Multi-detector GPC Characterization Drew Poche’

Outline Basics-On the mechanism of GPC Detection –Light Scattering –Viscometry Putting it together- multi-detector GPC Lots of numbers-What’s it good for?

How big is big? Drew Poche’ Materials Characterization Dow Chemical, Plaquemine

Alphabet Soup SEC-Size Exclusion Chromatography Includes rigid stationary phases GPC-Gel Permeation Chromatography “Soft” gel stationary phases GFC-Gel Filtration Chromatography Separation of biological molecules (nature’s polymers) in an aqueous environment

HPLC? You bet. Mobile phase pump auto-injector column(s) detector(s) data acquisition Temperature control

Putting it in perspective Typical organic molecule vs typical polymer molecule Mass spec GC-MS, LC-MS NMR Modeling, quantum mechanics Other colligative property based measurements EASY TOUGH Measuring size and molar mass

Polymer standards--Column Calibration

Can it get worse? Typical synthetic organic molecules in a pure sample are all the same molar mass Typical synthetic polymer molecules in a pure sample may differ not only in molar mass but also in molecular shape Ordinary small molecule sample Ordinary synthetic polymer sample

GPC Mechanism Wiggling (chain conformations) determines average dimensions and pore permeation Eliminate enthalpic interactions Entropic effects alone govern

Getting it right Problems, Problems Polymer chains are not created equal MaMa MbMb McMc = = VaVa VbVb VcVc < > Solutions Absolute molecular weight detectors (light scattering, viscometry) Universal calibration

Bent out of Shape First, let’s select a couple of chain conformations... Then, stuff them into a confined space and see what happens Forbidden conformation Allowed conformation Loss of conformational entropy dictates partitioning between pore and non-pore space Center of mass too close to wall

Let’s clarify Bottom line: or

Who wants to be a millionaire? If the polymer chains are restricted to one configuration (e.g. rods), what drives the partitioning between pore space and non-pore space? a) rotational orientationb) pore gremlins c) there’s no such thing as rodd) Huh? shaped chains

If GPC really separates by SIZE, which chain dimension correlates with elution order? I don’t know It’s a rather complicated question because pore characteristics and chain geometry influence the magnitude of the equilibrium constant, K GPC Leading candidates: radius of gyration, R g hydrodynamic volume, R h 3 or V h (universal calibration) For the million dollars….

Column selection FIPA

Making sense of the chromatogram Synthetic polymers are composed of a distribution of chain sizes We use statistics to get average dimensions to describe the bulk sample Commonly computed from GPC: M n the arithmetic mean M w weight average Computing Mw and Mn is sensible since these averages “fall out” naturally from experiments used to measure molar mass –M n from colligative or counting methods (NMR, osmometry, and those boring experiments you did in freshman chem) –M w from methods sensitive to molecular size (LS, centrifugation)

Time to count

Where do n i and M i come from?

Multiple numbers of standards Column Calibration That’s one source of M i Problem: only equivalent M i is obtained

E pluribus unum Universal Calibration Gives molar mass without regard to chain architecture Valid? Nearly always. Suggests: L  V h

Wait a minute! If I don’t know how M and [  ] are related for my polymer, how do I use universal calibration? YOU DON’T Mark-Houwink (empirical power law)

“…too much dancing and not nearly enough prancing...” C. Montgomery Burns, commenting on GPC prior to molar mass sensitive detectors Visible light scattering used for polymer characterization has been around almost as long as chemists have believed in polymers However, GPC detectors based upon the technique are relatively new (1970s) Light scattering, by its nature, returns the weight average molar mass

Visible Light vs. polymer chain Particle view: Incident light “pushes” electrons, producing transient dipoles Thermo view: Incident light couples to concentration gradient found in real solutions

How to get M w from the measurement MALLS uses Eq 1 and 2 and returns M w and R g LALLS and RALLS use Eq 3 and return M w caveat: RALLS requires a shape correction when R g approaches (  /50)n Scattering contains dn/dc Particle form factor

How LS returns other molar mass averages Simple assumption….monodisperse fractions from the GPC columns. Therefore, M w,i = M i This assumption may lead to an over- estimation of M n

“I’m going to describe the apparatus first before I set it motion. Then you’ll be able to follow the proceedings better.” Franz Kafka Advantages –MALLS gives molecular architecture information without assumptions IF there is a measurable angular dependence on the scattered light intensity –RALLS is more forgiving of dusty samples and returns essentially the same information as LALLS IF the polymer is small compared to  –LALLS is more sensitive, requires no correction over a huge range of molar mass

“Do you suppose,” the Walrus said, “that they could get it clear?” “I doubt it,” said the Carpenter, and shed a bitter tear. Lewis Carroll DUST, GELS, or assorted particulate vs. Light Scattering

Column Calibration? Not!

Specific refractive index increment If polymer solvent combo is isorefractive, no scattering will be observed The bigger the better Depends on: solvent temperature light wavelength  n = n - n o

Why dn/dc matters

The plot thickens-Viscosity Viscometers as GPC detectors are based upon the measurement of a differential pressure between pure solvent and polymer solution   sp

How to get [  ] i Software computes both  sp,i and  rel,i Solomon-Gottesman [  ] i = 2 1/2 (  sp,i -ln(  rel,i ) 1/2 /c Important point:  sp and  rel are concentration dependent [  ] is, by definition, a “zero” concentration property

Like LS, the viscometer is sensitive to bigger chains

All that work for two numbers? Re-visit universal calibration…units analysis M w x[  ]  (R h ) 3 gmol -1 xcm 3 g -1 =cm 3 mol -1 From two simple measurements we can estimate size or volume! Implication: chain architecture elucidation

Let the fun begin Getting M i and [n] i from GPC fractionation mean: –Rapid M-H relationships –Molecular architecture determinations –Calculation of other polymer dimensions –Correlation to physical properties –Identification of tiny fractions of high molar mass material

From a few months to a few minutes!

Behold the Power of M-H [  ] = KM a a parameter:approaching 0 ; spheres 0.5 ;theta condition for linear chains ; expanded coils 1.8 ; ideally rigid rod a may or may not change with branching K parameter:shifts with comonomer composition or branching density

What happens when branches are present Star branched

Had enough? More commonly encountered long chain branching Have you noticed that the hydrodynamic dimensions of a branched polymer are “shrunken” compared to its linear counterpart?

Branching? YIKES! Triple detection GPC measurements (LS,VIS, DRI) Determine [  ]-Mw relationship (M-H values) Compare [  ]-M w relationship to that of a linear sample Apply appropriate branching model to calculate branching density  Possibilities: star, off-center star, comb, random long chain branching, H, super-H, Pom-Pom

Dependence of Performance Properties on Molar Mass