Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
A Semiempirical Scaling Model for the Solid- and Liquid-State Photopolymerization Kinetics of Semicrystalline Acrylated Oligomers Patrice Roose,*,† Hugues Van den Bergen,† Annemie Houben,‡ Dirk Bontinck,† and Sandra Van Vlierberghe‡ †
allnex Belgium, Anderlechtstraat 33, Drogenbos B-1620, Belgium Polymer Chemistry and Biomaterials Group, Center of Macromolecular Chemistry, Department of Organic and Macromolecular Chemistry, Ghent University, Krijgslaan 281, Building S4-Bis, Ghent B-9000, Belgium
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‡
S Supporting Information *
ABSTRACT: The recent introduction of semicrystalline acrylated oligomers exhibiting fast photoinitiated free radical polymerization in the solid state calls for a deeper understanding of the mechanisms behind the reaction kinetics. The photoinduced polymerization of an acrylated urethane-based poly(ethylene glycol) precursor was studied in detail at temperatures below the melting point using differential photocalorimetry. In isothermal conditions, the exothermal heat flow profile is characterized by an acceleration step followed by a gradual deceleration. In contrast to liquid-state photopolymerization, the well-known gel effect cannot be invoked to account for the reaction acceleration in the crystallized resin. By revisiting the kinetics of free-radical polymerization, it appears that the acceleration results from the buildup of the radical concentration toward steady state in a reaction−diffusion driven process. The kinetic behavior is examined in terms of conversion for which any structure-dependent kinetic effect is described by a power-law approximation based on scaling arguments from experimental evidence and polymer physics. This results in a closed-form analytical expression that compares well to experimental data for the photopolymerization kinetics of a semicrystalline acrylated urethane precursor upon adjustment of three parameters. The model is extended to include the additional kinetic complexity for liquid (meth)acrylates and provides a unified approach to free-radical polymerization built on fundamental insights. Crystalline State” was issued by Morawetz and co-workers.3,4 FRP initiated by γ-radiation was then explored in many crystalline monomers including vinyl stearate and salts of acrylic and methacrylic acid. In the same period, experiments conducted with ultraviolet irradiation demonstrated the photoinitiated free-radical polymerization in polycrystalline calcium and potassium salts of acrylic acid, yet with very slow kinetics.5 Three decades later a few other papers were published referring to the solid-state polymerization of monomer compounds such as cyclic acetal-containing acrylates, octadecyl (meth)acrylate, and vinyl ether, but acrylated oligomers were never studied.6−9 The monitoring of the photopolymerization kinetics of multiacrylate compounds by established techniques, such as differential photocalorimetry (DPC) or real-time infrared spectroscopy, reveals qualitative similarities irrespective of the initial physical state whether liquid or solid, which are
1. INTRODUCTION Recently, solid-state photopolymerization emerged as an efficient postprocessing step in the manufacturing of insoluble objects for biomedical applications starting from telechelic acrylated urethane-based oligomers of limited molar mass ( x3, e.g., for inactivation (trapping, caging) processes taking place effectively close to the end of the polymerization. Along with eqs 15 and 16, a compact semiempirical expression with five independent parameters is provided in the end, i.e., E
DOI: 10.1021/acs.macromol.8b00706 Macromolecules XXXX, XXX, XXX−XXX
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Figure 2. (a) Storage (G′, thick line) and loss (G″, dashed line) modulus versus UV-exposure time for solid (20 °C, gray) and liquid (50 °C, black) AUP. The noisy curves represent the corresponding conversion profiles as determined by time-resolved FTIR spectroscopy. (b) Loss factor profiles (G″/G′) as a function of exposure time at three oscillation frequencies for the liquid AUP at 50 °C. The dashed line indicates the conversion level at the gel point according to the Winter−Chambon approach.
Figure 3. 3D representation of the undistorted heat flow profiles recorded for the AUP upon exposure to UV light at polymerization temperatures between −15 and 90 °C. Prior to photopolymerization, the AUP was crystallized in isothermal conditions at 20 °C. Left: autoinitiation without additional PI; right: after addition of 0.2% w/w PI.
