Characterization of Polymer Chain Architecture:Size-Exclusion

Chapter 3

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Characterization of Polymer Chain Architecture: Size-Exclusion Chromatography with Intensity and Dynamic Light Scattering and Viscometric Detectors Patricia M. Cotts Corporate Center for Analytical Sciences, DuPont Central Research and Development, Wilmington, DE 19880

The architecture of a polymer chain is critical to the properties of the polymeric material in film or bulk. The presence of branches of various types, backbone rigidity, polyelectrolyte effects or dense multimolecular aggregates all can be classified as architectural properties in solution that can dramatically affect bulk properties. Advances in on-line detection of light scattering (both static and dynamic) and viscosity enable characterization of polymeric architecture simultaneously with determination of molecular weight. Brief introduction and description of these light scattering and viscometric analyses are given, followed by specific applications. Particular emphasis is given to the most recent development of dynamic light scattering

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© 2005 American Chemical Society

In Multiple Detection in Size-Exclusion Chromatography; Striegel, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 2004.

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Introduction The vast majority of size exclusion chromatography (SEC, or equivalently, gel permeation chromatography, GPC) analyses are done to determine a polymer molecular weight and molecular weight distribution. Usually, a series of polymers of known molecular weight is analyzed and a curve relating the molecular weight to the elution time is constructed. The molecular weight distribution of polymers of interest are then evaluated from their elution time by reference to this curve. This works well when the polymers are the same, but series of polymers of known molecular weight are available for only a very few polymers. Even with these, concentration effects or column interactions can frequently affect elution times. For the many polymers not available as a molecular weight characterized series, the universal calibration is popular. An empirical correlation of elution time with a hydrodynamic molecular volume (defined as the product of intrinsic viscosity and molecular weight) has been shown to exist for a wide variety of polymers. Thus polymers of equivalent hydrodynamic volume are expected to elute at the same elution volume even if molecular weights are different. At the same molecular weight, more compact polymers (branched, or with heavier sidegroups) elute later than more extended polymers. The intrinsic viscosity ([η], expressed in dL/g or mL/g) is an indication of the spatial dimensions of the polymer molecule in dilute solution. The dependence οϊ [η] on the molecular weight M can be used to determine the dimensions of the polymer, and its architecture, especially when this information is available over a range of molecular weights. Alternative measures of the polymer size are the root-mean-square radius of gyration from the angular dependence of intensity light scattering, and the limiting diffusion coefficient obtained from dynamic light scattering. Direct determination of these parameters asfractionatedpolymers elute from an SEC column is a powerful tool for structural charaterization. A review of the theoretical relationships among these various size parameters, experimental data, and their dependence on polymer chain architecture is included in a recent book by Graessley. Frequently, determination of the intrinsic viscosity, [η], is used to determine the molecular weight indirectly through use of a known Mark-Houwink relation, [7]]=KAf. If it is assumed that the universal calibration (the product [η]M as a function of elution volume) is valid for a given polymer, and a viscosity detector is used to determine [η], then M may be determined from the universal calibration curve, yielding M and independently across the distribution. This 1



54 information may be used to assess architectural variations such as branching, stiffness or aggregate formation. Addition of a light scattering detector provides a direct determination of molecular weight that is not based on any empirical correlation with elution time. This presents a number of advantages, especially for architectural studies where subtle changes in size as a function of M are critical. Although Mark-Houwink relations for many polymers are reported in the literature, typically a large range of the parameters Κ and a is reported for a given polymer, and a linear relation is only valid over a limited range of M Finally, use of the universal calibration can introduce systematic uncertainties that can be misleading for architectural determinations. Direct independent determination of both molecular weight and dimensions is greatly preferred.

Light Scattering

Intensity or Static Light Scattering Classical light scattering has long been a primary tool for evaluation of polymer molecular weight. For a more detailed discussion, see the chapter by Wayne Reed in this volume. A recent book on polymer solutions by Teraoka also provides an excellent introduction to this topic. Excess scattering (minus solvent scattering) is determined for polymer solutions as a function of scattering angle and concentration, and data is reduced using a Zimm plot or other means to extrapolate to zero scattering angle and concentration: 2

(1)

where

/>-'(?) = 1+ 2

2

(2)

with K-47ên (dn/dc) /N X', where dn/dc is the differential refractive index increment and the scattering vector q-{4m/X)sin(®2). Symbols have their usual A


55 meaning, Θ is the scattering angle, A is the second virial coefficient, and R is the root-mean-square radius of gyration. Equation 2 for the single chain form factor or internal structure factor P(q), yields R independent of shape for qR l, the form factors P(q) for different architectures begin to deviate from each other, as shown in Figure 1. These differences are often used to determine particle shapes for scattering at much higher q, as for neutrons and X-rays. 2

g

g

g

g


w

g

0

1

2

3

4

5

Figure I. Particle form factor for spheres, random coils and rods. In this plot k is used to represent the scattering vector rather than q as in the text. From reference 2.

