Download Intrinsic Viscosity: Chain Linkage in Polyvinyl Alcohol

Chemistry 3303
PVOH
Winter 2012
Intrinsic Viscosity:
Chain Linkage in Polyvinyl Alcohol
Recommended Preparatory Reading
•
Experiment 27 in Shoemaker
Introduction
The basic chemical structure of a synthetic polymer is well understood. However, many
of the physical properties of polymers depend on characteristics such as chain length, degree of
chain branching, and molar mass, which are not easy to specify in terms of chemical formula.
Also, in a given sample of polymer, chain length is seldom uniform leading to a distribution of
molar masses, another important characteristic.
A monodisperse polymer is one in which all of the polymer molecules have the same
molar mass; a polymer which is polydisperse consists of molecules with varying molar masses.
A sample of a monodisperse polymer can be prepared from polydisperse starting material by a
process called fractioning (done on the bases of solubility in various solvent mixtures).
In this experiment the fraction of head-to-head (reverse) linkages in a sample of polyvinyl
alcohol (PVOH) will be determined. PVOH has a minimal amount of branching of its chains and
is unusual among synthetic polymers in that it is soluble in water. This makes the use of PVOH
important as a component in gums and as a foaming agent in detergents.
Another interesting characteristic of PVOH is the consistency of orientation of monomer
units in the chain. Figure 1 shows the normal (head-to tail) linkages in PVOH and how a
reversed monomer unit yields a reverse (head-to head) linkage in the chain:
Tail
Head
Reversed Monomer
— ( CH2 — CHX )n — CH2 — CHX — CHX — CH2 — CHX — CH2 — ( CHX — CH2 )n — …
head-to-tail linkage
head-to-head linkage
tail-to-head linkage
tail-to-head linkage
Figure 1 – a portion of a PVOH polymer molecule illustrating the occurrence of head-to-tail and head-to-head
linkages (where X is OH).
Here, X is OH. During the synthesis of PVOH, reverse linkages commonly occur because the
activation energy required for a reverse linkage is only slightly greater than that required for a
normal linkage. This agrees with the finding of Flory and Leutner that the frequency of abnormal
additions increases with increasing temperature.
Flory and Leutner’s method (ref. 2), as described by Shoemaker, is used to determine
the fraction of reverse linkages in a sample of PVOH. The intrinsic viscosity of aqueous PVOH
solutions is obtained from viscosity measurements using an Ubbelohde viscometer. The sample
is then cleaved at reverse linkage sites by treatment with periodate, and the intrinsic viscosity is
remeasured. This is possible due to the fact that each reverse linkage yields a 1,2-glycol
structure which is cleavable by periodate. The average molecular weights of both the original
and the cleaved polymer are calculated and, hence, the fraction of reverse linkages in the
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Chemistry 3303
PVOH
Winter 2012
original sample can be found.
It is a general property of fluids that an applied shearing force that produces flow in the
fluid is resisted by a force that is proportional to the gradient of flow velocity in the fluid. This
phenomenon is known as viscosity, 𝜂. In the case of liquids, it is often measured by determining
the time of flow of a given volume, 𝑉, of liquid through a vertical capillary tube under the
influence of gravity. The viscometer that will be used for this experiment is slightly different than
the one illustrated in shoemaker. It can be shown that for a given volume of fluid:
𝜂
= 𝐵𝑡
𝜌
Equation 1
Where 𝜌 is the density of the fluid, 𝐵 is an apparatus constant which must be determined using a
liquid of known viscosity (water is often used), and 𝑡 is the time for the volume of fluid to flow
through the capillary tube.
Einstein showed that the viscosity of a fluid in which small rigid spheres are present in
dilute and uniform suspension is related to the viscosity of the pure solvent, 𝜂! , by the
expression:
𝜂
5𝜐
−1=
𝜂!
2𝑉
Equation 2
where 𝜐 is the volume occupied by all the spheres and 𝑉 is the total volume.
specific viscosity, 𝜂!" .
!
!!
− 1 is called the
Intrinsic viscosity, 𝜂 , is defined as the ratio of the specific viscosity to the weight
concentration of solute, 𝑐, in the limit of zero concentration:
𝜂!"
1 𝜂
= lim ln
!→! 𝑐
!→! 𝑐
𝜂!
𝜂 = lim
Equation 3
𝑐 is usually expressed in grams of solvent per 100 mL of solution yielding 𝜂 with units of 100
!!"
!
