwink constants for polystyrene (K,a) a universal calibration curve (Z vs. v), based on hydrodynamic volume is constructed. Z is calculated from... 

Using the intrinsic viscosity data and the universal calibration curve( ) a secondary molecular weight calibration curve can be constructed for the polymer of interest as shown by the following equation ... 

Figure 10 shows DRI and viscometer traces for the NBS 706 polystyrene standard. Based on the information from these two chromatograms in conjunction with the universal calibration curve, one can calculate the intrinsic viscosity EnJCv) and molecular weight M(v) at each retention volume as shown in... 

A universal calibration curve was developed, using the retention volume vm corresponding to the DRl detector peak maximum of eluting polystyrene calibrants. Data were fitted with the GPC-II program to an equation of the form ... 

Therefore, the method of universal calibration would mean that a plot of the logarithm of [h]M versus SEC elution volume V would behave like a master calibration plot that is unique for a particular SEC column set. Through the years, there have been numerous results published in support of the universal calibration practice in SEC. This is indeed true as illustrated by our data shown in Figures 12, 13 and 14. The very different MW and [hi calibration curves of the four different polymer types shown in Figures 12 and 13 all converge to a single universal calibration curve based on the product of M [b] in Figure 14. 

As illustrated in Figure 15, the search for the MW calibration of an unknown polymer from the universal calibration curve requires an on-line SEC viscosity detector. Since narrow MW standards are not available for most commercial and experimental polymer samples, the determination of the polymer [b] calibration would not be possible without an on-line SEC viscosity detector. Once the [q] calibration for the unknown polymer is established, the polymer MW calibration can then be deduced from the universal calibration curve as indicated by the approaches shown in Figure 15. 

Figure 1 Universal calibration curve established using a single broad-MWD PS standard of known M and Mn-...

Figure 2 Universal calibration curves established using a series of narrow-MWD PS and PMMA standards.

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