Determination of the Molecular Weight of Polymers from Viscosity Measurements PDF

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Ashlee Perkinson March 19, 2012 Determination of the Molecular Weight of Polymers from Viscosity Measurements Introduction The purpose of this experiment was to determine the molecular weight of polystyrene dissolved in toluene by means of utilizing viscosity measurements. To accomplish this, different concentrations of polystyrene in toluene were prepared, and the various flow times were measured. Flow time in this experiment is defined as the amount of time it took for the given solution to pass from an initial point, Pi, to a final point, Pf, as gravity pushed it down through the viscometer. The experiment was conducted at a constant 25°C, with given “K” and “a” values of 3.7x104 and 0.62 respectively. With this information, the molecular weight of the polystyrene in toluene was determined and compared to a theoretical range of values is: 32,000-1,300,000

g . mol Albert Einstein was the first to connect specific viscosity to determine molecular weight. He realized that once specific viscosity was determined, a graph of specific viscosity v. concentration would allow determination of the limiting viscosity of the solute. This would eventually allow the molar mass of the solute to be determined using previously defined constants. Because of his original experiments, we can now easily perform this experiment to determine the molar mass of polystyrene. [1] Theory The flow properties of solutions composed of a given polymer depend almost entirely upon the molecular weight of that polymer given that the experiment is conducted under constant temperature conditions [1]. This relationship between the viscosity and molecular weight may be

better understood through Einstein’s derivation of the specific viscosity equation. Equations 1 and 2 represent the specific viscosity ( ŋsp ¿ of a dilute suspension of small unsolvated and uncharged rigid spheres to the volume fraction ( Φ ¿ ŋsp =

ŋ−ŋ ŋ

occupied by the spheres.

Eq. 1

( 52 )( VV ) =( 25 )Φ

ŋsp =

Eq. 2

o

Both relationships are dependent upon concentration, therefore he was able to obtain Equation 3 which describes how the limiting viscosity ( [ ŋ ] ¿ can be obtained from a graph of specific viscosity v. concentration and then extrapolating to zero concentration. ŋsp 1 ŋ =¿ lim ln c ŋo c →0 c [ ŋ]=lim ¿

Eq. 3

c →0

Viscosity is proportional to the density ( ρ ¿

of the liquid and flow time (t), as well as

A, a characteristic constant of the viscometer, seen in Eq.4. Because the diluted polymer solutions are similar to that of the solvent, Eq. 4 can be rewritten as Eq.5. ŋsp =

Aρt −1 A ρo t

Eq. 4

t ŋsp = −1 Eq. 5 t Using a plot of 1/cLn( ŋ/ŋo ¿ vs. c, [ ŋ]

can be obtained, shown in Eq. 6. Because

second and higher order terms can be neglected, the limiting viscosity number can be related to the molecular weight of a high polymer via Eq.7. K and a, constants describing the specific polymer, depend on the temperature and solvent and are previously determined. ln

ŋ 1 =ln ( 1+ŋ sp) =ŋsp − ŋ2 sp +… Eq. 6 2 ŋo

[ ŋ]=K M a Eq. 7

Experimental Chemicals and Equipment

     

Toluene Polystyrene Viscometer Analytical Scale Thermometer Variable Temperature Thermostat Toluene, also known as methylbenzene, was the solvent used for dilutions in this

experiment. This is an aromatic hydrocarbon that has a strong odor similar to that of benzene that may cause dizziness upon inhalation. Toluene is a clear and colorless chemical that is often used as an industrial solvent for the production of various chemicals [2]. The polymer used in this experiment was polystyrene. This aromatic polymer is widely used in the production of plastics [2]. An analytical balance, variable temperature thermostat, and viscometer were the main pieces of equipment used in lab. The variable temperature thermostat can be seen below in Figure 1 and the viscometer can be seen below in Figure 2.

Figure 1. Variable Temperature Thermostat. Allows viscometer to reach thermal equilibrium with thermostat.

Figure 2. Viscometer. Using to determine the viscosity of a fluid by measuring the amount of time it takes for the fluid to pass through the instrument.