−50 °C, in contrast to the AUP cross-linked at 20 °C that recrystallizes upon cooling. The data in Figure 2a were measured at an oscillation frequency of 10 Hz. According to Winter and Chambon, the gel point during network formation from a liquid precursor can be determined by detecting the crossing point of the viscoelastic loss factor (= G″/G′) curves recorded at varying oscillation frequencies.40 Figure 2b shows a rare example in which this approach could successfully be applied and demonstrates that upon photopolymerization at 50 °C the gel point is reached at a conversion below 5%. With the low amount of double bonds present in this system, the determination of conversion in real time using specific absorption bands is nearly impossible, and correlation over a broad spectral range is required to extract profiles with an acceptable signal-to-noise ratio. However, the level of noise still prevents any reliable quantification of the conversion value. The monitoring of the heat flow by calorimetric techniques provides a straightforward way to determine the conversion rate and the actual conversion (by integration) in FRP processes. Upon exposure to UV light, the polymerization kinetics of photosensitive resins can be followed, but often, however, the instrumental response time of conventional DSC instruments leads to limitations in terms of kinetic monitoring, in particular for fast reactions. In this work, the latter issue was partly offset by filtering out the psf from the measured signal to recover the undistorted polymerization exotherm. Still, with a characteristic time scale of 0.7 s for the instrumental response,
controlled exclusively by reaction diffusion. The initial acceleration reflects the transient toward the steady-state regime whereas the deceleration is explicitly dominated by first-order kinetics and diffusion control of the propagation until structurally driven arrest at the final conversion. On the other hand, high k0t,d/k0p values result in a sudden jump toward steady state followed by an acceleration period driven by the retarding termination process. After the maximum, the rate decays similarly, irrespective of the k0t,d/k0p value.
4. RESULTS AND DISCUSSION The unique behavior of AUP is nicely illustrated from Figure 2a where the photoinitiated polymerization was followed by monitoring the small-strain viscoelastic properties along with the spectral conversion in real time. The shear moduli G′ and G″ reflect the initial state of the material, i.e., an elastic solid at 20 °C (G′ ≫ G″) and a viscous liquid at 50 °C (G′ ≪ G″). While significant changes are evidenced upon curing at 50 °C (G′ ≈ 0 → 2 MPa) owing to the transformation of the physical state, less effect is noticed at 20 °C (G′ ≈ 60 → 120 MPa). However, up to 65%, the conversion profiles are obviously close but levels off more quickly at 20 °C, thereby not achieving full conversion in the end. After photopolymerization at 20 °C, the storage modulus of the AUP is ≈1 MPa at 50 °C, in agreement with the lower conversion and cross-linking density compared to its equivalent polymerized at 50 °C. Noteworthy, the latter material is amorphous with a low Tg ≈ F
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Figure 4. Rate−conversion profiles for the photopolymerization at 20 °C of the AUP in the solid state after crystallization at 20 °C. The rainbow colors from blue to red represent experiments conducted at increasing light intensities ranging from I0,365 = 0.2 to 55 mW cm−2. The black lines result from a NLLS comparison of eq 19 to the experimental data. (a) Autoinitiation without additional PI; (b) after addition of 0.2% w/w PI.
Figure 5. Plot of the adjusted parameters x1 (a), x2 (b), and x3 (c) as a function of the incident light intensity at 365 nm after NLLS comparison of eq 19 to the experimental data. The limiting conversion at the end of polymerization is plotted in (d). The open and solid symbols refer to the photopolymerization kinetics in the absence of and with additional PI, respectively. The fit errors are always smaller than the symbol size as illustrated for one data set of x1.
