In the Laboratory

JChemEd.chem.wisc.edu • Vol. 75 No. 11 November 1998 • Journal of Chemical Education 1479

Use of a Reliable Homemade Dilatometer To Study theKinetics of the Radical Chain Polymerization of PMMA

An Undergraduate Polymer Chemistry Laboratory Kinetics Experiment

Olga Martín, Francisco Mendicuti,* and Maria Pilar TarazonaDepartamento de Química Física, Universidad de Alcalá, 28871 Alcalá de Henares, Madrid, Spain

The best methods to determine polymerization rates arebased on the measure of change of any physical property thatdiffers for the monomer and polymer (e.g., refractive index,ultraviolet or infrared absorption, density)(1). These tech-niques have an inherent advantage over some chemicalmethods. Polymerization does not need to be stopped todetermine the percent of conversion, which, as a consequence,can be followed on the same reaction sample. Dilatometry is atechnique that uses the volume decrease (density increase) thatoccurs upon polymerization to follow the conversion time.

In this laboratory experiment we will demonstrate thekinetics scheme of a radical chain polymerization by using avery simple and reliable homemade dilatometer. Orders ofreaction with respect to the monomer and the initiator con-centrations were obtained.

Principles (2, 3)

A typical example of a radical chain (addition) polymer-ization is the methyl methacrylate polymerization in toluenein the presence of benzoyl peroxide as the initiator. Assumingthe steady-state for the macroradicals, the polymerization rateRp can easily be obtained as

Rp = (kp/kt1/2)(kd f )1/2[I]1/2[M] (1)

where kp, kt, and kd are the rate constants for the propagation,termination, and initiator decomposition processes, respec-tively, f the efficiency for the last process, and [I] and [M]the initiator and monomer concentrations. By keeping theinitiator concentration constant at low conversion times, eq1 becomes a pseudo-first-order reaction that by integrationwill be

ln [M]0/[M]t = kappt (2)

where the subscripts 0 and t of [M] represent concentrationsat the initiation of the reaction and at any time t, respectively,and kapp is a pseudo-first-order rate constant. When using anyexperimental method that provides a change in a physicalproperty λ proportional to the monomer concentration withtime t, eq 2 can be written as

ln(λ0 – λ∞)/(λt – λ∞) = kappt (3)

The magnitude λ∞ is not usually available for several reasons,one of which is that the previous equations are valid at lowconversion times. There are, however, several methods withwhich to estimate λ∞. We have satisfactorily used the Kezdy–Swinbourne method (5), which consists in measuring λ atregular time intervals ∆t. The following equation can easily

be obtained:

λt = λt+∆t e kapp∆t + λ∞(1 – e kapp∆t) (4)

A plot of λ t+∆t vs λ t should be linear. If we also plot thestraight line λ t = λt+∆t in the same graph according to eq 4,the lines will intersect at λ t = λt+∆t = λ∞.

Experimental Procedure

This experiment requires previously distilledmethylmethacrylate (MMA) (4), benzoyl peroxide (reagentgrades), toluene, and also methanol (practical grades) if youwant to precipitate the polymer obtained. Even though benzoylperoxide contains a considerable amount of water, this doesnot have to be removed at the concentrations used in theexperiment. Simply take it into account when calculating theinitiator concentration.

CAUTION: MMA, toluene and methanol are toxic, irritant,and noxious. Toluene and methanol are highly flammable.Benzoyl peroxide is irritating and reactively unstable and itcan explode with any source of ignition (e.g., shock, strongfriction, or direct fire). The vapors formed when benzoyl per-oxide burns are also flammable. The use of safety goggles and aface shield is recommended. Adequate ventilation is essential.Caution is required when using glass vessels. Special care mustbe taken when using the dilatometer.

The reaction is carried out in a dilatometer. This is avessel equipped with a small-diameter tube in which the liquid

Figure 1. The setup usedfor the dilatometric mea-surements.

