Hydrodynamic volume calibration curves

Non-linear Hydrodynamic Volume Calibration Curve. The hydrodynamic calibration curve, log. V shown in Figure lb, is generated using the commercially available narrow MWD polystyrene standards listed in Table 1 and published values (28, 29) of the Mark-Houjjink parameters K and a for polystyrene in THF a 25°C, (K=1.6 x 10, o = 0.706 for > 10,000 and K = 9.0 x 10, a = 0.5 for Mw <10,000). The experimental data points composing the non-linear calibration curve were fitted with the phenomenologically based Yau-Malone equation.(30) This equation is derived from diffusion theory and is expressed as follows ... 

An internal calibration method based on the universal calibration concept " was used to establish a hydrodynamic-size calibration curve which gave the relationship between the retention volume (V ) and the... 

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. 

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. 

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. 

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

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... 

When the total polymer response, is known as a function of retention volume, the molecular weight distributlon can be obtained in the usual manner with the appropriate molecular weight calibration curve. The molecular weight calibration curve can be obtained (a) by using the Runyon (65) copolymer molecular weight scale approach, or (b) by using a hydrodynamic volume approach if the Mark-Houwink constants for the polymer of interest are known or can be determined, or (c) by using a hydrodynamic volume approach in conjunction with an on-line viscosity detector. 

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). 

Apart from one compound (II), the lignin model compounds that had free phenolic groups eluted at close to the retention times predicted by the calibration curve from the polymer standards and not from the derive tized model compounds. This could simply be a result of the underivatized models having a similar variation in hydrodynamic volume with molecular weight as the polymer standards. However, it is to be expected that solvation of the underivatized model compounds should occur with THF as solvent (10), with hydrogen bonding of one THF molecule to each under-... 

Grubisic et al. (3) showed that for many polymers a single calibration curve can be drawn through a plot of the product of intrinsic viscosity and molecular weight ( [7/] M) vs. retention volume. This relationship certainly supports the model of molecular separation based on hydro-dynamic volume since [77] M is proportional to the hydrodynamic volume of the molecule in solution. Hence, molecular weights of the two polymers (calibration standard polymer and sample) which have identical retention volume under identical GPC analytical conditions can be expressed in terms of each other by combining the Grubisic relationship ... 

Since size exclusion chromatography separates polymer molecules by their size (especially hydrodynamic size), plotting the molecular size vs. the retention volume should be universal, regardless of the polymer molecular weight. The universal calibration curve is given as ... 

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