the data are truncated within the first few seconds. Figure 3 shows the sets of undistorted heat flow profiles following psf deconvolution for the investigated AUP after isothermal crystallization at 20 °C. The temperature axis refers to the photopolymerization temperature and demonstrates that the resin reacts in the solid state with increasing heat flow from −20 °C up to the fusion temperature range, even without the addition of a specific photoinitiator. With additional PI, the polymerization slows down significantly in the molten state characterized by profiles stretched over longer time periods. The collapse of the reaction rate upon melting suggests that the autoinitiating sites producing primary radicals are located
near or at the acrylate double bonds which are packed together in the solid state owing to the formation of PEG crystallites (i.e., a kind of self-assembly).51,52 Upon melting, the local concentrations of double bond and initiating moieties are diluted. The addition of 0.2% w/w of PI boosts the polymerization rate in solid and molten conditions without substantial decrease in the melt. With a uniform distribution of the PI in the AUP, no dilution effect is really expected upon melting. As clearly evidenced, heat flow profiles changing steeply within the first seconds suffer from truncation after psf deconvolution. Similar 3D plots for the photopolymerizations conducted after dynamic crystallization (down to −20 °C) are G
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Macromolecules provided in SI-6 and reveals qualitatively the difference in crystallinity resulting from the distinct thermal history. Before analyzing the heat profiles of Figure 3 using the semiempirical model introduced in section 3, the influence of UV intensity is first examined for the photopolymerization of the AUP at 20 °C after crystallization in isothermal conditions at 20 °C. As noticed earlier, the fraction of UVA light at 365 nm is used as an intensity gauge for the polychromatic irradiation source. Upon scaling and integration, the undistorted heat flow profiles are transformed into rate− conversion plots as shown in Figures 4a and 4b in the absence and the presence of PI, respectively. While the conversion rate increases with incident light intensity (from I0,365 = 0.2 to 55 mW cm−2) as anticipated, the limiting conversion clearly crosses a maximum. The experimental data were compared using nonlinear least-squares optimization to eq 19, derived for an FRP process for which termination is governed by reaction diffusion. The agreement is excellent after adjustment of the three x parameters, and eq 19 obviously captures the overall phenomenological behavior where the acceleration period reflects the transient behavior toward the steady-state regime. Many studies have underestimated or overlooked this aspect, but a few papers address nonsteady kinetic behavior in cross-linked amorphous systems albeit on a purely empirical basis.32 It should be noted that in Figure 4b the initial rate value at zero conversion for the kinetic profiles with the fastest rates is an artifact due to the instrumental response limit. The values of the three adjusted parameters as well as the limiting conversion are plotted in Figures 5a−d. The errors are smaller than the symbol size while several curves were measured twice. The single parameter with an a priori predicted dependence of the incident light intensity is x1 = Rik0p. Proportionality is satisfied up to an intensity of ≈10 mW cm−2. The deviation at higher intensities likely suggests that fast radical production results in quick recombination (e.g., primary radicals)27 in the confined space reducing the initiation efficiency, and hence Ri, for subsequent chain propagation. For intensities within the linear range it is assumed that Ri behaves fairly constant throughout the course of the polymerization. The presence of PI enhances the UV absorption significantly, but still, the thin film approximation Ri(λ) = φiI0,λελ[PI] holds closely over the spectral range of the light source as verified from eq 4 and αλ = ελ[PI]d using the molar attenuation (ελ) data of HCPK provided in SI-3, for a layer of 200 μm and [PI] ≈ 9−10 mmol L−1 (i.e., 0.2% w/w). Furthermore, the initiation rate at maximum efficiency (i.e., φi = 1) can be estimated over the full spectrum as shown in Figure 6 for an incident light intensity scaled to I0,365 = 1 mW cm−2. The magnitude of Ri,max turns around 10−6 mol L−1 s−1 for the most prominent spectral lines and learns that the initiation rate is very low, resulting in a minor consumption of PI over the course of the photopolymerization which in turn supports the steady-state assumption for radical initiation. When PI is present, the linear trend of x1 = Rik0p at low intensities has a slope of 0.025 cm2 mW−1 s−2. From this value and the Ri,max data a lower bound is provided for the propagation coefficient k0p at other wavelengths of the light source, as shown in Figure 6. Irrespective of the excitation wavelength, the order of magnitude for k0p,min is ≈104 L mol−1 s−1, not unreasonable when compared to values reported in the literature.41 The second parameter x2 = AM0 varies from 1.5 to 4 for autoinitiation and from 0.5 to 2 in the presence of PI, which is
Figure 6. Red: estimation of the maximum initiation rate at an intensity I0,365 = 1 mW cm−2 for 0.2% w/w HCPK over the spectral range of the UV light source. Blue: lower bound of k0p estimated from the slope of x1 in Figure 5a (with PI) using the Ri,max data, as explained in the text.
