Universal calibration method

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. 

Note that the weight and Z average molecular weights so obtained are only approximate and less than the true values. This is a consequence of the universal calibration method giving the instantaneous number average molecular weight across the chromatogram. 

The peak position and universal calibration methods rely on peak position calibration with known polymers of narrow molecular weight distribution. Several other calibration procedures requiring only a single broad moleculau weight standard have been proposed [77,439]. These procedures are quite c< plex and have a major drawback in that, unlike the peak position methods, instrumental peak broadening must be accounted for correctly if accurate results are to be obtained. 

A direct consequence of the development of hydrodynamic volume theory In SEC has been the universal calibration method as introduced by Benoit (17). Universal calibration methodology is based upon the fact that retention in SEC can be described as a function of the hydrodynamic volume of polymer molecules. 

Table VI lists the results of this study of calculated molecular weight accuracy as a function of calibration method with the PVC poljnners. A PVC polymer sample was analyzed and molecular weight averages were calculated by means of each calibration method. All SEC peak processing parameters used for calculation of MWD values were held constant. As shown in Table VI, the universal calibration method provided a somewhat more accurate value than the Q-factor approximation method or the linear, poly-disperse standard method.

In comparing the linear calibration method to a universal calibration method for PVC polymers, the universal calibration method appeared to be slightly more accurate suggesting that universal calibration methodology be applied whenever possible. In cases where universal calibration can not be utilized, the linear calibration method provides a viable alternative. 

The size exclusion chromatography for this study was done in the routine manner execept for the inclusion of an online viscosity detector called a Differential Viscometer <3> (Viscotek Corp., Porter, Texas, USAl. This instrument together with an RI concentration detector permits the calculation of intrinsic viscosities across the chromatogram. An IBM PC data system with software is also provided (5). The software acquires data from both detectors, and performs calculations of intrinsic viscosity and molecular weight distributions using the Universal Calibration Method. 

The objective of this present work was to investigate the feasibility of using GPC/DV for absolute molecular weight determination of hydroxypropylated lignins. In order to verify the validity of the universal calibration method, vapor phase osmometry (VPO) was used to provide reference number average molecular weight values. Comparisons with LALLS results have also been made and will be reported in another publication. 

Studies of GPC separations have shown that polymers appear in the eluatc in inverse order of their hydrodynamic volumes in the particular solvent. This forms the basis of a universal calibration method since Eq. (3-37) is equivalent to... 

The necessary conditions for application of the universal calibration method and for calculation of molecular weights through Eq. (6) is the knowledge of the [r]]i values, which are obtained from the Mark-Houwink equations when the pertinent values of K and a constants are known. An alternative way is to make a continuous measurement of [t]]i at the different elution volumes with an on-line viscometer detector coupled to the usual concentration detector system. 

In 1966, the universal calibration method was established at the University of Strasbourg, France [1]. It used, as a parameter, not molecular weight M, but the hydrodynamic volume represented by the product... 

XRF analysis was used for the determination of ruthenium, tin, sodium and chlorine content. Solid catalysts samples were examined by automatic sequence RTG spectrometer (ARE 9400 XP). Elements loadings were evaluated by UNIQUANT analyzer. The program used a universal calibration method. 

Empirically, it is known that if different polymers have the same elution volume from a given GPC column, the product [x] M will be constant, where [ ] is determined under the same conditions Tand solvent). This follows from the Einstein-Simha relation, whereby the quantity xi M is proportional to the hydrodynamic volume. The hydrodynamic volume depends on temperature and solvent, and is roughly half the volume calculated from Sg. Using the universal calibration method, molecular weight determinations can be made for a polymer using known standards of a different polymer (Grubisic et al., 1967 Puskas and Hutchinson, 1993 Kuo et al., 1993). These molecular weight standards are commercially available for various polymers. From Eq. (3.13),... 

Approximate molecular weights can be obtained when the single broad standard method or universal calibration method is not feasible (8,46). The accuracy of this method depends upon the unknown polymer having the same structure and molecular weight distribution as the standard. 

KK and a are Mark-Houwink constants that account for the molecular weight dependence of the intrinsic viscosity. The universal calibration method is broadly applicable given the availability of Mark-Houwink constants. Reference 87 summarizes Mark-Houwink constants for a number of common polymers. Sources of error for the universal calibration method are discussed in References 8, 86, and 88. As can be expected, serious errors occur if mechanisms other than size exclusion are at work. Cassassa stated that [r ]MW is not a true universal elution parameter, although both theory and experience indicate good results for species... 

Recently, Veith and Cohen (3) analyzed nylon 6 in TFE using the universal calibration method and peak retention data from narrow PMMA fractions. Silanized silica columns obviate the solvent incompatibility problem of TFE with styrene-based packings and give reproducible results. The accuracy of the calculated nylon 6 molecular weights was cross-checked with an independent end-group analysis (for M ) and intrinsic viscosity measurement (forMJ. 

Basically, three calibration methods have been used for the SEC analysis of cellulose. These three methods, which by no means are unique to the SEC analysis of cellulose, include (1) the peak position method (i.e., DP versus elution volume), (2) the universal calibration method, and (3) the LALLS... 

Thus calibration of the apparatus with, for example, polystyrene standards with known values of K and a in the particular solvent at a particular temperature permits the absolute molecular mass to be calculated via the universal calibration method [9]. A further advantage of the detector is its ability to be used at temperatures up to 150°C, thus permitting the analysis of polyolefins. The study of branching in polymers is also possible with this system. This new detector probably represents the most significant advance in detectors for size exclusion chromatography in recent years. 

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