Experimental Procedure See attached document Data Raw Data Table 1: Data For Molecular Weight Determination Type of Solution Concentration, C Average Flow times (g/100mL) (seconds) Pure Solvent -----(75+76)/2=75.5 ½c 1.0248 (151+152)/2=151.5 ¼c 0.5124 (105+106)/2=105.5 1/8 c 0.2562 (89+89)/2=89.0 1/16 c 0.1281 (82+82)/2=82.0

ηsp 0 1.007 0.397 0.179 0.086

The concentrations of each dilution in the above table were determined by calculating the amount of grams of polystyrene per 100 mL of toluene solvent. 1.0248 g of polystyrene were initially added to 50 mL of toluene to yield a concentration of 2.0496 g/100mL for the pure solvent. The subsequent concentrations were obtained by simply multiplying the concentration by the appropriate desired proportion. The average flow times were determined by averaging two trials of each dilution, as seen above. The calculations for specific viscosity can be seen below in the data work up.

Data WorkUp  75.0  sec  76.0 

t  0

 

Avgt0 mean t 0 Avgt 75.5s 0

 151.5   105.5  tavg  sec  89.0   82.0    1/16C

Experimental flow times for pure solvent, toulene Definition of average flow time Average flow time of toluene

Average flow times for diluted polymer solutions with concentrations 1/2C, 1/4C, 1/8C, and from top to bottom respectively.

Determining Specific Viscosity i 0 3

Range Variable tavg

nsp  i

i

Avgt

 1

0

Defining the specific viscosity

 1.007  0.397  nsp   0.179     0.086 

Specific Viscosities for 1/2C, 1/4C, 1/8C, and 1/16C from top to bottom

1.0248   0.5124 gm  c    0.2562 100mL  0.1281   nsp nspc  i

c

Concentrations of 1/2C, 1/4C, 1/8C, and 1/16C solutions from top to bottom.

i

i

Defined function for finding the specific viscosity of the concentration.

 0.098 0.078 m3 nspc   0.07  kg  0.067  

Calculated values for specific viscosity over the concentration.

Determining the Limiting Viscosity Number

Specific Viscosity VS Concentration Specific Viscosity

0.1 0.09 nspc 0.08 0.07 0.06

0

2

4

6

8

10

12

c

Concentration (gm/100mL) Graph 1: Graph of how specific viscosity changes with concentration.

n intercept(c nspc )

viscosity

Extrapolating when c=0, which yields the yintercept used to calculate the limiting number.

3

m n 0.061 kg

Limiting viscosity number

Determining the Molar Mass a 0.62  4

k  3.710

100

mL gm

Constant for toluene-polymer solution at 25 celsius

1

M 

 n k 

a

Derived function to calculate the molar mass of polystyrene using the limiting viscosity and a given constant, k.

number, n, 5

M  1.555 10

Unit-less molecular weight

gm Polymermolweight M mole

Equation to add units to the molecular weight

kg Polymermolweight 155.522 mol

Molecular weight with units added

The molar mass range for polystyrene in toluene at 25°C is 32,000-1,300,000

g . Our mol

experimental molecular weight therefore falls well within the reference frame. The exact molar mass is not known, therefore a specific percent error cannot be calculated.

Results and Discussion As demonstrated by the raw data, a more dilute polymeric solution has a shorter flow time and therefore a smaller specific viscosity. Therefore, the more concentrated a solution, the more viscous it should be. In Graph 1, Specific Viscosity v. Concentration, it was expected that the specific viscosity would be directly proportional to the change in concentration. Though the

relationship is not perfectly linear, it is apparent that as concentration increases, the specific viscosity does as well. There are many sources of error that potentially caused the graph to have a slightly curved trend line. If the pipettes were not properly rinsed between dilutions, concentrations and therefore viscosities would have been altered. This error would have propagated through calculations and altered the final molar mass calculated of polystyrene. Also, there is some variability associated with the flow times for specific concentrations; the average was taken to reduce error but there may still be some error associated with the measurement. It is difficult to stop the timer accurately for each trial; there is some error associated with measurements of flow time. Our experimentally determined molecular weight for the unknown polystyrene sample

was 155.522

kg . As previously stated, we do not have an exact reference value for mol

comparison, but we do know that the molar mass range for polystyrene in toluene at 25°C is

32,000-1,300,000

g . Our experimental molecular weight therefore falls well within the mol

reference frame.

References [1] Atkins, Peter. Elements of Physical Chemistry, Oxford University Press, Great Britain, 2009. [2] "Material Safety Data Sheet: Polystyrene." SigmaAldrich. Sigma Aldrich, Inc, Nov 2010. Web. 16 February 2012. .

[3] "Material Safety Data Sheet: Toluene." SigmaAldrich. Sigma Aldrich, Inc, Nov 2010. Web. 16 February 2012. ....