consistent with the prognosis that A is not directly affected by the intensity. By scaling x2 with the initial local concentration M0 of packed double bonds, where the global value M0 ≈ 0.6 mol L−1 of the oligomer provides a lower limit, it appears that the order of magnitude of A agrees with previously reported data for the FRP of mono- and multiacrylates which typically ranges between ≈2 and 4.17−19,27,28,36 The reaction diffusion parameter A was formerly used as a probe for chain-lengthdependent termination in free-radical cross-linking.28 Our results corroborate the weak dependence found for acrylates when initiation parameters are varied. Similarly, the exponent x3, which accounts for the deviation of first-order kinetics owing to the gradual diffusion control for propagation and the possible structural hindrance of radical activity, is not anticipated to be strongly sensitive to incident light intensity. Nevertheless, the values increase from ≈1.5 to ≈2.5 at low intensities and return to approximately 2 at higher intensities. This trend can be related to a shift of the onset of radical deactivation toward earlier times in the reaction characterized by a lower exponent which would correlate with the behavior of x1. Additionally, the limiting conversion pf reveals a maximum value between 1 and 10 mW cm−2 with a gradual decrease at higher light intensities. The parameter analysis suggests that when radical generation is too fast in the confined arrangement, the likelihood of local recombination will enhance relative to propagation. Figure 5a shows that the addition of the photoinitiator has a pronounced effect on the slope of x1 with a 5-fold increase for 0.2% w/w HCPK in comparison to autoinitiation. However, the linearity range is similar, which again indicates that the rate of radical generation rather than the actual amount of PI is important. The profiles shown in Figure 3 at different polymerization temperatures were measured at the linearity limit of intensity, i.e., I0,365 ≈ 11 mW cm−2, in order to probe the widest temperature range to the lower end. In Figure 7, the rate− conversion profiles of the photopolymerizations conducted in the solid state are shown for temperatures between −15 and 25 °C after dynamic crystallization upon cooling to −20 °C (similar plots are supplied in SI-7 for isothermal crystallization at 20 °C). The addition of PI enhances the amplitude of the curves compared to the autoinitiated case. An NNLS comparison of eq 19 shows again an excellent agreement H
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Figure 7. Rate−conversion profiles for the photopolymerization of AUP in the solid state after dynamic crystallization upon cooling to −20 °C. The color code agrees with Figure 3 and refers to polymerization temperatures from −15 to 25 °C in steps of 5 °C (I0,365 ≈ 11 mW cm−2). The black lines result from an NLLS comparison of eq 19 to the experimental data. (a) Autoinitiation without additional PI; (b) after addition of 0.2% w/w PI.
Figure 8. Arrhenius plot showing the temperature dependence of the limiting conversion pf (a) and the adjustable parameters x1 (b), x2 (c), and x3 (d). The blue and red data refer to results obtained after NLLS comparison against eqs 19 and 18, respectively. The vertical lines delimit the temperature range for melting. To the right (lower temperatures, blue), the AUP resin was photopolymerized in the solid semicrystalline state after isothermal crystallization at 20 °C (triangles) and dynamic crystallization to −20 °C (circles), whereas on the left side, the AUP resin was initially liquid (red diamonds). The red diamonds in (c) are fixed values as explained in the text. Open symbols: autoinitiation; filled symbols: in the presence of PI. The fitted line is shown for one data set.
