Susan C. Ross
|1998 - present:||Director, Center for Science and Mathematics Education, USM|
|1994 - 1998:||Assistant Professor of Mathematics, USM|
|1993 - 1994:||Instructor in Mathematics Department, Berry College|
|1989 - 1993:||Graduate Assistant, The University of Georgia|
|1986 - 1989:||Mathematics teacher, Itawamba County Schools|
low this conversion. Another reason for measuring the polymerization rate at low conversions is that during the early stages of the reaction, the initiator and monomer concentrations remain relatively constant, and you don't have to worry about measuring changes in these values.
Molecular weight can be moderated through the addition of chain transfer agents such as an alkylmercaptan. One which is widely used is dodecyl mercaptan. This molecule readily transfers a hydrogen from the sulfur to a carbon radical:
The various relations of the rate constants ktr, ki, and kp and how they affect the rate of polymerization can be summarized as:
There is a characteristic chain transfer constant (Ctr) for each chain transfer agent - monomer system defined as:
1. kp >> ktr and ki` ~ kp no change in Rp 2. kp >> ktr and ki` < kp decrease in Rp 3. kp << ktr and ki` < kp large decrease in Rp 4. kp << ktr and ki` ~ kp no change in Rp 5. kp >> ktr and ki` > kp no change in Rp 6. kp << ktr and ki` > kp no change in Rp
In this experiment the rate of polymerization will be measured by the use of dilatometry. Dilatometry utilizes the volume change that occurs upon polymerization to follow conversion versus time. The conversion is conveniently followed in a dilitometer whose volume includes a capillary region. The dilatometer is placed in a constant temperature bath and the volume change of the polymerizing system, which is quantitatively related to the percent conversion, is followed with time. Dilatometry is not useful for most step polymerizations where there is a small molecule by-product that results in no appreciable volume change upon polymerization.
As the dilatometer is placed into the constant temperature bath, initial meniscus movement is due to two factors:1. thermal expansion of the styrene monomerAfter approximately 5-10 minutes the effects due to thermal expansion become negligible. If the capillary cross-section area is determined, usually in terms of volume as a function of length, the change in height of monomer in the capillary may be expressed as a volume change. Thus the slope of a plot of meniscus height versus time would give us DH/Dt, which can easily be converted to a volume to give DV/Dt. Some dilatometers have the capillary calibrated in volume increments, thus DV/Dt is directly accessible.
2. contraction due to polymerization.
The total fractional change in volume corresponds to complete conversion to polymer of density d2 from W1 grams of monomer of density d1. The weight of the polymer would also be W1, since in an addition polymerization, no weight is gained or lost. For the total fractional change in volume, this gives:
which simplifies to:
The degree of monomer conversion would then be:
where D[M] is the incremental change in monomer concentration [M] and DV is the change in volume from the initial volume Vo. This is true, since the term (d2-d1)/d2 is the fractional volume change which would occur at 100% conversion and DV/Vo is the fractional volume change at any time Dt. The ratio of these two quantities should give the fraction of conversion. Note that the quantity is dimensionless, so that D[M] and [M] could be in units of grams, moles, or molar quantities since the units cancel out. Now if both sides of Equation 17 are divided by Dt, incremental time, and rearranged, then
The value -d[M]/dt has been previously defined as the overall rate of polymerization, Rp. Equation 13 can be tested by varying the initiator concentration. Additionally, this experiment will test the effect of a chain transfer agent, dodecyl mercaptan, on the rate of the polymerization.
1. Clean and dry the dilatometer. Concentrated nitric acid works well for cleaning out any residues . Then rinse with DI water first, acetone second and then dry with nitrogen.
2. Load the dilatometer with the mixture you made for Free-Radical Polymerization (NOTE: The volume of the dilatometer is approximately 10 ml), Use a rubber pipette bulb to bring the polymerization mixture into the capillary tube so that the liquid level is equal to the lowest graduation. There should be no bubbles anywhere from the bottom of the stopcock to the liquid level in the capillary. While the level is being held in the capillary, the stopcock is closed so that the only opening is at the top of the capillary. (NOTE: Total volume of precision bore capillary is 1.400 ml ± 0.015 ml. The smallest graduation is 0.005 ml.)
3. The dilatometer is clamped in a constant temperature bath at 70oC. Timing is started as soon as the dilatometer is placed in the bath. Initial meniscus movement is due to two factors: Thermal expansion of the liquid and contraction due to polymerization. The liquid level is monitored as a function of time approximately every 2-3 minutes until the level is outside of the calibration marks or for 30-40 minutes.
4. The polymerization mixture is emptied from the dilatometer. If the mixture is allowed to remain in the apparatus too long, it will be impossible to remove. The dilatometer is cleaned, as in step 1.
5. The dilatometer is now cleaned, dried, and stored
1. Prepare a table listing time (t) and a measure of capillary volume, either direct volume (V) or liquid height in the capillary (H) for each run.
2. Make a graph of either V vs t or H vs t, depending on which quantity was measured, and take the slope of the straight portion of the line. If the graph is V vs t, the slope will be DV/Dt. If the graph is of DH/Dt, this quantity can be changed to DV/Dt by the use of the calibration constant in ml/cm.
3. Using Equation A we can determine 3. D[M]/ Dt since we have DV/Dt from the previous step. d1 and d2 are the densities of styrene and polystyrene respectively (0.860 and 1.046 g/m; respectively at 70oC), and the term [M]/Vo can be calculated where Vo is the original volume (bulb + capillary) and [M] is the molar concentration of styrene. If we assume that the amount of DDM does not affect the concentration of styrene in bulk styrene, we can use the density (0.860 g/ml) and the to get the concentration in mol/l .
4. The overall rate of polymerization should be calculated for all three samples so that the effect of initiator concentration of the rate may be verified (samples 1 and 2) and also the effect of a chain transfer agent on the rate may be investigated (samples 1 and 3).
1. Pearce, Eli M., Carl E. Wright, Binoy K. Bordoloi. Laboratory Experiments in Polymer Synthesis and Characterization. Educational Modules for Materials Science and Engineering Project, 1982.
2. Odian, G. Principles of Polymerization 2nd Edition, Wiley-Interscience, New York, pp. 192-193.
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