Intrinsic Viscosity of Polyvinyl AlcoholKyle GrodenNovember 4th and 10th, 2015(Partner: Zakariya Alshukaili)AbstractUsing a size 150 Oswald Viscometer, the intrinsic viscosities of uncleaved and cleaved (KIO4treated) Polyvinyl Alcohol were determined. The intrinsic viscosity for the uncleaved polymer wascalculated to be .1820 .0541 cm3/g, while the intrinsic viscosity for the cleaved polymer was.06868 .00834 cm3/g. Additionally, the average molar mass of the uncleaved sample was found to be4243 853 g/mol and the average molar mass of the cleaved polymer was found to be 1172 72 g/mol.The values calculated for the uncleaved polymer were quite low, as the data collected was found to beerroneous.
I. IntroductionThe goal of this experiment was to use an Oswald viscometer to calculate the viscosities ofvarious solutions of cleaved and uncleaved Polyvinyl Alcohol (PVOH) and water. To do this, we beginwith Poiseuille’s equation for flow in a cylindrical tube:𝑑𝑉 𝜋𝑟 4 (𝑝1 𝑝2 ) (𝐸𝑞. 1)𝑑𝑡8𝜂𝐿To reduce this, we note that r and L are constant for the system. Additionally, the volume that flows willnot change, so we can regard V as constant. We can use the following relationship for pressure: 𝑃 𝜌𝑔 ℎ (𝐸𝑞. 2)We can substitute this relationship into equation 1 and take g and h as constants for our viscometer.We need to leave the density variable because it is specific to the fluid in question. If we lump all ourconstants together into a single apparatus parameter and integrate with respect to t (from 0 to t):𝜂 𝐵𝑡 (𝐸𝑞. 3)𝜌In this formula, η is the viscosity of a dilute solution, 𝜌 is the density of the solution, t is time, and B isthe apparatus constant calculated through calibration of the viscometer with a known fluid (water). Thiscan be used to experimentally determine the viscosities of our solutions. We can also make use of thespecific viscosity of the solutions:𝜂𝑠𝑝 𝜂 1 (𝐸𝑞. 4)𝜂0Above, η0 is the viscosity of the pure solvent. By definition, intrinsic viscosity is defined as the ratio ofspecific viscosity to the weight concentration of the solute as concentration goes to zero. Physically, thisvalue describes the contribution of the solute to the total viscosity of the solution and can be givenmathematically by:𝜂ln (𝜂 )𝜂𝑠𝑝0[𝜂] lim lim(𝐸𝑞. 5)𝑐 0 𝑐𝑐 0𝑐Plotting these against concentration and extrapolating to c 0 will give the intrinsic viscosities for thepolymer samples.Flory and Leutner also showed that the intrinsic viscosity of a polymer in solution can be relatedto the viscosity-average molar mass by the following empirical relationship:𝑀𝑣 76000 [𝜂]1.32 (𝐸𝑞. 6)To calculate the average molar mass of the polymer, the gamma function is employed: 𝛤(𝑡) 𝑥 𝑡 1 𝑒 𝑥 𝑑𝑥 (𝐸𝑞. 7)0
Flory showed that the ratio of the average-viscosity molar mass and that average molar mass (𝑀𝑛 ) canbe described as:𝑀𝑣1𝑀𝑛 [(1 𝑎)𝛤(1 𝑎)]𝑎 (𝐸𝑞. 8)For PVOH, the value of a is .76. Therefore, the above equation reduced to:𝑀𝑣𝑀𝑛 1.89 (𝐸𝑞. 9)Additionally, from molar mass data from the cleaved and uncleaved polymers, the frequency of“backward” linkages can be calculated for the polymer in question. Consider a sample PVOH molecule:Figure 1. Sample PVOH molecule.The premise of this calculation is that cleavage only occurs between 1,2-glycol structures, marked by thered bond above. Therefore, because occurrences of molecules are inversely proportional to molar mass,we can subtract the inverse molar mass of the cleaved polymer by the inverse molar mass. Then, wecan divide by the total occurrences, which can be represented by the inverse molar mass of themonomer (Vinyl Alcohol, MW 44.0 g/mol), and rearrange to get the following formula: 83 (1𝑀𝑣′ 1𝑀𝑣) (𝐸𝑞. 10)II. Experimental