Calibration of the GPC System

In order to assign a molecular weight to each retention time slice for the eluted polymer, we must calibrate our system, or more specifically, the column set. There are several ways to do this, but the easiest is to use a relative calibration based on a set of well-characterized polymer standards with as narrow a molecular weight distribution as possible. Ideally, we would like to use a set of standards that are monodisperse, i.e., a single molecular weight, with the weight and number average ratio (dispersity) being equal to one, (M_w/M_n = 1).

The closest we can come to achieving this is to use polymer standards that are polymerized specifically for this purpose, such as the anionically polymerized polystyrene narrow standards. Standards cover a very broad molecular weight range, from monomer to molecular weights > 10,000,000, with a dispersity of < 1.10. For a calibration standard to be really considered narrow, and acceptable for use in GPC calibration, the dispersity should indeed be < 1.10. There are also ways to do a broad standard calibration, and Benoit's Universal Calibration procedure (with or without an on-line viscometer) may also be used. We will discuss each of these in some detail:

Relative, Narrow Standard Calibration

We call the conventional narrow standard calibration technique a relative calibration because the molecular weight averages obtained are relative to the calibrant. For example, if one were running polyethylene as a sample, and calibrated the column set with polystyrene narrow standards, the molecular weights obtained after integration would be based on polystyrene, and incorrect for polyethylene. This is fine for many people, however, who are simply comparing molecular weights obtained for an unknown against a set of "acceptable" values. Whether these molecular weight values are really "absolute" for their polymer of interest is unimportant; just as long as these values obtained are in the acceptable range.

There are a few other narrow standards available for organic GPC, such as poly(methylmethacrylates), polyisoprenes, polybutadienes, poly(THF), but certainly polystyrene is the major narrow standard used for organic GPC analysis. In the case of aqueous GPC, poly(ethylene oxides) are the most widely used, along with poly(ethylene glycols) for low molecular weight, and the pullulans, which are polysaccharides based on triose structures. After running the series of narrow standards, a polynomial fit is then performed, (usually third or fifth order), and the resulting log M vs. retention time (or volume) calibration curve is plotted.

Broad Standard Calibration

One can also calibrate the GPC column set using a broad standard that is the same polymer being run as the unknown. Broad standard can be purchased from a variety of different vendors, and the standard should be well characterized, i.e. the number, weight, Z and possibly viscosity average molecular weights have been determined by alternative methods, (membrane osmometry, light scattering, ultracentrifugation, for example). An alternative would be to use an actual "sample" of material (that is present in a significant quantity), where the molecular weight averages have been determined by these other techniques. The advantage to this is being able to use a polymer that has the same structure as the unknown samples being analyzed day in and day out.

The molecular weight averages that are known are entered into the software, and the broad standard is chromatographed in the usual manner, under the same conditions that the unknowns will be chromatographed. The software does a Simplex search routine, fitting the chromatographed broad standard shape to the given molecular weight averages. The resulting calibration curve will consist of the data points for each average. If only a number and weight average are provided, the resulting calibration curve will consist of these two points plus the peak molecular weight, or a three point calibration curve. This broad standard is based on work done by Hamielec in 1969. It is recommended that two broad standards of different molecular weights be used, to increase the molecular weight range of the calibration curve. Even with using two broad standards with two known molecular weight averages, only a six-point calibration curve is obtained, (using the peak molecular weight values from the result of the search routine). However, for the QC lab running the same polymer every day, in the same molecular weight range as the broad standards, this calibration works very nicely, and provides absolute molecular weight weights.

There are a few other narrow standards available for organic GPC, such as poly(methylmethacrylates), polyisoprenes, polybutadienes, poly(THF), but certainly polystyrene is the major narrow standard used for organic GPC analysis. In the case of aqueous GPC, poly(ethylene oxides) are the most widely used, along with poly(ethylene glycols) for low molecular weight, and the pullulans, which are polysaccharides based on triose structures. After running the series of narrow standards, a polynomial fit is then performed, (usually third or fifth order), and the resulting log M vs. retention time (or volume) calibration curve is plotted.