!
cm3 g-1. 𝜂 can be found by plotting either plotting
vs. 𝑐 or ln vs. 𝑐 and extrapolating
!
to zero concentration (the y-intercept of the best-fit line).
!
!!
In solution a long PVOH molecule contains many single bonds around which rotation is
possible, consequently the molecule is “statistically coiled” and resembles a loose tangle of yarn.
Simple statistical treatments show that the mean distance between the two ends of chain, and
also the effective mean diameter, 𝑑, of the coiled molecule, regarded as a rough sphere, should
be proportional to the square root of the chain length and thus to the square root of the molar
mass, 𝑀:
𝑑 ∝ 𝑀!
!
Flory and Leutner, working with a wide range of monodisperse specimens of PVOH
differing from one another in molar mass, established a correlation between the molar mass (as
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Chemistry 3303
PVOH
Winter 2012
determined from osmotic pressure measurements) and the intrinsic viscosity. They found that
for PVOH in aqueous solution at 25 oC:
𝑀! = 7.6×10! 𝜂
!.!"
Equation 4
The equation above is also valid for a polydisperse sample of PVOH but, it should be noted that
the molar mass so obtained is the viscosity average molar mass, 𝑀! .
When determining the molar mass of a polydisperse polymer, the result will be some sort
of average since the molecules do not have equal molar masses. An average molar mass
calculated from the measurement of a colligative property, such as osmotic pressure, is a
number average molar mass, 𝑀! . The molar mass obtained from viscosity measurements, as is
the case in this experiment, is not the same kind of average. It is a viscosity average molar
mass, 𝑀! , referred to above.
The two kinds of averages are not equal but can be related to one another using the
following expression (specific to polydisperse PVOH):
𝑀!
= 1.89
𝑀!
Equation 5
The goal of this exercise is to determine the fraction of reverse linkages (that is, the ratio
of reverse monomer units to total monomer units) in a chosen sample of PVOH. This fraction is
given the symbol Δ. For this determination of Δ it will be assumed that PVOH chain degradation
will result exclusively from cleavage of the 1,2-glycol structures by periodate and that all such
glycols are cleaved. Δ is equal to the increase in the number of molecules present in the
system, divided by the total number of monomer units represented by all molecules in the
system. These numbers are in inverse proportion to the respective molar masses, so:
1
Δ=
𝑀!!
1
−1
𝑀!
𝑀!
Equation 6
Where 𝑀! and 𝑀!! are the number average molar masses before and after cleavage,
respectively, and 𝑀! is the monomer molar mass, which in this case is 44 g mol-1. Substitution
of this molar mass into the previous equation yields:
Δ = 44
1
1
! −
𝑀! 𝑀!
Equation 7
Combining this equation with equation 5 gives an expression in which one can make use of
viscosity average molar masses to calculate Δ directly:
Δ = 83
1
1
! −
𝑀! 𝑀!
Equation 8
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Chemistry 3303
PVOH
Winter 2012
Experimental
Five polyvinyl alcohols are available for study. One will be chosen by your instructor for your
use:
a) ave M.W. 86,000 (100% hydrolyzed), 1979.
b) ave M.W. 50,000 (99+% hydrolyzed), 1993.
c) M.W. 85,000-146,000 (99+% hydrolyzed), 1993.
d) Average Mw 124,000-186,000 (99+ % hydrolyzed), 1997.
e) Average Mw 89,000-98,000 (99+ % hydrolyzed), 2000.
During this week’s lab period you will prepare your PVOH solutions and calibrate the
viscometer. Next week you will measure the viscosities of your PVOH solutions.
Solution Preparation (Part A)
1. Fill a 100.00 mL volumetric flask roughly up to the mark with distilled water. Clamp it in
the 25 oC bath (it will be used later to calibrate the viscometer).
2. Prepare a PVOH stock solution by weighing accurately (by difference!) 4.0 to 4.5 g of dry
PVOH into a 250 mL beaker containing a stir bar magnet and ~150 mL of hot distilled
water. The polymer must be added to the beaker containing water, not the other
way around!
3. Place the beaker on a hot plate and set the temperature to ~350 oC. While heating, stir
gently (you do not want to entrain bubbles or produce foam). Keep a watchful eye on the
process. If the solution begins to turn brown, immediately remove it from the heat and
inform your instructor. Bubbles will disappear as the solution cools.
