J. Phys. Chem. B 2002, 106, 6961-6965
6961
Fast Transient Fluorescence Technique for Determination of Gelation Activation Energies in Free-Radical Cross-Linking Copolymerization Demet Kaya and O 2 nder Pekcan* Istanbul Technical UniVersity, Department of Physics, Maslak, 80626 Istanbul, Turkey ReceiVed: June 25, 2001; In Final Form: March 13, 2002
Gelation during free-radical cross-linking copolymerization (FCC) of methyl methacrylate (MMA) and ethylene glycol dimethacrylate (EGDM) was studied using the fast transient fluorescence (FTRF) technique. Pyrene (Py) was used as a probe for the FTRF experiments. Fluorescence lifetimes of Py from its decay traces were measured and used to monitor the gelation processes in various EGDM contents at various temperatures. MMA consumption rates were measured during the gelation process by employing the Stern-Volmer kinetic model. Composite rate constants, kr, for FCC were determined for each EGDM content at different temperatures, and it is observed that as EGDM content and/or temperature is increased kr increased. Gelation activation energies, ∆EG, were measured for different EGDM contents, and it is observed that as ∆EG is decreased the EGDM content is increased.
Introduction Polymer molecules have various chain structure. They can be linear, branched (long and short branches), and cross-linked. A large percentage of the polymer products in use today are cross-linked, e.g., rubbers, thermosets plastics, and superabsorbents.1 During gelation, the molecules cross-link into larger clusters by forming covalent bonds in various ways.2 Freeradical cross-linking copolymerization (FCC) has been widely used to synthesize polymer gels. Several theories have been developed in the past half-century to describe gel formation in FCC, among which percolation theory provides a basis for modeling sol-gel phase transition.3-5 Statistical theories originate from Flory6 and Stockmayer7 assume equal reactivities of functional groups and the absence of cyclization reactions. Most statistical theories derived in the following decades are fully equivalent, differing only in mathematical language.8-11 In FCC, the formation of bonds building the network can be described using differential equations with reaction time or monomer conversion as the independent variable. The kinetic approaches can take into account all of the kinetic features of copolymerization and cross-linking reactions, which may suggest a more realistic approach to the mechanism of gelation, process.12-15 Kinetic models have been extensively used to describe the relations among the molecular weight of the polymer and the conversion or reaction time during the cross-linking process. In the classical kinetic theory, the rate constant is proportional to the product of the number of functional groups in each reactant. Modification of the classical kinetic theory by using rate constants that also depend on the structural features of the reactants has been done.16 When an organic dye absorbs light, it becomes electronically excited, and then fluorescence occurs from the lowest excited singlet state and decays over a time scale typically of nanoseconds.17,18 In addition to unimolecular decay pathways for deexcitation of the excited state, there are a variety of bimolecular interactions which can lead to deactivation. These are referred to collectively as quenching processes, which enhance the rate of decay of an excited-state intensity, I. For dilute * To whom correspondence should be addressed.
solutions of dye molecules in isotropic media, exponential decays are common. In more complex systems, deviations are often observed. Because of these features, fluorescence dyes can be used to study local environments. In that sence, because of its long excited singlet lifetime, pyrene (Py) as a chromophore17 is an attractive choice for studying dynamics in polymers. For about two decades, the transient fluorescence (TRF) technique for measuring fluorescence decay has been routinely applied to study many polymeric systems using chromophores.19-21 TRF spectroscopy with direct energy transfer (DET) from a donor to an acceptor chromophore and quenching of a donor by an acceptor has been used to characterize internal morphologies of composite polymeric materials.22 TRF and steady-state fluorescence (SSF) techniques were employed to study isotactic polystyrene in its gel state. A pyrene derivative was used as a fluorescence molecule to monitor the polymerization, aging, and drying of aluminosilicate gels.23 These results were interpreted in terms of the chemical changes occurring during the sol-gel process and the interactions between the chromophores and the sol-gel matrix. We reported in situ observations of the sol-gel phase transition in free-radical crosslinking copolymerization using the SSF technique.24-27 In this work, the FTRF technique was used to study the solgel transition in the FCC of MMA and EGDM. The quenching properties of the excited state of the Py molecule were used to study the monomer consumption rate in the free-radical crosslinking copolymerization of MMA. The rates of polymerization were determined at various cross-linker contents and temperatures. Gelation activation energies, ∆EG and ∆EI, for the FCC were determined for five different sets of experiments and observed that as cross-linker content is increased activation energies decrease. Unreacted monomers which are trapped in the gel during FCC were also measured and observed that high cross-linked gels trap more monomers than low cross-linked gels. Theoretical Considerations Fluorescence intensities of aromatic molecules are affected by both radiative and nonradiative processes.28 If the possibility
