Molar Mass of Polyvinyl Alcohol by Viscosity

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1 Molar Mass of Polyvinyl Alcohol by Viscosity Introduction Polyvinyl Alcohol (PVOH) is a linear polymer (i. e., it has little branching) of Ethanol monomer units: -CH 2 -CHOH- Unlike most high molar mass synthetic polymers this polymer is water soluble. In this experiment we will determine its molar mass using viscosity measurements on its aqueous solution. The structure of PVOH is determined by the structure of the Polyvinyl Acetate from which it is prepared by hydrolysis. Most of the monomer units are linked in a "head-to-tail" fashion, but a few are linked "head-to-head": -CH 2 -CHX-CH 2 -CHX-CH 2 -CHX-CHX-CH 2 - X = OH (head-to-tail) (head-to-head) The number of head-to-head linkages within the molecule depends upon the two rate constants for polymerization of PVOH; k α and k β : k α R +M R M normal reaction (1) k β R +M R M abnormal reaction (2) R. is the growing polymer chain and the arrows give the relative directions of the linking units. Since the rate constants depend on the activation energy of each pathway, the ratio of the rate constants can be expressed as k β k α e Eβ RT e Eα RT = e (E β E α ) RT (3)

2 and as E α < E β, the number of head-to-head linkages increases with polymerization temperature. Each of these head-to-head linkages forms a 1,2-glycol which can be quantitatively cleaved with Periodate (IO - 4 ). Therefore, a determination of molar mass before and after treatment with Periodate should provide an estimate of the fraction of head-to-head linkages in the molecule. A convenient method for the determination of polymers is via viscosity measurements. The apparatus to be used in these determinations is the Ostwald viscosimeter. The size of the capillary is marked '100'. mark a sample mark b The viscosity η of the solution is given by η = B ρ t (4) where B is an apparatus constant, ρ is the liquid density at the measurement temperature, and t is the time for the meniscus to go from the top fiducial mark (a) to the bottom mark (b). This will take about 50 s - 60 s for pure water. It has been shown that the ratio of the volume v of suspended particles in a total fluid volume V is proportional to the specific viscosity η sp ; defined as: η sp = η 1 v η 0 V (5)

3 where η is the viscosity of the solution, and η 0 the viscosity of the solvent. Note that η is directly proportional to t! The ratio of η sp to the solute concentration c (in grams per 100 ml of solution!!) in the limit of infinite dilution is called the intrinsic viscosity [η]: η sp [η] = lim c 0 c = lim 1 c ln η c 0 η 0. (6) Thus, 1/c. ln(η/η 0 ) and η sp /c can be plotted vs. concentration and extrapolated to c = 0 to give [η]. The problem now is to relate the molar mass to the viscosity. Since these molecules are long chains with many single bonds about which rotation can take place, parts of the molecule more than a few atoms apart are essentially randomly oriented and can therefore be treated statistically. As such it can be shown that the mean distance between the chain ends, which is also the effective mean diameter d of the molecule, is proportional to the square root of the chain length (or the molar mass M): d M 1 2. (7) The volume of a molecule can be approximated as (v M ) = d 3 and equation (7) then becomes: v M M 3 2. (8) Thus, the volume of all the molecules (v) is: v cv M M3 2 = cvm 1 2. (9) From equations (9), (5) and (6) follows KM 1 2 = η sp c = [η] (10) where K is a constant.

4 These calculations ignore the significant effect of the solvent by assuming that it is a poor solvent with no solvating effect which would make the molecular size increase; i.e., the statistical treatment assumes random orientation but in fact an atom in the molecule cannot be in the same space at the same time as a solvent molecule. Thus equation (10) above must be modified and is found for PVOH in aqueous solution at 25 C to be: [η] = (M v ) a where a = 0.76, and M v has units of g/mol. (11) where a = 0.76, and M v has units of g/mol. Equation (11) was derived by Flory and Leutner for monodisperse samples (i. e., all molecules have the same weight) but also holds for polydisperse ones (i. e. the sample is made up of molecules with a distribution of molar masses). In the latter case, the molar mass is M v, the viscosity average molar mass given by equation (12): ( M v ) a = M 1+a P(M)dM 0. (12) MP(M)dM 0 where P(M) is the molar mass distribution function. Other experimental methods (i. e. measurements of osmotic pressure) give number average molar masses M n : M n = MP(M)dM 0. (13) P(M)dM 0 For monodisperse polymers, M v = M n, but for polydisperse polymers the relationship depends on "a" and the distribution function P(M). If the chain lengths are random, this function is: P(M) = 1 M n e M /M n. (14) Along with the aforementioned value of "a" for PVOH of 0.76, it can be shown that M v and M n are related as follows: M v M n = (15)