4. While you are heating the polymer solution also place two 50 mL beakers of distilled
water on the hotplate. Rinse any glassware that has come in contact with the dry
polymer or polymer solution immediately after use (if the polymer dries on
glassware it is very difficult to remove!).
5. When the PVOH has dissolved completely, remove the beaker from the hotplate and
allow it to cool until it is comfortable to handle.
6. Transfer the polymer solution quantitatively to a 250.00 mL volumetric flask, rinsing the
beaker numerous times with very small quantities of hot distilled water, stopping only
when solution level is 1 – 2 cm below the calibration mark.
7. Do not make the solution up to the calibration mark now (it must be at room temperature
before you do this). Instead, allow it to sit, undisturbed, as you calibrate the viscometer.
Viscometer Calibration
You will find the viscometer (consult refs. 3 and 4 for design and use of the viscometer)
well cleaned with concentrated HNO3, rinsed, and oven dried. It is slightly different than the kind
of viscometer described in Shoemaker’s experiment. Immediately after use with any kind of
solution, it should be rinsed with copious quantities of hot water, rinsed with a good grade of
acetone, and then dried in a stream of N2 gas. When not in use it should be hung upside down
to prevent dust from collecting inside, which could easily plug the very narrow capillary.
8. Charge the viscometer with the distilled water that was previously clamped in the bath.
(Small funnels are available, but a dropping pipette may be more convenient.) Enough
water has been added when the level is between the two marks on the large bulb.
9. Place the viscometer in its metal holder and hang it in the constant temperature bath.
Allow it to sit in the bath for approximately 10 minutes to ensure equilibrium with the
bath’s temperature.
10. An instructor will explain how to use the viscometer. Ideally, it should hang vertically in
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Chemistry 3303
PVOH
Winter 2012
the bath. Unfortunately, however, the bath’s circulator pump causes a slight swaying
motion (source of error?)
A rubber tube attached to a pipette filling bulb is convenient for applying suction to the
tube containing the small capillary (fit the tubing only lightly over the top of tube so that it poses
no difficulty to remove). While applying suction you must keep a finger tightly sealing the other
small tube or bubbles will be drawn up the capillary. This will present a problem, especially
when performing measurements on the PVOH solutions. Continue applying suction until the
water is slightly above the upper mark. Remove the rubber tubing BEFORE removing your
finger sealing the other tube.
11. Measure the efflux time of the water, between fiducial marks, 2 times – starting the timer
precisely when the meniscus reaches the upper mark and stopping it when the meniscus
reaches the lower mark. You can use the magnifying glass provided to enhance your
view of the meniscus and fiducial marks.
12. Record the bath’s temperature (to two decimal places) at the middle of each run.
Solution Preparation (Part B)
13. If your PVOH solution is not at room temperature, it will need to be cooled with cold
running tap water.
14. Insure no bubbles are on the surface obscuring the meniscus. One successful, but
excessively time consuming, way of removing bubbles, if present, is by injecting them
with a gentle stream of N2 gas; another, by popping with a hot copper wire. Consult your
instructor if bubbles are a problem.
15. Carefully make the solution up to the mark, cap and invert 25 times to mix thoroughly.
16. Pipette 50.00 mL portions of stock solution into each of two 100.00 mL volumetric flasks.
(Allow longer than usual time to drain as the solution is quite viscous.)
17. Pipette 25.00 mL portions of stock solution into each of two other 100.0 mL volumetric
flasks.
18. Rinse the pipettes immediately with lots of hot water.
19. To ONE of the flasks with 50 mL of stock solution, add ~0.25 g KIO4(s). To ONE of the
flasks with 25 mL of stock solution, add ~0.13 g KIO4(s).
20. Label the four flasks with a glass marker to distinguish between concentration and
cleavage.
21. Heat to approximately 70 oC and swirl the flasks to dissolve the KIO4(s), diluting to 3/4 full
if necessary.
22. Make all 4 flasks up to just below the mark with distilled water.
23. Stopper and leave undisturbed until the following week. Your solutions can be stored in
the locker next to the sink in C-3041A. The solutions will have cooled and should be
bubble free by the next lab period. Continue the experimental procedure at that time.
Viscosity Measurements
Make up each of the 4 flasks to the mark, popping bubbles first, if necessary, and invert
25 times to mix thoroughly. Clamp 3 of the flasks into the 25oC bath. Charge the viscometer
with the 4th solution, allow time for thermal equilibration, and measure the efflux time in the same
manner as you did when calibrating with distilled water. This time it is imperative that your
finger seals the second tube very tightly. Remember to record bath temperature at the
middle of each run. Repeat the measurement two more times (i.e. do three measurements for
each solution). When changing solutions, empty the viscometer, rinse with copious quantities of
hot water followed by a good grade of acetone, then dry well with a stream of N2 gas.
