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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 Page 1 of 7 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 Page 2 of 7 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 Page 3 of 7 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 Page 4 of 7 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. Page 5 of 7 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. Page 6 of 7 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 Page 7 of 7