Calibration parameter, universal

Verification is the complement of calibration model predictions are compared to field observations that were not used in calibration or fidelity testing. This is usually the second half of split-sample testing procedures, where the universe of data is divided (either in space or time), with a portion of the data used for calibration/fidelity check and the remainder used for verification. In essence, verification is an independent test of how well the model (with its calibrated parameters) is representing the important processes occurring in the natural system. Although field and environmental conditions are often different during the verification step, parameters determined during calibration are not adjusted for verification. 

Parameter values considered universal for all 29 events were determined for the six events that were selected for calibration. These universal values are shown in Table 7.3. The remaining parameters—dependent on the actual event — were determined separately. 

Benoit and co-workers [18] proposed that the hydrodynamic volume, Vr which is proportional to the product of [17] and M, where [17] is the intrinsic viscosity of the polymer in the SEC eluent, may be used as the universal calibration parameter (Fig. 18.3). For linear polymers, interpretation in terms of molecular weight is straightforward. If the Mark-Houwink-Sakurada constants K and a are known, log [t7]M can be written log M1+ + log K, and VT can be directly related to M. The size-average molecular weight, Mz, is defined by this process ... 

In GPC, the product [77] M, (or the hydrodynamic radius Re) has been widely accepted as a universal calibration parameter. In the Ptitsyn-Eizner modification of the Flory-Fox equation the quantity 4>, which relates the dimensional parameters to the above product, is taken as a variable. The value of < depends upon molecular expansion in solution as represented by a function f(e). Because of this dependence polymeric species having the same [77] M value cannot have the same statistical dimensions (radius of gyration or end-to-end distance) unless they have the same e value. Thus, if [77] M is a universal calibration parameter, the statistical parameters cannot be used as such. A method is presented for obtaining the Mw/Mn ratio from GPC data even though universal calibration is used. 

Tn GPC the product [77] M has been widely accepted as a universal calibration parameter, where [77] is the intrinsic viscosity and M is the molecular weight. This product is defined by the Einstein-Simha viscosity expression (I) as... 

To extend the calibration to other polymers, a calibration parameter that is independent of the chemical nature of the polymer, that is, a universal calibration parameter, is required. Such a parameter has been found [19] experimentally to be the product of the intrinsic viscosity and molecular weight (i.e., [r]]M). Thus, as shown in Fig. 4.28, with tetrahydrofuran... 

In analytical practice, the logarithm of sample molar masses, or molar volumes, is plotted versus retention volumes in calibration dependences of low molecular substances while values or effective hydrodynamic volumes, are used as size parameters in gel chromatography of macromolecules [12,13]. is often called universal calibration parameter because in ideal gel chromatography of randomly coiled macromolecules, it enables the transfer of data from one polymer to another regardless of both the physical (linearity, branching, tacticity, etc.) and the chemical (composition) structure of macromolecules [12]. The hydrodynamic volume of a particular polymer is proportional to the product of its molar mass and limiting viscosity number [ij], in the solvent that is used as mobile phase [ij]Mm. 

The basis for universal calibration is the observation that the multiplication products of intrinsic viscosities and molecular weights are independent of the polymer types. Thus, [rj]M is the universal calibration parameter. As a result, a plot of log ([/7]M) versus elution volume yields a curve that is applicable for many polymers. The log([ /]M)/or a given column (or columns), temperature, and elution volume may be considered a constant for all polymers. 

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. 

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. 

Table III. Universal Calibration with Single Broad MWD PVC Standard with Known M and M - Effect of Peak Broadening Parameter(a) ([nfpR = 7.06 X 10-5 ...

The composite plots of the theoretical Kg curves (Equations 2, 3 and 4) for the three solute shapei ) in terms of the common reduced size parameter Rg (Equations 5/ 6, and 7) are shown in Figure 2. This plot shows that on an basis all solutes of different conformations should behave very similarly in an SEC experiment. (This result is consistent with the universal SEC calibration concept... 

Several assumptions were made in using the broad MWD standard approach for calibration. With some justification a two parameter equation was used for calibration however the method did not correct or necessarily account for peak speading and viscosity effects. Also, a uniform chain structure was assumed whereas in reality the polymer may be a mixture of branched and linear chains. To accurately evaluate the MWD the polymer chain structure should be defined and hydrolysis effects must be totally eliminated. Work is currently underway in our laboratory to fractionate a low conversion polydlchlorophosphazene to obtain linear polymer standards. The standards will be used in polymer solution and structure studies and for SEC calibration. Finally, the universal calibration theory will be tested and then applied to estimate the extent of branching in other polydlchlorophosphazenes. 