Universal Calibration

The concept of Universal Calibration was introduced by Benoit, et. al. in 1967. Instead of plotting the log molecular weight of a series of narrow standards vs. retention, the log of the product of the intrinsic viscosity [η] and molecular weight M is plotted vs. retention. The [η]M product is related to the hydrodynamic volume. Benoit found that plotting a series of hydrodynamic volume values for a variety of narrow standards resulted in a singular calibration curve. In other words, all of the points fit the same curve. Once this "Universal" calibration has been established, any random coil polymer can be run in the appropriate solvent, and the molecular weight determined based on the Universal curve. Benoit used a glass capillary viscometer to measure the viscosities of the narrow standards and samples. After establishing the Universal curve, we can also plot the log of the intrinsic viscosity vs. the log of the molecular weight for the narrow standards. This plot is called the viscosity law plot, or, the Mark-Houwink plot. The slope of this plot is alpha, (sometimes called α), and the intercept is called log K. The resulting equation, known as the Mark-Houwink equation, is:

A Typical Universal Calibration curve and viscosity law plot for a series of polystyrene standards.

The Polymer Handbook contains many K and alpha values for a variety of different polymer/solvent combinations. One can input these empirical constants into many of the commercial GPC software packages available today, and obtain "absolute", or accurate molecular weights for many polymers. One must be sure that the values in the handbook are accurate for the polymer to be analyzed, or errors will occur. 

Today, we can use an on-line viscometer detector, along with the differential refractive index (dRI) detector, to directly obtain the molecular weight of each slice. The dRI is the concentration (C) detector, and the viscometer detector gives us the product of intrinsic viscosity and concentration ([η]C). Dividing the viscometer signal by the dRI signal gives us the intrinsic viscosity [n _i] of each slice across the polymer peak. We now know both the intrinsic viscosity and, of course, the retention time (or volume) of each slice, so we can go back to the Universal Calibration curve and obtain the molecular weight of each slice, M_i. This Universal Calibration concept has wide applicability, especially for random coil type polymers, which represents the majority of polymers being analyzed today. Other polymer conformations, such as rods, spheres, or globular shaped (such as proteins) may not behave the Universal concepts. There can be no interaction of the polymer and the eluent or column packing material for Universal Calibration to work.  

Another advantage to using Universal Calibration and on-line viscometry/dRI detection is the ability to determine how branched a polymer is, relative to a known linear polymer standard. This technique is quite sensitive to long chain branching (as opposed to short chain branching), and is important to help predict how a certain polymer will process, or what the final physical properties will be, in comparison to the linear counterpart. 

As an example, one can run a linear polyethylene broad polymer, (such as "NBS 1475", or any other known linear polyethylene), with the resulting Mark-Houwink values being determined from the experiment. The resulting Mark-Houwink plot (or viscosity law plot) will be linear, with a constant slope, (alpha will be constant across the molecular weight distribution). The K and alpha values can then be input into the software, and any subsequent unknown polyethylenes can be analyzed, with the viscosity law plot being compared to that of the known linear polyethylene.

If the unknown exhibits any long chain branching, the viscosity/molecular weight relationship is not linear; i.e. the viscosity will not increase linearly with molecular weight. The greater this deviation from linearity, the greater the level of long chain branching. An accurate alpha can be obtained for a branched polymer only at low molecular weights, where there is no long chain branching, and the slope is constant. Once the polymer is at a molecular weight where there is long chain branching, alpha is continuously changing, (may even approach zero), and becomes meaningless. A simple ratio of the viscosity law plot of the branched polymer to the linear polymer gives us the branching index, (g'), where: g' = [η ]_br/[η]_lin One can do further calculations to determine the branching frequency, what type of branch is present, etc. It is obvious that adding a viscometer detector on-line with a refractive index detector can provide much more information about your polymer, specifically:

