Chain Linkage in a Polymer

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Chain Linkage in a Polymer

• Intrinsic Viscosity Experiment

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Chain Linkage in a Polymer
Question How regular is the orientation of the
monomer units in a polymer?
The reaction rate for the head-to-head
polymerization step, ka , differs from the rate
for the head-to-tail step, kß
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The rates of the two depend upon their activation
energies
S is the steric factor which is the ratio of
probabilities for the head-to-head vs.
head-to-tail will not be prevented to bond by
steric or geometrical obstacles. Both the
steric factor and the thermal activation energy
difference can be found by measurements at
different temperatures.
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What is the frequency of head-to-head
occurrences? This is the fraction of
head-to-head linkages compared to the total
number of monomer units. This fraction is
?. Assume that cleavage only occurs at 1,2-glycol
structures and that all such are cleaved. ? must
be equal to the increase of the number of
particles in the system divided by the total
number of monomer units in all of the molecules
in the system. These numbers are inversely
proportional to their respective molecular
weights
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For polyvinyl alcohol (PVOH) the monomer
molecular weight is 44 and using the equation
relating the viscosity average molecular weight
to the number average molecular weight for PVOH,
we get
This allows viscosity average molecular weights
to be used directly in calculation of the ratio.
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Polymer Molecular Weights
Weight average molecular weight, Mw
Ci is the weight concentration in g/cm3. Mi is
the molecular weight of the i-th type particle.
Number average molecular weight, Mn
Ni is the number concentration in number/cm3.
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Because the viscosity is dependent on both size
and mass, it produces its own molecular weight,
the viscosity average molecular weight, Mv which
is that given by the Mark- Houwink relation. For
a monodisperse (all same weight) polymer, it can
be shown that Mv Mn M. For a polydisperse
polymer the two are related by a distribution
function such that
For PVOH, a 0.76. This leads to
When a gt 0.50, then Mv begins to approach Mw and
is the same when a 1.
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Physical Basis of Viscosity
Flow in fluids can be thought of as layers
flowing past each other. For example for a
fluid flowing through a cylindrical tube the
flowing liquid can be imagined as contiguous
cylindrical shells of decreasing radius that are
flowing. The layers flowing past each other
exert a drag, internal viscous force, that will
slow down the more rapidly flowing layer and
speeds up the slower moving layer. In essence,
momentum is being transferred from one layer to
the other. An external force can be imagined
that will oppose this drag and maintain a
constant velocity gradient between the layers.
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The force opposing the drag, f, and the velocity
gradient that is perpendicular to the direction
of flow, du/dx, are related by
A area upon which the force acts ? viscosity
( or coefficient of viscosity)
This is a phenomenological equation and all of
the interesting properties are contained in the
coefficient of viscosity. Upon what molecular
properties will the viscosity depend?
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Molecular properties contributing to viscosity

• Molecular size
• Molecular shape
• Intermolecular interactions
• Structure of the liquid itself

There are many equations that relate viscosity to
composition, but none are always applicable. An
example is
where a and b designate components and X mole
fractions
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• Viscosity is particularly influenced by solutions
  of polymers.
• Polymer solutions viscosity depend on
• Concentration of the polymer solute
• Molecular weight of the polymer
• Shape of the polymer
• Specific viscosity, ?sp relative increase in
  the viscosity due to the
• addition of
  solute.

where the subscript o refers to the pure
solvent. The solute concentration ( c )
dependence can be expressed as
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? intrinsic viscosity, cm3/g and k is
constant that is around 0.35 in a good solvent
and less than that in a poor solvent where the
solute-solvent interactions are poor. It is
desirable to have a viscosity that is independent
of the concentration. This is achieved by
defining the viscosity at infinite dilution this
is the intrinsic viscosity, ?
The intrinsic viscosity is sometimes called the
limiting viscosity number.
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The intrinsic viscosity can be related to the
molecular weight of the solute. For molecular
weights up to about 8000 dalton
Where M is the molecular weight. For solutions
of polymers of molecular weights above 10,000
dalton there is the so-called Mark-Houwink
relation ? KM a
The various Ks and a are constants that are
specific to the particular solvent-solute pair
and a is particularly related to the shape of
the solute molecule. Tables of these constants
for many systems can be found in the literature.
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• Characteristics of a
• For rod-shaped molecules a 2
  (theoretical)
• For randomly coiled chains a 0.5 0.8
• For hard spherical molecules a 0

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Absolute measurement of viscosity is difficult
and time-consuming. Usually relative viscosities
that compare the effect of the viscosity of a
given liquid to a standard are more common. The
capillary method of Poiseuille is a direct
approach to measurement of viscosity that
determines the time of flow through a capillary
of a measured volume of liquid under constant
pressure head. Poiseuilles equation for laminar
flow is used
r radius of capillary p
pressure head t time of flow for volume, V
l length of capillary
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Ostwald Method

• Variation of Poiseuille method
• Measures relative viscosity
• Time for fixed volume of liquid to fall through a
  capillary into a reservoir
• Depends on density
• Depends on viscosity
• Reference liquid is used

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Taking the subscript 2 to refer to the
reference liquid, and dropping the 1 subscript,
gives the relative viscosity, ?r
For high precision work, a kinetic energy
correction (lt1) may be incorporated
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Experimental Considerations

• Viscometer must be CLEAN for each measurement
• Control temperature to 0.1Co. The temperature
  coefficient of viscosity is usually about 1 per
  K.
• Make sure the viscometer is vertical
• Filter liquid before use to prevent solids from
  clogging capillary

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• Raise liquid level by forcing air into the
  reservoir end rather than by pulling air out of
  capillary end.
• In putting the tubing onto the viscometer, hold
  the end to which the tubing is being attached.
  Do not hold by the other end since even a small
  torque may break the viscometer.
• In removing the tubing, push it off the tube.
  Never pull tubing off a tube since it will
  contract and adhere more tightly.

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Calculations

• From standard sources determine the density of
  water and viscosity at your operating
  temperature. Water is the reference liquid.
• Calculate the viscosity and concentration (g/100
  ml solution) of each solution studied

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• Calculate ?sp/c and (1/c)(ln ?/?o) and plot
  both against c.
• Extrapolate the best straight line to c 0.
  (least-squares)
• Obtain ? for both the pristine and
  degraded polymer
• Obtain Mv from the Mark-Houwink equation for
  both
  the pristine
  and degraded polymer systems.
• Calculate ?.
• Report values with the polymerization
  temperature.
• Discuss the relationship between ? and ka
  and kß.
• Discuss questions raised in the DISCUSSION
  section of the text for this experiment.