Komit6 for Levnedsmidler (NMKL)]. The standard presents a universal validation approach for chemical analytical methods in the food sector. This includes methods for the main constituents and also for trace components. Therefore, the NMKL procedure focuses on primary validation parameters, such as specificity, calibration, trueness, precision, LOD or LOQ and does not refer to special requirements of pesticide residue analysis. 

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.

Fundamental Parameters (FP) are universal standardless, factory built-in calibration programs that describe the physics of the detector s response to pure elements, correction factors for overlapping peaks, and a number of other parameters to estimate element concentration while theoretically correcting for matrix discrepancies (e.g., Figure 1987). FP should be used for accurately measuring samples of unknown chemical composition in which concentrations of light and heavy elements may vary from ppm to high percent levels. 

The cosmological parameters and a can be determined from the Hubble diagram, provided that we have some well-calibrated cosmological standard candle that can be observed across a wide range of redshifts. This is precisely the approach adopted by Riess et al. (1998) and Perhnutter et al. (1999) when they used the type la supernovas. Pilar Ruiz-Lapuente at the University of Barcelona and Renald Pain at the University of Paris both made contributions to this exemplary cosmological programme. 

Gruendling T, Junkers T, Gullhaus M, Bamer-Kowolllk C (2010) Mark-Houwink parameters for the universal calibration of acrylate, methacrylate and vinyl-acetate polymers determined by online size-exclusion chromatography-mass-spectroscopy. Macromol Chem Phys 211 520-528... 

Considering the derivations of equation (1), it can be predicted that all molecules having the same value of [rj M would have the same value of Vh, the hydrodynamic volume. Also, if v/, is the parameter that uniquely determines the elution volume, Ve, these molecules should have the same elution volume. The arguments presented by these authors do not predict that the relationship between these parameters should necessarily be linear. Most universal calibration curves shown in the literature that cover 4 to 6 decades of M show a definite upward curvature at high values of M (28). 

Values for system peak parameters were found using a narrow distribution polystyrene standard (PS68K) before calculating MWD data for the lignin samples from universal calibration. To check software and instrument operation, several narrow MWD polystyrene and one broad MWD polymethylmethacrylate standards were treated as unknown samples and subjected to analysis with the universal calibration curve assembled from all polymer standards files. It was found that the MWD could be estimated for the recalculated polymer standards with errors between 5 and 10% of the original value indicated by the supplier of the standard (e.g., Mw for PS11K and Mw and M for PMMA17K-6). 

The ratio (Re/R)3 = (I)3 is thus implicit in the value of in the Flory-Fox equation and has a value of 0.49, corresponding to the Flory-Fox value of 2.1 X 1023. It is clear from Equations 1, 2, and 3 that [77] M cannot be related to the statistical polymer dimensions h and R without a knowledge of , i.e., < , which varies with solvent for a given polymer. It follows, that if all species having the same [77] M elute together from the GPC columns, then only Re can be the universal parameter, since will not be the same for all solute-solvent pairs and h and R will not be equally correct for universal calibration. 

We calibrate the radial displacement parameter so that it coincides with the geodesic radius, and find the remarkable result that, on sufficiently large scales, the calibrated radius of a sphere centered on the chosen origin in the model universe then varies as the square root of the mass contained within the sphere. 

In support of the WVDP, eight column tests were conducted at the University at Buffalo using WVDP groundwater spiked with nonradioactive Sr2+, over four durations 10, 20, 40, and 60 days. A single Kdof 2045 mL/g was calibrated from data from one of the 60-day columns, then used to successively predict the results for the other columns (Figure 5, 10-day data omitted for brevity). The importance of the specified boundary condition was highlighted by comparing results from various calibration schemes. For example, specification of a constant-concentration entrance boundary led to similar model fits but estimated Kd values that were 50% lower. Even when the recommended third-type BC was applied, efforts to simultaneously calibrate both the sorption and dispersion coefficient yielded similar fits for several combinations of parameters. Specification of the dispersion coefficient to a value obtained from an independent tracer test was necessary to obtain a robust estimate of the sorption coefficient. 

For determining the molar mass of branched polymers gel permeation chromatography can be used. An important quantity in this connection is the hydrodynamic volume of the polymer coil, which, as shown before in Eq. (9.27), is proportional to the product [rj M. According to Benoit and co-workers (1966) the hydrodynamic volume is the key size parameter in the establishment of a universal calibration curve for gel permeation chromatography columns (see Chap. 2) if log (h/]M) is plotted versus the elution volume for a variety of polymers, the data fit a single curve. 

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