1500

500

thermometer

bulb

1000

h∞

h0

ht

3 mm diameter glass tube

dilatometer

0

*Corresponding author.

In the Laboratory

1480 Journal of Chemical Education • Vol. 75 No. 11 November 1998 • JChemEd.chem.wisc.edu

level can be measured upon polymerization. Figure 1 depictsthe simple dilatometer we used in our experiments. The designdepends mainly on the expected volume change and the rateof polymerization. However, we can easily manipulate someparameters, such as polymerization temperature and initiatoror monomer concentrations, in order to obtain an adequatevolume change and polymerization rate for the dilatometerwe designed for our laboratory experiment.

Ask your glass blower to build a dilatometer by simplyfusing a 3-mm i.d. tube (preferably graduated) approximately35 cm long, with a glass stopper on top, to a bulb of ap-proximately 47 mL. Place the dilatometer in a large beakerfull of water (up to 1/4 of the length of the tube). Cover thisbeaker with a stopper made of an isolation packaging material,(e.g., polystyrene foam) in which a hole has been made forthe dilatometer as depicted Figure 1. Immerse the whole beakerin the reaction bath. It is also a good idea to cover the watersurface of the bath in which the beaker is immersed with afloating isolation material, to avoid water evaporation as muchas possible. This reaction works very well (in a relatively shortperiod of time for a student laboratory experiment) between70 and 80 °C.

As in other laboratory experiments (6, 7), one of ourobjectives is to encourage cooperation and competitionamong students. This makes the exchange of individual dataessential to obtain the final results. Each student (or group)should therefore proceed as follows.

1. Prepare a 50-mL 2 M monomer solution in toluene,which should also contain the benzoyl peroxide ini-tiator in the concentration determined by the advisor,and keep it in an ice bath. The MMA and tolueneshould preferably have been degassed by using anultrasonic bath before the solutions were prepared.(The experiment works well with initiator concentrationsin the range of 1.5 × 10�3–2.5 × 10�2 M.)

2. Place the full water beaker containing the emptydilatometer in the bath to bring the reaction dilatom-eter bulb to the desired temperature. (All reactions werecarried out at 80 °C).

3. Use a syringe to slowly add the monomer-plus-initiatorsolution to the dilatometer, filling it to approximately3/4 of the length of the tube. Cover the dilatometerwith the glass stopper and seal it adequately with Teflontape. The volume of the solution and thus the level ofthe liquid in the tube will increase. Wait 5–10 min toequilibrate the temperature of the dilatometer contents.

4. Start counting the time. Note the value of the scale ast = 0 (h0) if the dilatometer tube is graduated. If thisis not the case, just use an appropriate glass markerpen to draw a signal on the tube. Mark the level ofthe liquid in the tube at 15-min intervals for approxi-mately 11/2 hour to collect h t values at each t. It isafter this time period, approximately, that deviationof the linearity of eq 3 will take place.

5. To stop the reaction, cool the dilatometer by immers-ing it in an ice bath and precipitate the polymer bydropping the contents of the dilatometer over coldmethanol. Filter or decant it and dry it in the vacuumoven. You could extend the experiment by obtainingthe molecular weight of these polymers by using anytechnique available. This could yield valuable infor-mation about transfers to the monomer and the ini-tiator (8).

Figure 2. The application of the Kezdy–Swinbourne method to geth∞ for each reaction.

0 5 10 15 20 25 30

0

5

10

15

20

25

30

h∞

h t+∆

t / c

m

ht / cm

Figure 3. First-order plots of the PMMA radical chain polymeriza-tion at 80 ºC. The plots are from the experimental measurementsperformed by keeping constant the MMA monomer concentration(2M) and changing the benzoyl peroxide initiator concentration:[I] = 22.5 × 10�3 M (�); 17.2 × 10�3 M (�); 13.5 × 10�3 M (�);and 3.80 × 10�3 M (•).

