Universal molecular weight calibration curve

Herein are reported improved methods of molecular weight calibration where simultaneously, peak broadening parameters (a) are obtained through the use of multiple polydisperse molecular weight standards. There are two basic methods covered. The first and most reliable method employs the universal molecular weight calibration curve obtained using narrow MWD polystyrene standards. 

Methods Based on Universal Molecular Weight Calibration Curve... 

The nonlinear universal molecular weight calibration curve may be expressed as shown in equation ( ). 

There are three imknowns, K, a and. One might question the availability of Mark-Houwink constants for the polymer in the open literature. Mark-Houwink constants in the literature differ widely for the same polymer and it is difficult to decide on the correct pair to employ. Another problem which can arise is that the universal molecular weight calibration curve may not apply exactly for the polymer in question. The use of the true Mark-Houwink constants would therefore introduce an error in the molecular weight calibration. Calibration with a broad MWD standard should eliminate this error. The Mark Houwink constants obtained in the calibration would in this instance be effective rather than true values. 

Figure L Molecular weight calibration curve for polystyrene an universal molecular weight calibration curve based on polystyrene ((%) [rj]Mw (U) w)...

The second method assumes that the molecular weight calibration curve is linear on a semilog plot and should be employed where universal calibration is not practical as with aqueous SEC. Several variants of these methods involving different molecular weight data for the standards are discussed. The proposed methods have been evaluated using aqueous SEC and polydextran standards and nonaqueous SEC with polyvinylchloride standards. 

Figure 3. Molecular weight calibration curves for polyvinyl chloride obtained using universal calibration and one and two broad MWD standards (two broad standard method (0) [rj = 7.06 X 10 single broad standard method ...

Universal calibration methodology has been successfully applied to PVC and many other chemical types of polymers (22). However, availability of Mark-Houwlnk constants can limit the utility of universal calibration. In these cases, the use of a linear, polydlsperse standard calibration method Is a viable alternative for generation of a molecular weight calibration curve. 

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 ... 

The characterization of star-branched polymers has been performed using triple detection because it was not obvious, in the beginning of this study, that universal calibration could be applied to star-branched polymers. In fact, the GPC software used handles experimental data as a double dual detection, GPC-viscometry and GPC-LALLS. Experimentally, it has been found that excellent agreement between results from these two sets of data can be obtained. GPC-viscometry uses a universal calibration curve and GPC-LALLS is free of any molecular weight calibration curve. Therefore, the universal calibration works well with very long chain branched polymers, even with a very particular... 

A universal calibration curve was established by plotting the product of the limiting viscosity numbers and molecular weight, Mw[iy], vs. the elution volume, EV, for a variety of characterized polymers. The major usefulness of the universal calibration curve was to validate individual molecular-weight values and to provide extended molecular-weight calibration at the ends of the calibration curve where fractions of narrow dispersion of the polymer being analyzed are not available. The calibration curve was monitored daily with polystyrene fractions certified by Pressure Chemicals. The relationship between the polyethylene fractions and polystyrene fractions was determined using the universal calibration curve. 

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. 

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. 

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. 

It was shown that the logarithm of the product of intrinsic viscosity and molecular weight of polymers of different chemical and stereochemical composition, configuration, or molecular weight is linearly related to the elution volume.81 A plot of log (r) M) vs. elution volume provides a single calibration curve, useful for samples of similar composition, and is termed a universal... 

For many polymers K and a values can be found in the Polymer Handbook [23]. In a recent study by Vanhee et al. [30] the universal calibration has been applied using the polystyrene (PS) calibration curve to characterize rigid rod poly(p-phenylenes) (PPP). It turned out that due to its larger persistence length, PPP with a certain mass requires a much larger volume than PS for the same molecular weight. Ron et al. employed universal calibration for the characterization of erodible copolymers [58]. 

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. 

Usually the function [Cn) M] (intrinsic viscosity times molecular weight) is used to represent hydrodynamic volume which is plotted versus elution volume. For such a plot the calibration curves of many polymers fall on the same line irrespective of polymer chemical type. Universal calibration methodology usually requires knowledge of Mark-Houwink constants for the polymer/ temperature/solvent system under study. 

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. 

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... 

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