10.1021/jp012405r CCC: $22.00 © 2002 American Chemical Society Published on Web 06/14/2002
6962 J. Phys. Chem. B, Vol. 106, No. 27, 2002
Kaya and Pekcan
of perturbation due to oxygen is excluded, the radiative probabilities are found to be relatively independent of environment and even of molecular species. Environmental effects on nonradiative transitions that are primarily intramolecular in nature are believed to arise from a breakdown of the BornOppenheimer aproximation.29 Years ago, Birks et al. studied the influence of solvent viscosity on fluorescence characteristics of pyrene solutions in various solvents and observed that the rate of monomer internal quenching is affected by solvent quality.30 Weber et al. reported the solvent dependence of energy trapping in phenanthrene block polymers and explained the decrease in fluorescence yield with the static quenching, caused by the solvent induced trapping states.31 A matrix that changes little with temperature will enable one to study molecular properties themselves without changing environmental influence. Poly(methly methacrylate) (PMMA) has been used as such a matrix in many studies.32 Emission of the fluorescence is the radiative transition of an electronically excited molecule from its singlet excited state to its ground state.17 Fluorescence quenching normally refers to any bimolecular process between the excited singlet state of a fluorescence dye and the second species that enhances the decay rate of the excited state. Many types of processes lead to quenching. Kinetically, quenching process can be divided into two main categories: dynamic and static. In dynamic quenching, diffusion to form an encounter pair during the excited state lifetime of the dye leads to quenching. In static quenching, diffusion does not occur (which is out of our interest). Dynamic quenching is most likely to occur in fluid solution, where the dye or quencher is free to move. In general, the lifetime, t, of the excited molecule is given by the following relation call Stern-Volmer equation:
τ-1 ) τ0-1 + kq[Q]
T (°C) t0 (min) τ0 (ns) kq × 106 (M-1s-1) kr × 10-3 (s-1)
% 0.015 EGDMa 55 60 76 36 314 304 8.1 8.4 8.6 10.6
65 27 313 8.4 11.8
70 19 296 9.4 20.2
T (°C) t0 (min) t0 (ns) kq × 106 (M-1s-1) kr × 10-3 (s-1)
% 0.020 EGDM 55 60 54 39 297 315 8.0 8.4 9.3 11.3
65 24 286 8.4 11.7
70 15 285 7.9 22.0
T (°C) t0 (min) τ0 (ns) kq × 106 (M-1s-1) kr × 10-3 (s-1)
% 0.025EGDM 55 60 51 33 291 296 8.4 8.1 9.7 13.1
T (°C) t0 (min) τ0 (ns) kq × 106 (M-1s-1) kr × 10-3 (s-1)
% 0.030 EGDM 55 60 40 30 275 290 8.0 7.8 11.1 15.6
65 20 275 8.0 13.5
70 14 287 9.3 20.3
T (°C) t0 (min) τ0 (ns) kq × 106 (M-1s-1) kr × 10-3 (s-1)
% 0.035 EGDM 55 60 36 23 238 190 13.8 12.5 16.3 17.0
65 17 245 11.8 17.2
70 12 216 13.1 21.8
65 22 289 9.0 13.6
70 14 279 8.94 22.2
a T; reaction temperature. t0; onset of gelation time. τ0; unquenched lifetimes of pyrene. kq; quencher rate constant. kr; composite rate constant for FCC.
(1)
where τ0 is the lifetime of excited molecule where no quenching takes place, [Q] represents the quencher concentration, and kq is the quenching rate constant. The first step in free-radical polymerization is the decomposition of the initiator molecule into two species carrying unpaired electrons called free radicals. A free radical can then react to open the double bond of a vinyl monomer and add to it, with one electron remaining unpaired. In a very short time, usually a few seconds or less, many more monomers add successively to the growing chain. Finally, two radicals react to the end of each other’s growth activity and form one or more polymer molecules. This bimolecular process is called the termination reaction. During the free-radical cross-linking copolymerization (FCC), addition of divinyl monomers to the growing chain results in the formation of polymer molecules with reactive sites (“pendant vinyl groups”). These reactive sites on polymer chains offer the possibility of forming chemical structures of macroscopic dimensions called polymer gels. The rate of consumption of monomer concentration, [M], is usually called the rate of polymerization and is given by the following equation:33
[M] ) [M0] exp(-krt)
TABLE 1: Experimentally Measured Parameters for EGDMa
(2)
where [M0] is the concentration of monomer at t ) 0 and kr is the composite rate constant. Experimental Section Materials. EGDM has been commonly used as cross-linker in the synthesis of polymeric networks. As for EGDM, it is chosen for its chemical similarity in molecular structure to that
