Polystyrene -based calibration

BPF, which has low solubility in both water and organic liquids, was used. Phosgene was bubbled into the chloroform/water/salt slurry, and sodium hydroxide was added at a rate to maintain pH 10.5. Gel permeation chromatograms of these polymers showed a bimodal distribution the smaller peak was attributable to cyclic carbonates (1-10% ). Soxhlet extraction with dimethoxymethane reduced these to 1% or less, and subsequent to extraction Mw/Mn = 2.5-3.5 apparent Mn s (based on a polystyrene GPC calibration) were 25,000-50,000. (Corresponding osmo-metric molecular weights are roughly one-third greater.)... 

This makes it possible to use standards of one polymer for characterization of another if the corresponding Mark-Houwink constants are known. For most known polymers, Mark-FIouwink constants are tabulated. For example, a polystyrene (PS)-based calibration could be used for characterization of polymethylmethacrylate (PMMA). 

The polystyrene sizes were not the sizes commonly assumed for polystyrenes based on extended chains, but instead were determined from the viscosities (measured by Arro Labs, Joliet, Illinois) as described in Reference 8. Other types of standards and methods of calibration have been used for the GPC of residua samples (3, 9), including the Benoit universal calibration (10). However, these all relate the molecular weight to elution time, and for this work a molecular-size-elution-time relationship was needed. The polystyrene and n-alkane sizes were used to construct a In size vs. elution time calibration that was fit to a fourth-order polynomial to give a smooth curve. 

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. 

Calculations for Rp as a function of the relevant experimental parameters (eluant ionic species concentration-including surfactant, packing diameter, eluant flow rate) and particle physical and electrochemical properties (Hamaker constant and surface potential) show good agreement with published data (l8,19) Of particiilar interest is the calculation which shows that at very low ionic concentration the separation factor becomes independent of the particle Hamaker constant. This result indicates the feasibility of xmiversal calibration based on well characterized latices such as the monodisperse polystyrenes. In the following section we present some recent results obtained with our HDC system using several, monodisperse standards and various surfactant conditions. 

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

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... 

Figure 16 SEC molar mass distribution of poly(p-phenylene) P3 in THF after universal calibration based on Equations (31) (dashed) and (36) (dotted) and with polystyrene calibration (solid line). 

GPC calibration curves are established based on the radius of gyration of known-molecular-weight polymers, such as well characterized, narrow-molecular-weight distribution polystyrene. Branched polymers have a lower radius of gyration for their molar mass than the corresponding linear molecule. Thus, as branching increases the GPC numbers become less and less accurate and so should only be used for trends, and not exact calculations as some authors have done. 

The Q-factor approach is based upon the weight-to-size ratios (Q-factors) of the calibration standard and the polymer to be analyzed. The Q-factors are employed to transform the calibration curve for the chemical type of the standards (e.g. polystyrene) into a calibration curve for the chemical type of polymer under study. The inherent assumption In such a calibration approach is that the weight-to-size ratio is not a function of molecular weight but a constant. The assumption is valid for some polymer types (e.g. polyvinylchloride) but not for many polymer types. Hence the Q-factor method is generally referred to as an approximation technique. 

Carefully constructed Probe Mixtures based on small molecules and polystyrene standards are used as standardized reference points to better define the functional capabilities of individual columns and column combinations. The result using the method of Probe Mixtures to evaluate columns is better than can be attained from calibration curves alone and is especially useful in this high resolution capability situation. 

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... 

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... 

The use of a continuous GPC viscosity detector in conjunction with a DRI detector permits the quantitative determination of absolute molecular weight distribution in polymers. Furthermore, from this combination one can obtain Mark-Houwink parameters and the bulk intrinsic viscosity of a given polymer with a GPC calibration curve based only on polystyrene standards. Coupling these two detectors with ultraviolet and infrared detectors then will permit the concurrent determination of polymer composition as a function of molecular weight and... 

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 ... 

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