For light scattering, determination of R as afonctionof M is more useful as a determination of polymer chain architecture. While previously this required large amounts of polymer, tedious fractionation, and extensive analytical measurements, the availabilty of multi-angle light scattering instruments for coupling to an SEC has greatly advanced this capability. R can now frequently be determined over a decade in M on narrowfractionsusing less than 1 mg of polymer! Combining a few different molecular weights can extend this to several decades, which is important for semi-flexible polymers, as dicussed near the end of this chapter. For flexible Gaussian polymers, the R determined by light scattering is a zaverage, whereas the molecular weight determined by light scattering is a weight-average. This complicates determination of polymer dimensions for broad distribution polymers. This problem is greatly reduced when the polymers are separated using SEC. However, at a given elution volume, there is still a distribution of molecular weights, and the differing averages for R and M should g

g

g

g


56 be kept in mind in data interpretation. When used as a detector for SEC, light scattering is typically determined at very high dilution, often nearly an order of magnitude lower concentration than off-line light scattering. Thus, the second term in Equation 1 can usually be neglected, even in good solvents where A is large. In off-line light scattering, excess scattering intensities are typically similar in magnitude to solvent scattering. With on-line light scattering, it is possible to determine excess scattering intensities that are only 5% of the solvent scattering. This is primarily due to the experimental advantages of the on-line instrmentation, in which the SEC column acts as a very efficient filter, the flow through cell eliminates extraneous scattering at the air-liquid interfaces, and the fixed photodiodes permit calibration of small variations in scattering volume.


2

When only a concentration detector, such as refractive index or UV-Vis, is used, the mass of the polymer injected onto the column is often chosen independent of the molecular weight. With light scattering and viscometric detectors, the response is nominally proprotional to the molecular weight. Thus, low molecular weight polymers must be analyzed at higher concentrations, and very high molecular weight polymers must be analyzed at very low concentrations. Fortunately, this is very consistent with the requirements of effiicient separation by size exclusion columns. In particular, very large polymers (very high molecular weight, or highly extended) must be injected at very high dilution to minimize overloading effects in separation. While these effects can be difficult to detect with only a concentration detector, with a light scattering detector, this is often detected as an inflection in the logarithmic dependence of the molecular weight as a function of elution volume. For very narrow distribution polymers, the width of the peak is characteristic of chromatographic band broadening rather than the molecular weight distribution, and the molecular weight from light scattering is usually independent of elution volume across the narrow peak.

Dynamic Light Scattering Dynamic light scattering (DLS), also known as quasi-elastic light scattering (QELS) or photon-correlation spectroscopy (PCS) is the most recent addition to on-line detectors for SEC. For more detailed introduction to dynamic light scattering, a number of references are available. " The introduction of small solid state diode lasers, as well as avalanche photodiodes, and single-mode fiber optics, permits a tremendous reduction in size for instrumentation for dynamic light scattering. While typical off-line instruments reside on a large optical table, and use a motorized goniometer to access different scattering angles, the on-line 2

5



57 instruments utilize fixed photodetectors, and are predominantly limited to a single scattering angle, typically 90 degrees. Dynamic light scattering is widely used as a technique for particle sizing in the sub-micron range. These analyses are done on colloids and suspensions of particles which are compact and essentially rigid. Particle sizing instruments are often limited to 90 degreees scattering. As discussed below, while this often adequate for rigid particles, it is frequently not adequate for flexible chain polymers, where an angular dependence is often present, and sizes are smallOne of the advantages of dynamic light scattering is that it utilizes essentially the same instrumentation as intensity light scattering, requiring only the addition of a correlator and some modification to the detector optics. Close examination of the scattering intensity as a function of time reveals fluctuations that appear to be noise, but actually reflect the dynamics of the scattering entities. While intensity light scattering measures the average intensity, dynamic light scattering is used to determine the time scale of the fluctuations. In this sense, some requirements of the instrumentation are less stringent; the solvent scattering does not need to be subtracted, the scattering volume need not be known as accurately, and accurate concentration and dn/dc are not needed to obtain a particle size. One modification to detector optics is the addition of an amplifier discriminator to the photomultipier tube (PMT) or avalanche photodiode (APD). This converts the analog scattering intensity into a series of photon pulses that can be counted by the correlator. The correlator then calculates the product of the scattering intensity at time t and t+τ, as a function of v.

For τ—>0, there is a high correlation in the intensity I(t) and I(t+r), and the initial value of the autocorrelation function is (I ). At long delay times, all correlation is lost, and the autocorrelation function decays to the square of the average scattering intensity, (if , as shown in Figure 2. The factor f is the coherence factor, 0

Characterization of Polymer Chain Architecture:Size-Exclusion

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