of MMA and the symmetry of the two vinyl groups. Here, for our use, the monomers MMA (Merck) and EGDM (Merck) were freed from the inhibitor by shaking with a 5% NaOH solution, washing with water, and drying over sodiumsulfate. They were then distilled under reduced pressure over copper chloride. The initiator, AIBN (Merck), was recrystallized twice from methanol. The radical copolymerization of MMA and EGDM was performed in bulk in the presence of 2,2′-azobisisobutyronitrile (AIBN) as an initiator. The initiator concentration was held constant at 0.26 wt %. The Py concentration was taken as 4 × 10-4 M. The samples were deoxgenated by bubbling nitrogen for 10 min, and then radical copolymerization of MMA and EGDM was performed for five different sets of experiments. In each set of experiments, FCC was performed at four different temperatures (55, 60, 65, and 70 °C) in a given EGDM content which are 0.015, 0.020, 0.025, 0.030, and 0.035 vol % EGDM as presented in Table 1. Fluorescence Measurements. In situ fluorescence decay experiments from which Py lifetimes can be determined were performed using Photon Technology International’s (PTI) Strobe Master System (SMS). In the strobe, or pulse sampling technique,34 the sample is excited with a pulse light source. The name comes about because the PMT is gated or strobed by a voltage pulse that is synchronized with the pulsed light source. Because the strobe technique is intensity-dependent, the strobe instrument is much faster than single photon counting (SPC) and even faster than the phase instrument. Because of these advantages, SMS is used to monitor gelation processes, which take around a few hours. All lifetime measurements were made at 90° position, and slit widths were kept at 10 nm. The gelation experiment was
FTRF Technique for Determination of Energies
J. Phys. Chem. B, Vol. 106, No. 27, 2002 6963
Figure 1. Fluorescence decay profiles of the excited pyrene (Py), at various gelation steps performed at 70 °C for the sample with 0.015 vol % EGDM content. I(t) is the Py intensity. Numbers on each curve present the gelation time, tg, in minutes.
performed in a round quartz cell, which was placed in the SMS, and the fluorescence decay was collected over three decades of decay. The sample was then illuminated with 345 nm excitation light and pyrene fluorescence emission was detected at 395 nm. Results and Discussion To monitor gelation processes, the decaying fluorescence intensity, I(t), is measured and fitted to the following equation:
I(t) ) A exp(-t/τ)
(3)
where A is the preexponential factor. The observed fluorescence decay of a sample, φ(t), is related to the actual fluorescence decay, I(t), and the SMS light pulse, L(t - t′) via the following convolution integral:
φ(t) )
∫0tL(t - t′)I(t′) dt′
Figure 2. Plots of lifetimes, τ, of Py, during gelation at (a) 55, (b) 60, and (c) 70 °C temperatures respectively for the 0.015 vol % EGDM content sample. t0 is the onset of gelation time.
that τ0 values were determined after the gelation is completed and the ideal solid gel is formed. To quantify these results Stern-Volmer type of quenching mechanism is proposed for the fluorescence decay of Py during gelation process, where eq 1 can be employed and rewritten as follows:
(4)
Typical decay curves of Py are shown in Figure 1 for the increasing gelation times, tg, during gelation at 70 °C for 0.015 vol % EGDM content sample. Deconvolution of I(t) from eq 4 is performed to obtain τ values using the linear-least-squaresd fitting technique. The uniqueness of the fit of the data to the model is determined by χ2 (χ2 < 1.20), the distribution of weighted residuals, and the autocorrelation of the residuals. It is observed that as the gelation time, tg, increases excited pyrenes decay slower and slower by indicating that quenching of excited pyrenes decrease during gelation. τ values were produced at each gelation step and are plotted versus gelation time, tg, in Figure 2a-c for the 0.015 vol % EGDM content sample at the reaction temperatures of 55, 60, and 70 °C, respectively. As seen in Figure 2, Py lifetimes, t, increased drastically above a certain gelation time called the onset of gelation time, t0, from very low values (12 ns) to their unquenched τ0 value during gelation at each temperature. The onset of gelation time, t0, decreased as the temperature increased, indicating that an early gelation process takes place at high temperatures. The measured τ0 and t0 values for each set of experiments are presented in Table 1. Here one has to notice
τ-1 ) τ0-1 + kq[MMA]
(5)
Because MMA is the only quencher for Py and by knowing the [MMA0] value as 9.4 M, kq values are measured before the polymerization has started and are listed in Table 1. Using the kq and τ values, monomer concentrations, [MMA], are obtained from eq 5. The produced [MMA] curves versus tg obey the relation in eq 2 where (tg - t0) is defined as the “effective gelation time” at which the sol-gel phase transition takes place. In other words, the behavior of MMA versus (tg - t0) predicts the rate of loss of MMA, which increases by increasing the reaction temperature, T, during gelation. The logarithmic forms of [MMA] versus (tg - t0) are plotted in Figure 3a-c for the 0.015 vol % EGDM content samples at the reaction temperatures of 55, 60, and 70 °C, respectively. In Figure 3, the slope of the linear relations produce the composite rate constants, kr, according to eq 2, for the FCC polymerizations at the reaction temperatures of 55, 60, and 70 °C. Similarly produced kr values for each experimental set are presented in Table 1. The plot of kr versus temperature for the 0.015 vol % EGDM sample is shown in Figure 4, where it is seen that, as the temperature is raised, the composite rate constant increased as expected.