• "Absolute" or accurate molecular weights for your polymer via Universal Calibration
• Calculation of the intrinsic viscosity of your polymer
• Determinationof branching

Performing a GPC Analysis

The most important criteria in preparing to do a GPC analysis is finding a suitable solvent to dissolve the polymer. This sounds trivial enough, but remember that GPC is a separation technique based on the size of the polymer in solution. Polymer chains will open up to a certain relaxed conformation in solution, and the solvent chosen will determine what this size will be. Many polymers are soluble at room temperature in various solvents, but in some cases, (especially for highly crystalline polymers), high temperature is required for dissolution. Another important aspect for GPC sample preparation is the concentration chosen. If the mass loading of the sample onto the column set is too high, there may be concentration or viscosity effects, which will give rise to incorrect elution volumes. Another consideration is whether or not to filter the polymer solution. We will discuss some of these sample preparation considerations.

Solvent Selection Guide for Room Temp. Aqueous Soluble Polymers 

Note that in many cases where sodium nitrate is shown, many workers have used acetate, sulfate, sodium chloride, etc. We recommend sodium nitrate, which has shown to minimize ionic interferences very consistently for neutral and anionic compounds. The reason for these various eluents is because of the overall anionic charge of the packing material. The methacrylate based gel packing for aqueous GPC has an overall anionic charge, which can cause ion exclusion for anionic samples and ion adsorption for cationic samples if run in water alone. 

One should always filter the eluent under vacuum before use in the chromatographic system. With the organic solvents, a fluorocarbon filter is generally used. The filter pore membrane size is generally 0.45m (micron). For aqueous GPC (filtration of the water), an acetate type of membrane filter is used. If one is preparing to do a light scattering analysis, it may be a good idea to filter the eluent though a 0.20m filter. Some organic solvents such as DMF are very viscous and do not wet the surface of the fluorocarbon filter very well. A good tip is to wet the filter surface initially with methanol, then quickly start the DMF filtration. You would then discard this small volume of methanol/DMF mixture, then start the DMF filtration before the filter dries out.

Concentration

Once we have chosen the proper solvent for the analysis, the next step is to prepare the narrow standard and sample solutions. We need to be careful to use enough concentration to be able to get an acceptable signal-to-noise, but at no risk of overloading the column and risking concentration effects. The table below is a general "rule of thumb" to be used as a guide as to what concentration should be prepared. These concentrations are in percent, where 1.0 mg/ml is 0.10%. No correction is made for temperature, so everything is assumed to be prepared at room temperature. Remember that if viscometry or light scattering analysis is being performed, the exact mass injected needs to be determined. This will require density corrections if the analysis is being done at elevated temperature. These concentrations shown are to be used assuming a maximum of 100ul injection volume per column. 

Preparing the Sample

Now that we have successfully dissolved the standards and samples in our chosen solvent, and have installed our GPC columns, we are ready to start making injections. The next choice we have to make is whether or not we should filter the sample solution. In nearly all cases, we should filter the sample solution prior to injection.  

Generally, as in the case of the solvent filtration discussed previously, we would choose a 0.45 m membrane fluorocarbon filter. In some cases, where there is very fine particulate material (such as carbon black, titanium dioxide, silica, or other fillers), a 0.20 m filter may be used.  

Obviously, when we start to use very fine filter sizes, polymer shear may become a concern. Filtering a high molecular weight polymer through a 0.20m filter would certainly cause some shear degradation. One may have to choose not to filter the sample at all, and hope there is no pressure increase due to plugging of the system in-line filter or column frit.  

Now we can start making injections of the standards and samples. As mentioned previously, we will inject a maximum of 100ul per column, at the concentrations shown in the table. Our run time will be approximately 15 minutes per column at a flow rate of 1.0 mL/min so the analysis time for a three column set would be ~45 min.  

Once the sample set has been run, it is time for the data handling system to process the results according to the integration method we designated and furnish a completed report. This can be done automatically in a "Run and Report" mode in Empower  Software, or we may choose to go in to each raw data file and manually integrate each sample.