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Chemistry 3303
PVOH
Winter 2012
IMPORTANT NOTE: Try to keep your finger tight over top of viscometer’s second small tube
when applying suction to the tube containing the capillary. Moistening your finger might help. A
bubble inadvertently sucked up into the capillary from an inadequately sealed tube may take a
long time to get rid of (if at all) if you are working with a very viscous solution. This poses a
problem because it may be impossible to determine when the meniscus coincides with the
fiducial marks if it is obscured by bubbles. In this case the only way to remedy the situation is to
remove the solution from the viscometer, clean it thoroughly and begin again.
Results
Calculate the average flow time for pure water, then the apparatus constant B in equation
1. At 25 oC the density of water is 0.99708 g cm-3 and the viscosity is 8.909 x 10-3 g cm-1 s-1 =
0.8909 cP (the poise (P) is a convenient cgs unit of viscosity). If you did not perform the water
runs at exactly 25.00 oC you will have to linearly interpolate to find the density of water and the
viscosity at the temperature at which you performed the measurements, given that these values
are:
0.99757 g cm-3 and 0.9317 cP at 23 oC and…
0.99654 g cm-3 and 0.8525 cP at 27 oC.
Next calculate the average flow time for each of the polymer solutions. Knowing B, use
equation 1 to determine the viscosity η of each of the polymer solutions.
Now calculate the concentration of polymer in your stock solution (in g/mL) then in each
of the diluted solutions. The concentration that you need, c, is in grams of polymer per 100 mL
of solution. Convert the concentrations of the diluted solutions to this unit.
Determine the specific viscosity 𝜂!" of each diluted solution then calculate
!
!
ln
!
!!
!!"
!
and
where 𝜂! is the viscosity of pure water at the temperature that you performed the
polymer runs. Considering the original and degraded polymer solutions separately, plot
!
!
ln
!
!!
!!"
!
and
vs. 𝑐 for each (4 plots). Perform a regression analysis and report the two values of 𝜂
obtained at 𝑐 = 0 for the original and degraded solutions. Calculate the average value of 𝜂 for
the original and degraded polymer solutions.
Use equation 4 to determine the viscosity average molar masses of the polymer
molecules before and after degradation, 𝑀! and 𝑀! ′, in the original and degraded solutions.
Also, calculate the number average molar masses, 𝑀! and 𝑀! ′, using equation 5.
Finally, calculate the fraction of reverse linkages, Δ, in your PVOH sample using only the
viscosity average molar masses.
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Chemistry 3303
PVOH
Winter 2012
Discussion
Examine agreement of the values of [η] obtained by the two different methods and the
validity of assumptions made in each determination. You may consult Stokes and Mills (ref. 3)
for development of hydrodynamic theory presented in Shoemaker.
Do the experimental molar masses of the original polymer agree with that specified by
Sigma-Aldrich®? Why might they differ?
Compare your value of Δ with common values for polymers and for PVOH in particular if
available. Consult Jellinek (ref. 5) for the theory of degradation of vinyl polymers.
Equations 7 and 8 were derived based on the assumption that a 1,2-glycol structure will
result from every reverse monomer addition. What is the result of two successive reverse
additions? Is the assumption completely valid? If not, is your experimental value of Δ too high
or too low?
References
1.
Shoemaker, Garland, Nibler, "Experiments in Physical Chemistry, 8th ed." McGraw-Hill
Publishing Company, Toronto (2009)
2*.
P.J. Flory and F.S. Leutner, J. Polym. Sci. 3, 880 (1948); 5, 267 (1950).
3*.
Stokes, R.H., and Mills, R., "Viscosity of Electrolytes and Related Properties," Permagon
Press, London.
4**.
Kline, Gordon M., ed., "Analytical Chemistry of Polymers, Part II," Interscience
Publishers, New York (1962).
5**.
Jellinek, H.H.G., "Degradation of Vinyl Polymers," Academic Press Inc., New York
(1955).
6**.
R.W. Lenz, "Organic Chemistry of Synthetic High Polymers," pp. 261-271, 305-369,
Wiley-Interscience, New York (1967).
* Available only in C-3041
** Available only on reserve at the QEII Library
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