MethodThe experimental method used to collect viscosity measurements was very similar to that givenby Garland et. Al in Experiments in Physical Chemistry1. However, slight modifications were made.Instead of preparing fresh PVOH solutions from a solid, dilutions were made using a premade 24%solution of PVOH (DuPont Elvanol 51-04). From this solution, approximately 1, 2, 3, 4, and 5 volumepercent solutions were tested for the uncleaved polymer and approximately 2, 3, 4, 5, and 6 percentvolume percent solutions were tested for the cleaved polymer. We conducted three trials for eachsolution. Additionally, the bath for the viscometer was not maintained at 25 C. Instead, the bath wasassumed to have equilibrated with the room temperature. Also, a vacuum tube was used in place of apipette bulb to draw the solution up through the viscometer. Finally, due to lack of equipment, a
Westphal balance was not used to measure the density of each solution. Instead, the densities weretaken to be that of the pure solvent (water).III. ResultsAfter collecting the time data for all the trials, equation 3 was used to compute the viscositiesfor all the solutions using the averages time values. The mass concentrations for each of the solutionswere computed using the density of PVOH (1.19 g/cm3) as follows:𝑔𝑥 𝑚𝑙 𝑃𝑉𝑂𝐻 1.19𝑔 (𝐸𝑞. 11)100𝑚𝑙100𝑚𝑙1𝑚𝑙Additionally, the specific viscosities for each solution were calculated using equation 4. The intrinsicviscosities for both solutions were then calculated by plotting both the limit quantities in equation 5 foreach polymer against concentration, extrapolating to zero for each plot, and then averaging the twoquantities for each polymer.The data for this experiment were plotted and then linear regression was performed for eachset of data:Cleaved Polymer Intrinsic Viscosity Plots0.2y 0.0181x 0.0572R² 0.92390.18nsp/c and ln(n/n0)/c0.160.140.12ln(η/η0)/c0.1y 0.0056x 0.0802R² 0.83420.08ηsp/cLinear (ln(η/η0)/c)0.06Linear (ηsp/c)0.040.0200123456C (g/100mL)Figure 2. Cleaved Polymer Plots to Determine Intrinsic Viscosity. Standard Error ln(η/η0)/c versus c: .00541Standard Error ηsp/c versus c: .0112878
Uncleaved Polymer Intrinsic Viscosity Plots0.35y 0.011x 0.2486R² 0.4092nsp/c and ln(n/n0)/c0.30.250.2ln(η/η0)/cηsp/c0.15Linear (ln(η/η0)/c)0.1Linear (ηsp/c)y 0.0181x 0.0787R² 0.92390.05001234567C (g/100mL)Figure 2. Uncleaved Polymer Plots to Determine Intrinsic Viscosity. Standard Error ln(η/η0)/c versus c: .0288Standard Error ηsp/c versus c: .0795Extrapolating to zero for all these plots gives us the intrinsic velocity. Upon averaging the values ofthese for each of the polymers:𝐶𝑙𝑒𝑎𝑣𝑒𝑑 𝑃𝑜𝑙𝑦𝑚𝑒𝑟: [𝜂] .06868 .00834cm3𝑔𝑈𝑛𝑐𝑙𝑒𝑎𝑣𝑒𝑑 𝑃𝑜𝑙𝑦𝑚𝑒𝑟: [𝜂] .1820 .0541cm3𝑔We can further calculate the average molar mass for both polymers using equations 6 and 𝑒𝑑 𝑃𝑜𝑙𝑦𝑚𝑒𝑟: [𝜂] 1172 72𝑚𝑜𝑙𝐶𝑙𝑒𝑎𝑣𝑒𝑑 𝑃𝑜𝑙𝑦𝑚𝑒𝑟: [𝜂] 4243 853From this information, we can calculate the delta value for this sample of PVOH: .05126
IV. DiscussionFrom an email exchange between a DuPont chemical employee2, the average molar mass ofPVOH was determined to be 31600 g/mol. Compared to our value, we receive an 86.57% error, which isextremely high.To propagate the error for this experiment, we notice that the average of the intercepts for theregression lines was the intrinsic viscosity. To estimate the error expected, we can use a form of thefollowing equation:𝑑𝐹 2𝑑𝐹 2𝑑𝐹 222(𝑑𝐹) () (𝑑𝑥1 ) () (𝑑𝑥2 ) () (𝑑𝑥𝑛 )2 (𝐸𝑞. 12)𝑑𝑥1𝑑𝑥2𝑑𝑥𝑛2For this experiment, the only measurement taken was time. Therefore, the above equation becomes:𝑑𝜂 2(𝑑𝜂)2 ( ) (𝑑𝑡)2 (𝐸𝑞. 13)𝑑𝑡To estimate the error expected, we can create an equation to estimate the slope along each line andpropagate error from that, as we can expect it to be close to the error for that of the intercept. For eachpolymer, we can average the errors for both to obtain the expected propagated error.