## Effects of Coupling Topology on Multidetector SEC Results

Many SEC Applications require use of more than one single detector. The different nature of the single detection technique and of the individual detector designs, introduces in such system a grade of complexity which needs accurate investigation and adaptation to the specific detector combination. Considering the fact, that signals obtained from different detectors are not used for themselve but introduced as an operand for calculation of terms in combination with the signals from the other detectors, it becomes clear that any slight undiligence in selection of topology will result into huge errors in final analysis results.

Autor: Carlo Dessy

Since reliable Viscometers and Light Scattering Detectors became available, the necessity came up to couple these detectors with an
appropriate concentration detector (most likely a Refractometer) in order to calculate the intrinsic viscosity [η]_{i}
in case of the viscometer, or M_{i} in case of the light scattering detector.

For Viscosity: [η]_{i} = η_{spi} / C _{i} and for SLS (constants omitted)
M_{i} = Signal / C_{i}

where the index i represent a single point on the signal traces of the detectors.

Only this operation allows then to calculate molecular weight distribution and its moments therefore it is absolutely necessary
to find for each point i on the SLS trace the correspondent point i on the
refractometer trace.

Whatever topology is selected (Daisy-Chain or Parallel Coupling), mainly three effects influence the signals from the individual detectors:

**A:** The different nature of signal sources and their respective selectivity and response

**B:** The particular design of each detector (cell volume, internal dead volume or signal filtering), and

**C:** Band Broadening within connecting tubing because of laminar flow.

The above means that a system consisting of different detectors, will deliver signals which do not necesserly overlay (they never do)
or even show similar peak width. A missing overlay of signals can (within limits) be corrected with an appropriate SEC Software while
large differencies in peak width are impossible to correct^{1} and must be avoided by careful selection of involved detectors
and coupling topology.

Investigations on structure as required by branching calculations, are performed best when both viscometry and static light scattering are used
for detection. This implies, that three (!) detectors (Refractometer, Viscometer and SLS) need to be coupled together² and their results must
be combined to obtain the seeked information.

The following case-study show clearly which magnitude topology alone has on final results.

**RI / Viscometer Dual-Detector and BI-MwA Coupling**

A WGE RI/Viscometer and a BI-MwA 7-angles light scattering detector were selected for this investigation. The WGE Ri/Viscometer has a unique design as the refractometer is integral part of the viscometer bridge. This design assures lowest possible interdetector delay volume and make sure that both concentration and viscosity, are measured based on exactly the same sample segment. Prior investigations concerning this instrument alone

^{3}, have shown the validity and excellent performance of this design compared to two separate instruments.

The BI-MwA is a innovative MALS detector, the flow through the cell is perpendicular to the laser beam and total cell volume is very low compared to other instruments.

Two topologies have been tested: Daisy-Chain and Parallel coupling. In Daisy-chain mode, the two detectors were connected one after the other with
the BI-MwA as first detector in the row. This was dictated by the necessity of the viscometer to be the last detector in a row^{4}.

In parallel mode, the flow outlet from the column was split with a commercially available adjustable flow splitter and partial flow for each branch was
adjusted to be 50% of total flow.

A Polystyrene Sample with a relatively broad distribution (Mw/Mn = 1.85) was selected for the investigation. Eluent was THF (unstabilized) at 1mL/min, three
columns with 5µm particles and poresizes ranging from 10E3 to 10E5 were used^{5}. A WGE Pump and Injector with 100 µL sample loop rounded up the test set-up. Data acquisition and SEC processing was performed with ParSEC Enhanced, further calculations were done with Origin Pro.

**Investigated parameter**

The final aim of a instrumental set-up of this type is to obtain as many information as possible about the structure of the investigated sample
and to be able to perform detailed calculations about branching. The basic idea is therefore to combine the absolute molar mass information delivered
by the SLS with the absolute intrinsic viscosity delivered by the viscometer. The combination of these two resolves exactly into structure information^{6}. Control of instrumental performance to this regards, can therefore obtained by calculating the coefficients of the empiric Mark-Howink equation
**[η] = k M ^{α}** and comparing these
results with published data.

For linear Polystyrene in THF

^{7}, literature reports k = 0.01363 and α = 0.714. These values have been validated by many sources and can be considered as reference for evaluation of value obtained with the equipment under evaluation.

**Daisy-Chain Coupling**

Figure 1 shows the elugram of an injection of the Polystyrene sample without any correction for interdetector delay. At a first glance, all signals
are nicely grouped together and it seems that only a small correction will be necessary.

Fig. 1: Daisy-Chain Elugram, no correction

Figure 2 displays the calculated concentration, molar mass and intrinsic viscosity versus elution volume. Both raw data and respective linear fits are shown. These calculations were performed without any correction for the interdetector delay volume.

