Molar Mass Dependence of Response Factors

In chromatography of polymers, the most frequently used detectors are the UV and the RI detector. Recently, we have introduced the density detector, which is very useful in the analysis of non-UV absorbing polymers.

The UV-detector responds to UV-absorbing groups in the polymer, which may be the repeating unit, the end groups, or both.

RI and density detectors measure a property of the entire eluate, that means, they are sensitive to a specific property of the sample (the RI increment or the apparent specific volume, respectively). It is a well known fact, that specific properties are related to molar mass:

K Mi where xi is the property of a polymer with the molecular weight Mi, xx is the property of a polymer with infinite (or at least very high) molecular weight, and

K is a constant reflecting the influence of the end groups.

A similar relation holds for the response factors for RI and density detection:

In a plot of the response factor, f, versus the molecular weight, Mi of a polymer homologous series (with the same end groups) one will obtain a straight line with the intercept fx (the response factor of a polymer with very high molecular weight, or the response factor of the repeating unit) and the slope K, which represents the influence of the end groups.

Once fx and K have been determined, the response factors for each fraction eluting from the column can be calculated using this equation (with the molecular weight obtained from the SEC calibration).

One more problem concerns preferential solvation: when a polymer is dissolved in a mixed solvent, the composition of the latter within the coils can be different from outside because of different interactions of the polymer chain with the individual components of the solvent. When the sample is separated on the column from the zone where the solvent would elute, a system peak (vacancy peak) appears, which is due to the missing component of the mobile phase. Obviously, the missing amount of solvent in the system peak appears in the peak of the polymer, the area of which is now different from what it would be in absence of preferential solvation.

Although this effect has been known for a long time, it is often neglected by chromatographers because they consider their mobile phase to be a 'pure' solvent, which is, however, generally not the case: even HPLC-grade solvents are seldom more than 99.5% pure and, if so, they take up moisture from the air, form peroxides and so on. The content of a second component (e.g. water or a stabilizer) can thus be much higher than the concentration of the sample when it leaves the column and enters the detector.

If the polarity of the end groups of a polymer is considerably different from that of the repeating units, their contribution cannot be neglected, and preferential solvation depends on molar mass.

Copolymers and polymer blends In the analysis of copolymers, the use of multiple detectors is generally inevitable. If the response factors of the detectors for the components of the polymer are sufficiently different, the chemical composition along the MMD can be determined from the detector signals.

When multiple detection is used, one has to be aware of errors arising from peak spreading between the detectors and from inaccurate shift time (just as in combinations with molar mass detectors). Typically, a combination of UV and RI detection is used, but other detector combinations have also been described.

If the components of the copolymer have different UV-spectra, a diode array detector will be the instrument of choice. However, one has to keep in mind, that nonlinear detector responses may also occur with UV detection. In the case of non-UV absorbing polymers, a combination of RI and density detection yields the desired information on chemical composition. The ELSD is not equally suitable because of unclear response to copolymers.

The principle of dual detection is quite simple: when a mass mi of a copolymer, which contains the weight fractions wA and wB (wB = 1 — wA) of the monomers A and B, is eluted in the slice i of the peak, it will cause a signal xh) in the detectors, the magnitude of which depends on the corresponding response factors /j;A and /j;B, where j denotes the individual detectors:

The weight fractions wA and wB of the monomers can be calculated using:

wA f X1

Once the weight fractions of the monomers are known, the correct mass of polymer in the slice can be calculated using:

and the molecular weight, MC of the copolymer is obtained by interpolation between the calibration lines of the homopolymers:

wherein MA and MB are the molecular weights of the homopolymers, which would elute in this slice.

A typical example is given in Figure 3, which shows the MMD of a block copolymer of ethylene oxide (EO) and propylene oxide (PO), as obtained by SEC (in chloroform) with coupled density and

log M

Figure 3 MMD and chemical composition of an EO-PO block copolymer (Figure 2), as determind by SEC in chloroform with density and RI detection. PEG # PPG.

log M

Figure 3 MMD and chemical composition of an EO-PO block copolymer (Figure 2), as determind by SEC in chloroform with density and RI detection. PEG # PPG.

RI detection. As can be clearly seen, this sample obviously contains polypropylene glycol as a byproduct.

The interpolation between the calibration lines cannot be applied to mixtures of polymers (polymer blends): if the calibration lines of the homopolymers are different, different molecular weights of the homopolymers will elute at the same volume.

The universal calibration is not capable of eliminating the errors originating from the simultaneous elution of polymer fractions with the same hy-drodynamic volume, but different composition and molar mass. Obviously it is feasible to use a combination of molar mass-sensitive detectors, such as a LALLS, MALLS and viscosity detector with two concentration detectors, from which the (average) composition for each fraction can be obtained, and thus the amount of polymer in the fraction. Nevertheless, discrimination of copolymers and polymer blends is impossible with one-dimensional chromatography.

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