Calibration hydrodynamic volume

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. 

Gels made in this way have virtually no usable porosity and are called Jordi solid bead packings. They can be used in the production of low surface area reverse phase packings for fast protein analysis and in the manufacture of hydrodynamic volume columns as well as solid supports for solid-phase syntheses reactions. An example of a hydrodynamic volume column separation is shown in Fig. 13.2 and its calibration plot is shown in Fig. 13.3. The major advantage of this type of column is its ability to resolve very high molecular weight polymer samples successfully. 

Calibration curves for PS and PMMA are shown in Figs. 15.3-15.5. The slight differences in courses of calibration curves for PS in THF, chloroform, and toluene, as well as the curve for PMMA in THF (Fig. 15.3), can be explained by the flow rate variations for different pumping systems and by the hydrodynamic volume effects, respectively. The calibration curves for PMMA in mixed eluents THF/toluene are shown in Fig. 15.4. Three percent of THF in toluene assured a reasonable SEC elution of PMMA. However, more chloroform was needed to obtain a good SEC elution of PMMA in mixed eluent chloroform/toluene... 

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. 

Yet as long ago as 1966 the problem of calibration in GPC was solved. In that year, Benoit and his co-workers recognised that GPC separates on the basis of the hydrodynamic volume of the polymer molecules in solution. The intrinsic viscosity [rj] is related to the hydrodynamic volume, V, by the equation ... 

Up to this point, all chromatographic information is in terms of elution volume. If a calibration file is available to the program, the chromatogram may be converted to log hydrodynamic volume. The chromatogram in terms of log hydrodynamic volume may be written to a file (with extension HYD) for later use. 

Unrecognized shifts in the calibration of the columns will affect the raw data, which are in terms of elution time of the components of the specimen from the chromatographic columns. Use of log hydrodynamic volume allows the operator to correct for such... 

Size exclusion chromatography (SEC) separates molecules of a polymer sample on the basis of hydrodynamic volume. When the chromatograph is equipped only with a concentration-sensitive detector, i.e. conventional SEC, a molecular weight distribution (MWD) can be obtained from the chromatogram only through use of a calibration function relating molecular weight and elution volume V (2). 

Compare molecular size/weight characteristics of branched and linear species eluting at V in each chromatogram. Under the universal calibration formalism branched and linear components have the same hydrodynamic volume at V ... 

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. 

Hydrodynamic volume of polymer (here considered equivalent to the separation parameter KM Table II for GPC calibration)... 

Branching in the polymer chain affects the relationship between retention and molecular weight.83 Universal calibration has been used with some success in branched polymers, but there are also pitfalls. Viscosimetry84-91 and other instrumental methods have proved to be useful. A computer simulation of the effects of branching on hydrodynamic volume and the detailed effects observable in GPC is available in the literature.92 93 In copolymer analysis, retention may be different for block and random copolymers, so universal calibration may be difficult. However, a UV-VIS detector, followed by a low-angle light-scattering (LALLS) detector and a differential... 

The molecular weight distributions were determined only in terms of the polystyrene equivalent from the polystyrene calibration of the GPC columns. This can only be regarded as semiquantitative, as the method determines only the relative hydrodynamic volumes. If the polysilane chain was significantly stiffer than polystyrene, the molecular weights would be estimated too high. If the chains are... 

The calibration function calculation uses multiple linear regression to obtain hydrodynamic volume as a polynomial function of elution volume for a given column set. 

Our system provides for several forms of calibration function, but we generally use "universal" calibration (5) and represent the dependence of the logarithm of hydrodynamic volume on retention volume by a polynomial, as in Figure 6. Note that the slope of the function changes dramatically near the ends of the range of applicability. The calibrants at the ends of the range exert a dramatic influence on the form of the fitted polynomial. This behavior demonstrates that the column set must be carefully chosen to fractionate the desired range of molecular sizes. 

The scatter of the points from the calibrants in Figure 6 shows that 95 confidence intervals for calculated hydrodynamic volumes amount to +/-10 or so over most of the experimental range. 

For some polymers, like polystyrene or poly(methyl methacrylate), narrow standards of known molar mass and small polydispersity are commercially available, which can be used for calibration. Unfortunately, such standards are not available for all polymers and then the obtained true molar masses of a specific polymer might differ by a factor of two from the value obtained by calibration with, e.g., polystyrene [30] (see Section 9.1). This problem can be resolved by the so-called universal calibration, which is based on the finding that the retention volume of a polymer is a single-valued function of the hydrodynamic volume of the polymer, irrespective of its chemical nature and... 

Fig Calibration curve for gel permeation chromatography based on hydrodynamic volume as expressed by the product [h] M. 

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. 

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. 

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... 

Universal Calibration. A function of the hydrodynamic volume [r ] M was plotted against the elution volumes of cellulose triacetate fractions and polystyrene standards run in dichloromethane have all indicated slight deviation from linearity as shown in Figure 2. 

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