Fig. 2: Calculated Mi and [η]i, Daisy-Chain, no correction

Data calculated as shown in Figure 2, was then used to calculate the Mark-Howink coefficients. Please note, that at this stage of evaluation,
only the α coefficient is considered. Result for the uncorrected data is α = 0.5504 and by this very far from the expected 0.714.

Fig. 3: Mark-Howink Plot of Original data and for corrected interdetector volume

Correction of the interdetector delay volume lead then to an α = 0.7167 which fits nicely the expected value with an error of only 0,37%.

However, the correction required was incredibly large, as shown in Figure 3, measuring 0.45 mL for both viscometer and refractometer, a value which cannot be confirmed
by evaluation of the raw elugram.

The reason for this effect lays in the nature of the correction itself. The interdetector delay volume is an
apparent value. The flow in the connecting tubing between the two instruments and the related "stretching" of the sample segment due to the
laminar flow, modifies results such, that a correction within reasonable range becomes impossible .

**Parallel Coupling**

In Figure 4, the elugram of the Polystyrene sample obtained with parallel coupling is shown. At first, this elugram does not look very different from
the one in Figure 1. Again, the signals are very well grouped together.

Fig. 4: Parallel Coupling Elugram, no correction

Figure 5 displays the calculated concentration, molar mass and intrinsic viscosity versus elution volume. Both raw data and respective linear fits are shown. As in Figure 2, These calculations were performed without any correction for the interdetector delay volume. Up to now, no real difference between the two methods can be discovered. The truth however, shows up in figure 6.

Fig. 5: Calculated Mi and [η]i, Parallel Coupling, no correction

In Figure 6 the Mark-Howink plot for the original and the corrected data is shown. Interesting, the value for α = 0.747 for the original
data, already comes very close to the expected value. Correction of the interdetector dely volume led then to α = 0.71445, a perfect value.
The necessary correction was 0.02 mL for the viscometer and 0.07 mL for the refractometer. Both these values are well within reasonable range
and also reflect the expected delay between refractometer and viscometer (0.05 mL).

Fig. 6: Mark-Howink Plot of Original data and for corrected interdetector volume

Now, we have the situation of correct α at reasonable correction values for delay volume, a situation which was not possible to reach in the daisy-chain coupling mode. It is therefore now possible to take care of the k value.

The Mark-Howink k coefficient is very difficult to determine with sufficient accuracy with a single SEC experiment. However, it is an important value especially when star-branched polymers are investigated, as in this case α is constant while k changes with number of arms present.

Figure 7 shows final results of Mark-Howink determination for a second Polystyrene sample we used to proof our results. After correction for
interdetector delay volume and correction for M - [η] shift^{8}, values for both k and α were found in excellent agreement
with literature data.

Fig. 7: Final Mark-Howink Plot of Polystyrene in THF

**Conclusions**

SEC is one of the strongest tool for polymer characterisation, the amount of information delivered by a single experiment is almost unreached by
other techniques. The detection technology available today, opens the gate to these information. However, careful selection of coupling topology
is an absolute necessity for achievement of correct, reliable results.

The daisy-chain method, althou simple and fast in realisation, leads to correction values beyond reasonable range thus making final
results questionable.

Parallel coupling, by far more complex due to the need of flow split, deliver the best possible conditions for correct, accurate and precise
result.

**Notes:**

**1:** The described influence functions convolute with the "pure" signal. Due to the unknown function and magnitude
of the single effects the attempt of deconvolution is questionable. A second method, used in one available SEC Software consisting in
convoluting the narrower peaks with a filter function in order to match peak width of the broadest detector, is questionable as well,
as it does not take into account the specific selectivity and response of the single detection methods.

**2:** In this paper the term "static light scattering" or SLS means Multi Angle Light Scattering Detector (MALS).
Single angle light scattering detectors are not suitable for structure investigation due to the limited information they deliver.

**3:** Prior studies investigated performance of separately coupled Refractometer and viscometer compared to performance of
the dual-detector. These studies clearly showed the dual-detector provides higher sensitivity and lower band broadening.

**4:** Due to the bridge design, the sample is diluted infinitely inside the viscometer bridge. Therefore, a detector
connected after the viscometer would receive no sample information at all.

**5:** Columns had individual pore sizes and were not "mixed-Gel" type as for structure studies, the highest possible
separation resolution is required.

**6:** In this paper I will not go deeper into branching calculations. Enough said that introduction of the determined M and [η]
in the Einstein-Stokes equation resolves to Rh^{3}. This can then be used to calculate hydrodynamic ratio g' or help
determine gyration ratio g.

**7:** It is important to keep in mind that the Mark-Howing relation is only valid for sufficiently fractal polymers.
In case of Polystyrene, molar mass should be higher than about 20 000 g/mol to fullfill this condition.

**8:** The nature of the M - [η] shift is still not fully understood and is
currently object of investigation (Feb. 2010)