In the Laboratory
An Interferometric Study of Epoxy Polymerization Kinetics Melissa A. Page and W. Tandy Grubbs* Department of Chemistry, Stetson University, Unit 8271, DeLand, FL 32720; *
[email protected] It has been estimated that nearly half of all industrial chemists work in some area of polymer chemistry. Nevertheless, polymers and polymerization are topics often neglected in the undergraduate curriculum, especially in the laboratory. Although some experimental procedures introduce students to the synthesis and properties of common organic polymers (1), only a handful are available for the investigation of polymerization kinetics (2). Described here is a simple method for monitoring the cure kinetics of an optically transparent polymerizing medium. The experimental apparatus consists of a low-power helium–neon laser, a home-built Michelson interferometer, and a photodiode light detector. When a polymerizing sample is placed in one arm of the Michelson interferometer, the refractive index change that accompanies polymerization will cause a corresponding variation in the phase of the coherent optical beam that passes through the sample, and the output of the interferometer will subsequently fluctuate between constructive and destructive interference. Oscillation in the interferometer output intensity is monitored as a function of time with the photodiode. The time between successive maxima (or minima) is utilized to define a phenomenological polymerization rate. We have used this device to collect and compare curing profiles of commercially available epoxy glues. Background The term “polymerization” refers to any reaction that occurs by the consecutive addition of monomers to form high molecular weight products. Polymerization reactions can be summarized by the following partial mechanism, where the kinetic rate law is indicated for each elementary step (vn = rate): 1. 2. 3. 4. 5.
monomer + monomer monomer + dimer monomer + trimer dimer + dimer dimer + trimer
→ dimer; → trimer; → tetramer; → tetramer; → pentamer;
v1 = k1[monomer]2 v2 = k2[monomer][dimer] v3 = k3[monomer][trimer] v4 = k4[dimer]2 v5 = k5[dimer][trimer]
The usual method of defining the overall rate of a chemical reaction in terms of the disappearance of a reactant (or appearance of a product) becomes intractable for a polymer reaction; polymerization can continue well after the monomer has been consumed. Simple rate laws can be obtained for polymerization if one assumes that the reactivities of the monomers, dimers, and higher-molecular-weight intermediates are independent of molecular chain length (i.e., k1 = k2 = k3 = … = kn) (3). In this instance, the rate law will depend only on the overall concentration of reactive sites. This assumption is usually considered valid as long as the chemical reaction is slow compared to molecular diffusion (4). However, during the course of many polymerization reactions, a “gel point” is ultimately reached where the time-scale for molecular diffusion intersects (and exceeds) the time-scale of chemical reactivity. In this case, an initially fast polymerization reaction will nearly “freeze-out” 666
and a complete reaction may never occur within an experimentally reasonable time period. The cure rate of real polymers can be further complicated by the presence of an evaporating component or, in the case of a condensation polymer, by the buildup of water within the polymer network. Since a rigorous (molecular) definition of polymerization rate can be unruly, it is often convenient to employ a phenomenological definition of rate that is based upon the variation of a physical property in time. Such an approach is frequently utilized in the field of polymer research (5, 6 ), allowing one to make quantitative comparisons of curing profiles for a given polymer system as a function of experimental variables such as temperature, stoichiometric ratio of reactants, initiator concentration, and plasticizer concentration. Phenomenological techniques based upon differential scanning calorimetry (6 ), linear expansion (7), and shear modulus measurements (5) have been developed to follow polymerization. In many respects, phenomenological techniques are superior to traditional spectroscopic methods of studying polymerization. For example, infrared absorption measurements are frequently used to follow the concentration of reactive sites during condensation polymerization (8). However, infrared spectroscopy is relatively insensitive to important phases of the curing process that occur after the gel point, such as structural relaxation and volume shrinkage. An understanding of these processes is of considerable technological importance; structural relaxation and volume shrinkage reduce internal stress in the polymer network, thereby minimizing cracking and peeling of the polymer film from its substrate (7). These physical changes accompanying polymerization are best investigated through techniques that exhibit a high sensitivity to polymer density. The interferometric technique described here is one such technique. It is based upon measurement of the refractive index variation that accompanies polymerization. According to the Lorentz– Lorentz formula (9), refractive index is strongly dependent on density. Therefore, it can be anticipated that interferometric measurements will be highly sensitive to the physical curing processes during polymerization. Experimental Procedure and Results The experimental apparatus is diagrammed in Figure 1. A beam from a low power helium–neon laser (5 mW, λ = 632.8 nm) is directed through a 50/50 beam splitter. One half of the initial beam is propagated a fixed distance to a flat mirror; the other half is passed through the sample and onto another flat mirror. Both beams are then reflected back to the beam splitter along their original paths and recombined. The superposition of these beams generates an interference pattern, which is monitored with a photodiode–amplifier. The intensity of light measured at the photodiode is dependent on the difference between the path lengths traveled by the sample and reference beams. If the difference is an exact multiple of the wavelength of the laser light, the recombined beams will
