Standards broad MWD

E. Universal Calibration Studies. The use of SEC-[n] and MW calibration using broad MWD standards will make it easier to study the accuracy of the universal calibration concept. By combining the D1/D2 and Ei/E2 calibration curves, the universal calibration (M[n]t can be generated directly as in equation 17. 

Previous methods of molecular weight calibration using broad MWD standards were of three basic types. Those which employ a broad MWD standard with known molecular weight distribution... 

Those which employ one or more broad MWD standards with known M or [n] and assume a linear molecular weight calibration curve and finally those which employ one broad MWD... 

Mjj and My or [q] for the broad MWD standard are taken as known quantities. Fy(v) is the normalized chromatogram for the broad MWD standard obtained with a mass detector. D2 is the slope of the molecular weight calibration curve at the peak position of the chromatogram (the equation of the tangent is given by M(v) = Dj exp(-D2v). is the variance of the single-species chromatogram... 

Universal Molecular Weight Calibration Curve One Broad MWD Standard. 

There are three imknowns, K, a and. One might question the availability of Mark-Houwink constants for the polymer in the open literature. Mark-Houwink constants in the literature differ widely for the same polymer and it is difficult to decide on the correct pair to employ. Another problem which can arise is that the universal molecular weight calibration curve may not apply exactly for the polymer in question. The use of the true Mark-Houwink constants would therefore introduce an error in the molecular weight calibration. Calibration with a broad MWD standard should eliminate this error. The Mark Houwink constants obtained in the calibration would in this instance be effective rather than true values. 

In principle, one could solve equations (la), (2a) and (3a) for K, a and. Unfortunately, and [n] are often highly correlated and it is recommended that only one of these data be used per standard. A practical procedure is to estimate using narrow MWD polystyrene standards leaving two unknowns, K and a. To illustrate the method, suppose Mjj and M data are available for the single broad MWD standard. Dividing equation (2a) by (la) eliminates a and one is left with a single-variable search for 3. 

Two Pieces of Molecular Weight Data Per Standard. This method uses the fact that when equations (la) and (2a) or (la) and (3a) with proper modification are multiplied the peak broadening parameter vanishes. The equations for two broad MWD standards where M and M are known follow ... 

A single-variable search for D2 is followed by a direct calculation of Dx using equation (lOc) for at least two broad MWD standards. A direct calculation using equations (lOa) or (lOb) pro-... 

Figure 2. Intrinsic viscosity-molecular weight data for polystyrene and polyvinyl chloride measured by osmometry and by SEC using broad MWD standard calibration (polystyrene (m) M = 7,06 X 10 in THF/1% PPG (O) [ ] =...

Figure 3. Molecular weight calibration curves for polyvinyl chloride obtained using universal calibration and one and two broad MWD standards (two broad standard method (0) [rj = 7.06 X 10 single broad standard method ...

Two improved methods of molecular weight calibration using broad MWD standards have been proposed and some evaluation has been done experimentally for aqueous and nonaqueous SEC. The experimental evaluations indicate that both methods appear very promising and justify further experimental investigation. It is recommended that these new calibration methods be evaluated for a wide range of polymers,packings and mobile phases. 

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. 

SEC calibration methods can be generally categorized into techniques which employ a series of narrow MWD standards and those which employ one (or more) broad MWD standards (2). Calibration techniques which utilize polydisperse, broad MWD standards have been found to be particularly useful when narrow MWD standards are not available or universal calibration methodology is impractical as for example with most water-soluble polymers or polymer/solvent/temperature combinations for which appropriate Mark-Houwlnk constants are not known or readily available. 

The search algorithm employs a successive approximation and accelerated convergence technique on the Independent variable in eqn (6), then approximates the dependent variable from the simultaneous solution of the equations for Mn and Mw moments of the polydisperse standard distribution. Convergence to within 0.1% of true and values of a broad MWD standard is usually achieved in six to nine iterations. 

Dow 1683 polystyrene standard was utilized as a broad MWD standard in the linear calibration method due to its distribution symmetry and particular lack of significant tail at the low end of its MWD. 

Figure 1. Master universal calibration curve obtained with a Beckman /z-Spherogel column system in THF. The fit of narrow MWD standards, polystyrene star polymers, and a single broad MWD standard (calculated with Unical 2.71 software) are shown.

If the Mark-Houwink constants of the polymer are unknown, then the two broad MWD standards method, with known Mn and Mw, is used. The molecular weight averages of the two polymer standards are expressed as ... 

Direct calibration of GPC-SEC columns requires well-characterized polymer standards of the same type of polymer one has to analyze. However, narrow molecular-weight distribution (MWD) standards are available for a limited number of polymers only, and well-characterized broad MWD standards are not always accessible. The parameter controlling separation in GPC-SEC is the size of solute in the chromatographic eluent. Therefore, if different polymer solutes are eluted in the same chromatographic system with a pure exclusion mechanism, at the same retention volume, molecules with the same size will be found. 

Methods for application of the universal calibration have been developed also for cases where K and a of the polymer of interest are not known and neither [r]]i values are measured. Such methods are based on the availability of two broad MWD standards, having different molecular weights, of the polymer under examination [5]. 

With a light-scattering detector, a log M versus elution volume calibration curve is constructed from a series of narrow molecular weight distribution polymer standards. A broad molecular weight distribution standard is then injected, and an iterative procedure finds the interdetector volume that superimposes the broad MWD standard calibration curve onto the one established by the narrow standards (38). 

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