0 1 2 3 4 5 6

0.0

-0.5

-1.0

-1.5

t / (103 s)

[M] 0

[M] t

ln

Figure 4. Plot of the ln kapp vs ln [I] obtained from the experimentalmeasurement performed at different initiator concentrations. Slopeand intercept are 0.49 ± 0.09 and �6.8 ± 0.5, respectively

-7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5 -3.0-12

-11

-10

-9

-8

-7

-6

ln k

app

ln [I]

In the Laboratory

JChemEd.chem.wisc.edu • Vol. 75 No. 11 November 1998 • Journal of Chemical Education 1481

Calculations and Comments on the Results

When each student has collected the values of ht, use eq4 to obtain h∞.1 Figure 2 depicts a plot to get this value byusing the Kezdy–Swinbourne method. Then apply eq 3 bydepicting ln[(h0 – h∞)/(ht – h∞)] vs t. A straight-line plot willdemonstrate order 1 with respect to the monomer concen-tration. The slope will give kapp.

Figure 3 shows the results of four experiments performedby different students. Table 1 collects results of kapp at eachinitiator concentration [I]. Each student contributes a kappcorresponding to his or her initiator concentration. A represen-tation of ln kapp vs ln [I] should give a straight line accordingto the kinetics scheme of a radical chain polymerization.

Figure 4 depicts the results collected from all individualexperiments. A slope of 0.49 ± 0.09 and an intercept of �6.8± 0.5 were obtained. The slope agrees with an order of 1/2with respect to the initiator concentration for this kind ofreaction. The intercept will yield ln kpkt

�1/2( f kd)1/2. Thedecomposition rate constant kd for the initiator in toluene atthis temperature is kd ≈ 7 × 10�5 s�1 (9, 10). In the absence

foseulaV.1elbaT k ppa tarotaitinItnereffiD

snoitartnecnoC[ I 01(/] �3 )M k ppa 01(/ �5 s�1)

04.1 4.305.3 6.608.3 8.501.5 7.606.6 5.557.6 7.6

3.11 6.95.31 5.72.71 3.115.22 5.81

of kp and kt literature data for the reaction in toluene, values ofkp ≈ 103 L mol�1s�1 and kt ≈ 5 × 107 L mol�1s�1 for the reac-tion in benzene, whose behavior is very similar to toluene’s,were used to compare with the experimental intercept. Theagreement was very good.

Acknowledgments

We thank DGICYT (PB94-0364) and the University ofAlcalá, (U.A.H: 017/95) for their support. O.M. gratefullyacknowledges fellowship FP93(8987904). We wish to expressour thanks to M. L. Heijnen for assistance with the prepara-tion of the manuscript. Suggestions of E. Rodenas are alsogratefully acknowledged.

Note

1. When using either eq 3 or 4, remember that h is the physicalproperty measured in this experiment.

Literature Cited

1. Collins, E. A.; Bares, J.; Billmeyer, F. W., Jr. Experiments in PolymerScience; Wiley-Interscience: New York, 1973; p 82.

2. Odian, G. Principles of Polymerization; Wiley: New York, 1981;p 188.

3. Billmeyer, F. W., Jr. Textbook of Polymer Science; Wiley: New York,1984; pp 56–68.

4. Hardgrove, G. L; Tarr, D. A. J. Chem. Educ. 1990, 67, 979–981.5. Connors, K. A. Chemical Kinetics: The Study of Reaction Rates in

Solution; VCH: New York, 1990; p 36.6. Marin, D.; Mendicuti, F. J. Chem. Educ. 1988, 65, 916–918.7. Marin, D.; Mendicuti, F.; Tejeiro, C. J. Chem. Educ. 1994, 71,

A277–A278.8. Odian, G. Principles of Polymerization; Wiley: New York, 1981;

pp 226–230.9. Brandrup, J.; Immergut, H. E. Polymer Handbook, 3rd ed.; Wiley:

New York, 1989; p II-32.10. Odian, G. Principles of Polymerization; Wiley: New York, 1981;

p 196.11. Brandrup, J.; Immergut, H. E. op. cit.; p II-72.

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