6964 J. Phys. Chem. B, Vol. 106, No. 27, 2002
Kaya and Pekcan TABLE 2: Gelation, ∆EG, and Initiation, ∆EI, Activation Energiesa EGDM (vol %)
∆EG (kcal mol-1)
∆EI (kcal mol-1)
0.015 0.020 0.025 0.030 0.035
12.04 ( 0.24 11.60 ( 0.18 11.15 ( 1.32 7.46 ( 1.66 3.92 ( 0.39
20.97 ( 0.80 19.32 ( 0.66 19.14 ( 0.19 15.87 ( 0.41 16.08 ( 0.17
a ∆EG and ∆EI are produced by fitting eqs 6 and 7 to kr and t0-1 versus T-1 data, respectively.
Figure 5. Plot of the (a) gelation, ∆EG, and (b) initiation, ∆EI, activation energies versus vol % of EGDM content. Figure 3. Logaritmic plots of [MMA] versus (tg - t0) for the samples prepared with 0.015 vol % EGDM and polymerized at (a) 55, (b) 60, and (c) 70 °C temperatures.
Figure 6. Plot of kr versus vol % of EGDM content.
Figure 4. Plot of composite rate constant, kr, versus gelation temperature, T, for the sample of 0.015 vol % EGDM content.
A simple Arrhenius treatment to the kr data in Table 1 can produce the gelation activation energies, ∆EG, where the following relation is used:
kr ) kr0 exp(-∆EG/kT)
(6)
where kr0 is the composite rate constant at infinite temperature
and k is the Boltzman constant. The produced ∆EG values are listed in Table 2 and plotted versus EGDM content in Figure 5a. As seen in Figure 5a, higher EGDM content samples need less energy to accomplish the gelation process. On the other hand, the plot of kr versus EGDM (see Figure 6) shows that a higher cross-linker density causes an increase in the composite rate constant. Combining the results in Figures 5a and 6 produce resonable understanding to the needs of activation energy; that is, a higher reaction rate needs a smaller energy during FCC, which is already predicted in eq 6.
FTRF Technique for Determination of Energies
J. Phys. Chem. B, Vol. 106, No. 27, 2002 6965 the τ0 values a week after the FCC process. Equation 5 can be used to calculate the amount of unreacted monomer concentration, [MMA]u, after the FCC process is completed, which is plotted in Figure 7 versus the EGDM content. It is seen in Figure 7 that more unreacted monomers trap in the gel prepared at high cross-linker contents. In summary, this paper introduced a simple kinetic model and a novel method, which used the FTRF technique to measure the gelation (∆EG) and initiation (∆EI) activation energies for different cross-linker contents. It is observed that smaller energies were used both to initiate and to proceed the FCC processes at high cross-linker (EGDM) contents. The most important finding in these experiments is that initiating of FCC processes needs higher energies than maintaining it. References and Notes
Figure 7. (a) Plot of τ0 values versus EGDM contents. Solid dots present the τ0 data a week after the FCC is completed. Empty dots are for the τ0 immediately after the FCC is completed. (b) Plot of the unreacted monomers [MMA]u versus EGDM contents.
In Figure 2, it is seen that the onset of gelation time, t0, decreased as the gelation temperature is increased. If one assumes that t0-1 is the “rate of initiation” of FCC process, the below Arrhenius relation
t0-1 ) t00-1 exp(-∆EI/kT)
(7)
can produce the energy, ∆EI, needed to initiate the FCC process. The produced initiation activation energies, ∆EI, are listed in Table 2 and plotted versus EGDM in Figure 5b. It is interesting to note that ∆EI values are found to be much higher than ∆EG values, which predicts that initiating the FCC process needs a much higher energy than the maintaining of it. The plot of ∆EI versus EGDM content presents similar behavior as ∆EG; that is, the higher reaction rates need a smaller energy to initiate the FCC process, which is already predicted in eq 7. On the other hand, careful analysis of Table 1 shows that τ0 values decrease as the EGDM content is increased which needs some explanation. τ0 values, for the gel prepared at 55 °C are plotted versus EGDM content in Figure 7, where it is seen that as the EGDM content is increased τ0 values decrease. This behavior of τ0 indicates that more unreacted monomers are trapped in high EGDM content samples than in low EGDM content samples, after the FCC processes is completed. However, after a week, τ0 values were remeasured, and it was observed that τ0 values level off because of the polymerization of the unreacted monomers. In Figure 7, solid dots represent
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