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Intrinsic Viscosity

Teaching Assistant: TA Name

Chem 375-003

Group #5

2/6/97

Performed: 1/23/97



Lab Partners:

Name 1

Name 2



Abstract

An Ostwald viscosimeter was used to study the effect of polymer length on viscosity. The particular polymer used was polyvinyl alcohol, both cleaved and uncleaved. The cleaved polymer was achieved by the addition of KIO4. From this information, the average molecular weight of the polymer is calculated.

Introduction & Theory

For a fluid in which small rigid spheres are uniformly distributed at low concentrations, the viscosity is related to the viscosity of the pure fluid 0 and the ratio of the total volume of the spheres v to the total volume (V) by

The left side of eq(1), when divided by the weight concentration of solute c as c goes to zero, defines [], the intrinsic viscosity.

At low concentrations, the quantities within the limits are reasonably linear allowing the value of [] to be determined by extrapolation from experimental values.

The single bonds of polyvinyl alcohol (PVOH) allow its molecules to fold in on themselves to form string that meanders randomly within a roughly spherical shape. The length of the molecule will then determine the size of the effective sphere, and the length is directly related to the molecular weight. As a result, the following relationship exists between intrinsic viscosity and molecular weight:

Where K and a are empirical constants associated with the polymer and the solvent used.

Experimental

The procedure described in the text(1) was followed as closely as possible. The largest deviation from this procedure was minor, the thermostat bath was kept at 23.5 C rather than the prescribed 25 C.

Results

The raw data for the experiment was as follows

Table 1 - Sample Flow Times (M:SS.HH)

Distilled Water Uncleaved, Initial Concentration Uncleaved, Second Concentration Cleaved, Initial Concentration Cleaved, Second Concentration
Run 1 1:03.29 2:07.64 1:29.71 1:21.21 1:06.84
Run 2 1:03.34 2:06.32 1:30.00 1:11.26 1:06.30
Run 3 N/A 2:06.45 1:30.15 1:11.43 1:06.37
Run 4 N/A 2:06.66 N/A 1:12.30 N/A
Average 1:03.32 2:06.77 1:29.95 1:11.80 1:06.50



Given that viscosity , density , and time t are related by the following formulas

and that water has a density of 0.9970 g cm-3 and viscosity of 0.8937 cP, the apparatus constant B can easily be calculated.

The units of the above are best left without simplification to allow easy cancellation when solved for . Assuming a density of pure water for each of the solutions, the viscosities of each of the solutions may then be determined by simple substitution into eq. (4).

The initial solution was made up of 4.2255 g solid PVOH in 250 mL distilled water. This initial concentration c1 was then 1.690 g / 100 mL. This solution was then diluted 1:2, resulting in a second concentration c2 of 0.8451 g / 100 mL.

The specific viscosity sp can then be determined by dividing the viscosity of the solution by the viscosity of the solvent (pure water) and subtracting 1.









By extrapolating these lines to c=0, [] may be determined from eq. (2). The intercept of the equation of the line representing /c for the uncleaved polymer is 0.4035, and 0.4209 for the line representing (1/c)(ln /0). From the data from the cleaved polymer, /c and (1/c)(ln /0) are 0.03991 and 0.04186 at c=0. Substitution into eq. (2) then yields []=0.1698 100 mL g-1 for the uncleaved polymer and []=0.001671 100 mL g-1 for the cleaved polymer.

As described in the text 1, Flory and Leutner determined a relationship between [] and the viscosity-average molecular weight, specifically

Substitution of the above values for [] gives a molecular weight of 7300 g mole-1 for uncleaved polymer and 16.4 g mole-1. Additionally, a number average may be determined as follows:

The ration of inverted monomer units to total monomer units is given by in the following formula:

Where the prime indicates the molecular weight of the cleaved polymer and M0 is the molecular weight of the monomer, specifically 44 g mole-1. This yields an inversion percentage of 519%.

Table 2 - Summary of Results*

Uncleaved, Initial Concentration Uncleaved, Second Concentration Cleaved, Initial Concentration Cleaved, Second Concentration
(cP) 1.789 1.270 1.013 0.9386
sp 1.002 0.4210 0.1335 0.05024
c (g/100 mL) 1.690 0.8451 1.690 0.8451
sp/c (100 mL/g) 0.5929 0.4982 0.07899 0.05945
(1/c)(ln /0) (100 mL/g) 0.4107 0.4158 0.07414 0.05800
Uncleaved Cleaved
[] (100 mL g-1) 0.1698 0.001671
Viscosity Avg. M.W. (g mole-1) 7300 16
Number Avg. M.W. (g mole-1) 3900 8.5

Combined

520%

*See Discussion for comments on validity.

Discussion

Many of the results from this experiment are clearly not valid. The averaged molecular weights of the cleaved polymer would be expected to be equal to or above 44 g mole-1 (the m.w. of the monomer). The averaged molecular weights of the uncleaved polymer are expected to be ~70000 g mole-1. The value of must be between 0 and 100%. The most likely reason for the disagreement is a flaw in the logical progression of calculations. This conclusion is based on the reasonable values obtained for viscosity and the complete deviation of results from possible values. The reliance of the process of calculations on empiracle parameters and variables without obvious physical meaning makes it difficult to judge the validity of the results at each step.

Two successive abnormal additions to the polymer chain would simply be cleaved into two monomer units upon degradation. The expression used to calculate a value for [eq. (8)] does not rely on any relationship between abnormal additions and previous additions. The results and formulas given by Flory and Leutner are precise to only two significant digits, and as my calculations are based upon their parameters, the precision of my results are limited to two significant figures.

References

1. D. P. Shoemaker, C. W. Garland, J. W. Nibler, Experiments in Physical Chemistry, 6th ed., chapter XII, The McGraw-Hill Companies (1996).