𝐶𝑙𝑒𝑎𝑣𝑒𝑑 𝑃𝑜𝑙𝑦𝑚𝑒𝑟: 𝑑[𝜂] .001007cm3𝑔𝑈𝑛𝑐𝑙𝑒𝑎𝑣𝑒𝑑 𝑃𝑜𝑙𝑦𝑚𝑒𝑟: 𝑑[𝜂] .002159cm3𝑔In comparison with the uncertainties calculated for the intrinsic viscosities, these propagatederrors are much lower than those experimentally calculated. Viscosity is a very difficult quantity tomeasure accurately, as the slightest change in a number of variables can affect it.The operation of an Oswald viscometer involves measuring the time required for a fluid to flowfrom the upper to lower fiducial mark. Because the viscometer used in this experiment was notautomated, this measurement needed to be completed by stopwatch. This introduces operator errorinto the experimental measurements. In order to minimize this, the size of the viscometer must belarger to require longer flow times. By lengthening time, operator error would be minimized becausehuman reflexes required are not as important as with a smaller viscometer (shorter flow time).Additionally, the densities of the solutions were not determined accurately. A Westphal balancecould have been used to accurately determine the specific gravities of the solutions in question. FromScudiero et al3, the density of the 24% Elvanol solution was measured to be 1.05683 g/cm3. Therefore,assuming our solutions were equivalent to the density of water (.99745 g/cm3 at 23.5 C) won’t giveresults to a high degree of accuracy.The solutions prepared in this experiment were not created to an appreciable degree ofaccuracy. Instead of starting from solid PVOH and measuring out precise masses and volumes for highlyaccurate concentrations, the solutions made were simply estimated for the percentages PVOH required.These measurements were taken with graduated cylinders, which is far from the best piece of
equipment to use if highly accurate results were desired. A burette, if available, would have been amuch better choice.In collecting data for this experiment, the initial experiment showed less than stellar results.The cleaved data did not show a proper correlation, as the time required did not increase withincreasing percentage PVOH. After retrial, this data appeared to follow the correct trend. Initially, theuncleaved data followed a correct trend, but calculations showed significant error. In an attempt to fixthis, the 3, 4, and 5 percent solutions for the uncleaved polymer were redone along with the cleavedpolymer solutions. Following this, analysis of the uncleaved data indicated that the 1 and 2 percentPVOH solutions may have been low, as the average molar mass was significant less than expected. Thismeant that the viscosities calculated were too low.In order to more accurately determine the viscosity of PVOH, further experimentation should bedone that includes more accurate solution and density determination. If this was done, the results ofsaid experiment would be expected to be significantly improved.V. References1. Carl W. Garland, Joseph W. Nibler, David P. Shoemaker, Experiments in Physical Chemistry 8th Ed.McGraw Hill 20032. Echt, Elliot. Molecular Weight data, Elvanol 51-04. Message to Gunnar A. Hoff. 08 March 2013.Email.3. Louis Scudiero, Angela Rudolph. Intrinsic Viscosity of a linear polymer (PVOH). Washington StateUniversity 2012.Appendix I: Raw DataAppendix II: Sample Calculations
treated) Polyvinyl Alcohol were determined. The intrinsic viscosity for the uncleaved polymer was calculated to be .1820 .0541 cm3/g, while the intrinsic viscosity for the cleaved polymer was .06868 .00834 cm3/g. Additionally, the average molar mass of