Journal of Chemical Education • Vol. 76 No. 5 May 1999 • JChemEd.chem.wisc.edu
In the Laboratory
interfere constructively and a corresponding maximum will be recorded by the photodiode. Conversely, a minimum intensity will be observed when the beams arrive out of phase. The effective optical path length (pe ) of a laser beam through a sample is dependent on the refractive index of the medium (n) and the path length of the sample cell (l ); pe = l n
(1)
Polymerization is normally accompanied by a sizable, yet continuous, variation in refractive index. As a result, the effective optical path length of a polymerizing liquid contained in a fixed-path-length cell will vary according to ∆pe = l ∆n
(2)
As pe varies over the order of several wavelengths of the laser beam, the intensity of the light recorded by the photodiode will oscillate in time in a sinusoidal fashion. We have recorded this “interferogram” by feeding the photodiode–amplifier signal into an analog-to-digital computer data acquisition system. If computer acquisition is unavailable, these data can be fed into an analog chart recorder. When assembling the apparatus, one should take measures to minimize vibrations; the Michelson interferometer output will be completely obscured by vibrations on the order of the wavelength of the light source. It is best to place the experiment in a low-traffic area that is away from mechanical motors such as vacuum pumps or hood fans. We have assembled our apparatus on an optical breadboard that is resting on two partially inflated bicycle tubes.
Arbitrary Intensity
Figure 1. Experimental diagram for collecting interference data.
We have studied the cure kinetics of two commercially available epoxy glues (“5 minute” and “30 minute” clear epoxy available from Devcon Consumer Products). An excellent article on epoxy polymerization has recently appeared in this Journal (10) and therefore the details of the epoxy curing mechanism will not be summarized here. Fast-drying epoxy adhesives are available in most department stores and are often packaged in a dual syringe dispenser. The epoxy reaction is started by mixing equal volumes of the two components, an epoxy resin and a polyamine hardener. For the experiments here, the components were vigorously mixed for 1 minute before the reacting mixture was placed in an optical cell and data acquisition was begun. Since a few minutes are required to get the sample in the cell and align the optical components, it is important to record this time so that it can be added to the kinetic data during analysis. In order for eq 2 to be valid, the path length (l ) of the optical cell must remain constant throughout the polymerization reaction. The cell used here consists of two 2 × 2-cm2 microscope slide windows separated by a 0.79-mm Teflon spacer. After an epoxy is mixed, a small portion of the viscous sample is applied to the surface of one window with a stirring bar, and then the second window (with the Teflon spacer) is dropped into place over the sample. The two windows are tightly sandwiched together by placing the cell inside a threaded metal retainer assembly. It is best if the cell is not completely filled, thereby leaving a small amount of air in the space between the windows. In this fashion, any contraction or expansion of the polymerizing medium will tend to cause flow lateral to the optical path and therefore will minimize unwanted pressure on the windows that could alter the path length. It is also helpful to mount the cell holder on the optical table so that its position can be adjusted perpendicular to the optical path. A position is desired where the laser beam can pass through the sample without encountering small air bubbles that may have been introduced during the mixing process. Since the sample is small and the glass windows act as thermal reservoirs, the polymerization reaction can be assumed to be isothermal. An interferogram for the 5-minute Devcon epoxy glue is shown in Figure 2. At the start of the polymerization reaction, the interferometer output oscillates between maxima and minima nearly once every second. However, the time for oscillation slows to almost 1000 seconds toward the end of this interferogram. A data acquisition rate of 1 sample per second is sufficient for resolving the oscillations beyond 300 seconds. A much faster sampling rate (and perhaps a smaller cell path length) should be used if one is interested in resolving the initial polymerization kinetics. The phenomenological cure rate is defined here as the change in refractive index with time (∆n/∆t). This quantity was calculated at different points throughout the reaction using the expression
∆n = λ ∆t l ∆t 0
1250
2500
3750
5000
6250
7500
Time / s Figure 2. Typical “interferogram” collected at room temperature (22 °C) for the 5-minute Devcon Epoxy adhesive (the computer acquisition rate was 1 sample/second).
