Multidetector GPC Characterization

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Multi-detector GPC Characterization

• Drew Poche

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Outline

• Basics-On the mechanism of GPC
• Detection
• Light Scattering
• Viscometry
• Putting it together- multi-detector GPC
• Lots of numbers-Whats it good for?

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How big is big?

• Drew Poche
• Materials Characterization
• Dow Chemical, Plaquemine

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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 (natures
  polymers) in an aqueous environment

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

• Typical organic molecule vs typical polymer
  molecule

Measuring size and molar mass

• Mass spec
• GC-MS, LC-MS
• NMR
• Modeling, quantum
• mechanics
• Other colligative
• property based
• measurements

EASY
TOUGH
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Polymer standards--Column Calibration
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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
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GPC Mechanism
Wiggling (chain conformations) determines average
dimensions and pore permeation
Eliminate enthalpic interactions Entropic
effects alone govern
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Getting it right

• Problems, Problems
• Polymer chains are not created equal

Mc

Ma
Mb

Vc
lt
Va
Vb
gt

• Solutions
• Absolute molecular weight detectors (light
  scattering, viscometry)
• Universal calibration

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Bent out of Shape
First, lets select a couple of chain
conformations... Then, stuff them into a
confined space and see what happens
Center of mass too close to wall
Forbidden conformation
Allowed conformation
Loss of conformational entropy dictates
partitioning between pore and non-pore space
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Lets clarify
Bottom line
or
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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 orientation b) pore gremlins
• c) theres no such thing as rod d) Huh?
• shaped chains

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If GPC really separates by SIZE, which chain
dimension correlates with elution order?
For the million dollars.

• I dont know
• Its a rather complicated question because pore
• characteristics and chain geometry influence the
  
• magnitude of the equilibrium constant, KGPC
• Leading candidates
• radius of gyration, Rg
• hydrodynamic volume, Rh3 or Vh (universal
  calibration)

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Column selection
FIPA
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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 Mn the arithmetic
  mean
• Mw weight average
• Computing Mw and Mn is sensible since these
  averages fall out naturally from experiments
  used to measure molar mass
• Mn from colligative or counting methods (NMR,
  osmometry, and those boring experiments you did
  in freshman chem)
• Mw from methods sensitive to molecular size (LS,
  centrifugation)

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Time to count
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Where do ni and Mi come from?
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Multiple numbers of standards Column Calibration

• Thats one source of Mi

Problem only equivalent Mi is obtained
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E pluribus unum

• Universal Calibration
• Gives molar mass without regard to chain
  architecture
• Valid? Nearly always.
• Suggests L ? Vh

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Wait a minute!

• If I dont know how M and h are related for my
  polymer, how do I use universal calibration?
• YOU DONT
• Mark-Houwink (empirical power law)

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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

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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
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How to get Mw from the measurement
Scattering contains dn/dc
Particle form factor
MALLS uses Eq 1 and 2 and returns Mw and Rg LALLS
and RALLS use Eq 3 and return Mw caveat RALLS
requires a shape correction when Rg approaches
(lo/50)n
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How LS returns other molar mass averages

• Simple assumption.monodisperse fractions
• from the GPC columns. Therefore,
• Mw,i Mi
• This assumption may lead to an over-estimation of
  Mn

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Im going to describe the apparatus first before
I set it motion. Then youll 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 lo
• LALLS is more sensitive, requires no correction
  over a huge range of molar mass

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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
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Column Calibration? Not!
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Specific refractive index increment

• The bigger the better
• Depends on
• solvent
• temperature
• light wavelength

Dn n - no
If polymer solvent combo is isorefractive, no
scattering will be observed
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Why dn/dc matters
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The plot thickens-Viscosity

• Viscometers as GPC detectors are based upon the
  measurement of a differential pressure between
  pure solvent and polymer solution
• ? ? hsp

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How to get hi

• Software computes both hsp,i and hrel,i
• Solomon-Gottesman
• hi 21/2(hsp,i-ln(hrel,i)1/2/c
• Important point hsp and hrel are concentration
  dependent
• h is, by definition, a zero
  concentration property

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Like LS, the viscometer is sensitive to bigger
chains
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All that work for two numbers?

• Re-visit universal calibrationunits analysis
• Mw x h ? (Rh)3
• gmol-1 x cm3g-1 cm3mol-1
• From two simple measurements we can estimate size
  or volume!
• Implication chain architecture elucidation

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Let the fun begin

• Getting Mi and ni 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

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From a few months to a few minutes!
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Behold the Power of M-Hh KMa

• a parameter approaching 0 spheres
• 0.5 theta condition for linear chains
• 0.7-0.8 expanded coils
• 1.8 ideally rigid rod
• a may or may not change with branching
• K parameter shifts with comonomer
  composition or branching density

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What happens when branches are present
Star branched
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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?
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Branching? YIKES!

• Triple detection GPC measurements (LS,VIS, DRI)
• Determine h-Mw relationship (M-H values)
• Compare h-Mw 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

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Dependence of Performance Properties on Molar Mass