5 As previously mentioned, PVOH can be specifically cleaved at "head-to-head" sites, thereby changing the number average molar mass M n of the uncleaved sample to M n ' of the cleaved sample. The fraction of the total monomer units bonded head-to-head is equal to the increase in number of molecules during cleavage divided by the total number of units present, as number is inversely proportional to molar mass in each case. = 1 / M n 1 / M n 1 / M0 (16) where M 0 is the monomer molar mass (= 44 g/mol for PVOH). Therefore (with all molar masses in g/mol), 1 = 44 M n 1 M n (17) and from (15) and (17) 1 = 83 M v 1 M v (18)

6 Procedure The viscosimeter is first cleaned by drawing through it with an aspirator some soap solution followed by large volumes of water. Then flush it with two small ( 5 ml) quantities of acetone and suck dry. The apparatus constant B will be determined by finding the time for a sample of known viscosity (i. e. water) to drop from one fiducial mark to the other. Clamp the viscosimeter in a 30 C constant temperature bath to a depth such that the upper fiducial mark is immersed, then pipette into it 10 ml of water. At least 10 minutes is required for equilibration. Place a 250 ml flask of water (for dilutions) into the bath. While waiting for the apparatus to equilibrate, filter through glass wool into a 250 ml beaker about 100 ml of 18 g/l PVOH stock solution (please don't waste it, it's a lengthy process to prepare). Being careful to minimize foaming of the solution, pipette 50 ml into a 100 ml volumetric flask, make up to the mark with equilibrated water (for a 1/2 dilution), and mix gently but thoroughly. Clamp this flask in the bath. The less your flasks etc. are removed from the bath, the less time is required for equilibration. By now the viscosimeter containing water should be equilibrated. In carrying out this experiment it is critical to get maximum reproducibility of readings of time. From equation (5) and since η t and η 0 t 0, it follows that η sp = (t/t 0-1). In certain dilute solutions t is very close to t 0 and timing errors of even 0.1 s become very significant. Therefore, make certain that the viscosimeter is at the same angle for all readings. Carefully use the aspirator to draw the liquid so that the top meniscus is above the top fiducial mark. Allow the liquid to drop, start the timer as the meniscus passes the top fiducial mark, and stop the timer as it passes the bottom fiducial mark. Repeat five times (this will allow a mean value and a standard deviation to be determined). Carefully clean and dry the apparatus between runs. Pipette 10 ml of the previously prepared 1/2 dilution PVOH into the viscosimeter (allow for equilibration) and 50 ml into a second 100 ml volumetric flask which is then made to the mark for the 1/4 dilution. Use the above procedure to obtain readings of t for the 1/2 dilution PVOH, then the 1/4 dilution. Finally make 50 ml of the 1/4 dilution to 100 ml and determine t for the 1/8 dilution thus prepared. Now pipette 50 ml of the previously filtered 18 g/l PVOH solution into a 250 ml Erlenmeyer flask, add about 25 ml of water and 0.25 g KIO 4, and heat on a hot plate to about 70 C until the KIO 4 dissolves. Cool the flask, then transfer the cleaved polymer quantitatively to a 100 ml volumetric flask and make to the mark with water (all the cleaved PVOH solution must be rinsed into the volumetric flask). Use the previous procedure to obtain readings of t for this 1/2 dilution

7 of cleaved PVOH, and then prepare and determine t for 1/4 and 1/8 dilutions. Finally, carefully flush the apparatus with water and dry with two small aliquots of acetone.

8 Data Analysis 1) Given that the coefficient of viscosity of water η 0 at 30 C is Pa s, use the data from your water measurement to determine the apparatus constant B from equation (4). Calculate the error. 2) Calculate c (in grams per 100 ml) of each solution. 3) Calculate the viscosity η of each solution. Determine the error from the standard deviation. 4) Calculate η sp. for both the cleaved and uncleaved polymer. Determine the error from the standard deviation. 5) a) Tabulate the values for η sp /c and c including the error for η sp /c. b) Make plots for both the cleaved and uncleaved polymer of η sp /c versus c. Don't forget the error bars. c) Obtain [η] from the intercepts at c = 0 and graphically determine the error for [η]. d) Determine the correlation coefficients for these linear fits. 7) Use equations (11) and (15) to find M v and M n for the original and degraded polymers. Estimate the error for both quantities. Discuss whether your result is reasonable. 8) Use the results from analysis step (7) to determine and calculate the error. 9) Tabulate your results of (M v, M n and ). 10) How is affected by k α and k β (equation 3)?

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