(3)
where l is the wavelength of the light source (632.8 nm), ∆t is the amount of time between successive maxima or minima on the interferogram, and l is twice the thickness of the Teflon spacer (the beam passes through the cell twice). The calculation of ∆n/∆t at various times is facilitated by importing the
JChemEd.chem.wisc.edu • Vol. 76 No. 5 May 1999 • Journal of Chemical Education
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In the Laboratory
interferogram data file into a computer spreadsheet program. ∆n/∆t is plotted against time for the 5-minute epoxy as curve a in Figure 3. Two distinct time scales can be identified in the relaxation of the refractive index for the 5-minute epoxy. The crossover between the two time scales occurs at the gel point of the polymer, which appears as a kink in the data around 650 seconds. This kink is a direct indication of a drastic decrease in the diffusion rate in the reacting medium due to molecular entanglement. Similar data have been collected for the slower curing 30-minute epoxy (curve b) and no kink is evident. In this case, the initial polymerization reaction is slower and the subsequent decrease in the molecular diffusion rate occurs in a more continuous fashion. Conclusions An interferometric method has been demonstrated that enables students to study the polymerization of optically transparent samples. The apparatus is relatively inexpensive and can be constructed from items commonly available in undergraduate laboratories. Alternately, one can purchase the components of the apparatus at a total cost of approximately $1600 (excluding the data acquisition hardware/software [11]). In contrast to traditional spectroscopic methods, this interferometric technique exhibits a high sensitivity to the “physical” aspects of the polymerization process, allowing one to explore dynamics after the gel point of a polymer. A typical advanced laboratory experiment could be carried out by students in about 3 hours and would involve collecting two 1-hour-long interferograms, one for a “5-minute” and one for a “30-minute” epoxy reaction. Students could also utilize this apparatus for more extensive polymer studies, such as determining how the curing profile depends on the ratio of resin to hardener. In principle, the technique is not limited to polymerization studies and could be utilized to investigate any optically transparent reaction that yields a sizable refractive index variation.
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Figure 3. Curing profiles of (a) 5-minute Devcon Epoxy and (b) 30minute Devcon Epoxy. The gel point is evident in curve a at 650 s.
Literature Cited 1. Nimitz, J. S. Experiments in Organic Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1991; p 422. 2. Thomson, R. A. M. J. Chem. Educ. 1986, 62, 362. Senogles, E.; Woolf, L. A. J. Chem. Educ. 1967, 44, 157. 3. Atkins, P. Physical Chemistry, 5th ed.; Freeman: New York, 1994; p 913. 4. Allcock, H. R.; Lampe, F. W. Contemporary Polymer Chemistry, 2nd ed.; Prentice Hall: Englewood Cliffs, NJ, 1990; p 261. 5. Wingard, C. D.; Beatty, C. L. J. Appl. Polym. Sci. 1990, 40, 1981. 6. Thakur, A.; Banthia, A. K.; Maiti, B. R. J. Appl. Polym. Sci. 1995, 58, 959. 7. Shimbo, M.; Ochi, M.; Arai, K. J. Coatings Technol. 1984, 57, 45. 8. Heise, M. S.; Martin G. C. J. Appl. Polym. Sci. 1990, 39, 721. 9. Beysens, D.; Calmettes. P. J. Chem. Phys. 1977, 66, 766. 10. Dewprashad, B.; Eisenbraun, E. J. J. Chem. Educ. 1994, 71, 291. 11. A 2-mW HeNe laser, the optics, and optical mounts can be purchased from Edmund Scientific, Inc., Industrial Optics Division, 101 E. Gloucester Pike, Barrington, NJ 08007-1380; a 24×24in. optical table can be purchased from Vere, Inc., P.O. Box 777, New Kensington, PA 15068.
Journal of Chemical Education • Vol. 76 No. 5 May 1999 • JChemEd.chem.wisc.edu