starting from −20 up to 25 °C) during which the material was photopolymerized in a solid semicrystalline state, (ii) a transition zone (between the dashed lines, i.e., 25−40 °C) in which the material is partly molten, and (iii) the temperature range where the AUP was polymerized from the liquid state and turned into a rubber-like material as shown earlier in Figure 2. In the semicrystalline solid state (blue data), the limiting conversion shows a fairly linear behavior toward higher temperatures reaching a value of 80−90% close to the
with the experimental data after adjustment of the three x parameters. The limiting conversion and the adjusted parameters of eq 19 are reported in Figure 8a−d according to an Arrhenius representation and span a temperature range from −20 to 40 °C for the four data sets referring to the two crystallization conditions with and without PI. Preliminary inspection of the limiting conversion pf in Figure 8a defines three temperature zones: (i) a premelting temperature range (on the right I
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Macromolecules melting zone. When polymerized from the melt (red symbols), full conversion is achieved as usual for a soft rubber. For photopolymerization in the solid state, the intensity data already showed that an increase of the limiting conversion could be correlated to a higher efficiency in initiation− propagation. This is also verified here from the behavior of the parameter x1 at temperatures below the melting zone. The near linear trend was fitted with a straight line between −15 and 15 °C for the four data sets resulting in slopes between −66 and −86 kJ mol−1, with an average of −75 kJ mol−1, predominantly related to the activation energy of the propagation coefficient k0p in the assumption that the initiation rate Ri behaves steadily. The activation energies reported for the propagation in the bulk polymerization of liquid acrylates are typically 4−5 times lower at the early stage of the reaction.41 However, there is evidence that the activation energies raise with motional hindrance of the reactive functions in a solid environment; e.g., for alkali acrylates and methacrylates values about ≈70−80 kJ mol−1 were reported.3,6,41 In Figure 8c, the inverse trend of x2 = AM0 = k0t,rd/k0p with slopes between 69 and 87 kJ mol−1 (79 kJ mol−1 on the average) in the same temperature interval is consistent with the order of magnitude found for x1 and hence k0p. From the parameter product x2x1 ≈ k0t,rdRi it is then further inferred that k0t,rd and/or Ri exhibit relatively weak temperature dependence with a roughly estimated activation energy of ≈8 kJ mol−1 falling within the error boundaries. Earlier reported values for the activation energy of the bimolecular termination of acrylate radicals agree with this order of magnitude.36,41 The power exponent x3 is mainly defined by the behavior of the conversion rate in the deceleration period and increases from ≈1.5 to 2.5−3 with temperature, likely suggesting a delay of radical trapping or diffusion-controlled propagation toward higher conversions. In parallel with the temperature study, the photopolymerization kinetics was also investigated beyond the melting transition during which polymerization starts from the liquid AUP resin. The complexity behind the kinetics is virtually enhanced by the release of the motional constraints inherent to the semicrystalline state. In order to describe the kinetic phenomenology for the transformation of a liquid to a crosslinked network, a model extension is required which is provided by eq 18. The photopolymerization was investigated from the melt at temperatures between 50 and 90 °C in steps of 10 °C, and as shown before in Figure 3, the heat flow profiles vary substantially less with temperature in this case. To illustrate, the rate−conversion curves at 50 °C are presented in Figure 9 and highlight the more pronounced effect of the added PI relative to autoinitiation. The finite rate at zero conversion is possibly a truncation effect, but it is also theoretically anticipated when translational diffusion control is operational in the termination process. Interestingly, the profiles do not show any singularity when the gel point conversion at ≈5% (cf. Figure 3) is crossed. To test the kinetic scaling model for polymerization of the liquid precursor, eq 18 was applied using five parameters first. Notwithstanding a good functional approximation, correlations between the parameters required a careful initial guess for the starting values of the parameters in the optimization process. The parameter x2 appeared as fairly constant after NLLS optimization, and in a second analysis, the average value x2 ≈ 20 was fixed to improve fitting stability. The results for x1 and x3 after adjustment are shown in Figures 8b and 8d, respectively. With typical activation energies below 20 kJ mol−1 for the radical
Figure 9. Rate−conversion profiles for the photopolymerization of molten AUP at 50 °C. The top curve (blue) was measured with additional PI whereas the lower cyan curve was recorded in the absence of PI. The thin black lines result from a NLLS fit of eq 18 to the experimental data.
propagation in liquid acrylates, the temperature dependence of x1 is expected to be weak and hard to quantify given the accuracy of the measurements. A significant gain by a factor ≈50 is noticed when 0.2% w/w HCPK is added. As the exponent x3 is mainly defined by the shape of the deceleration part, it is nearly insensitive to the choice of eq 18 or 19 and follows along the decreasing trend initiated in the melting zone (Figure 8d). Values of x3 below 1 correspond to very weak curvatures. In this case, the decaying rate is close to first-order kinetics, in agreement with the absence of vitrification and significant radical trapping in a weakly cross-linked rubber. The parameters x4 and x5 are strongly dependent on the initial kinetic behavior and do not provide reliable data for the slow polymerization behavior measured upon autoinitiation. With additional PI, the values of x4 = k0t,d/k0p decrease roughly from 100 to 60 and x5 = μ − ν turns around 17 between 50 and 90 °C. The magnitude of these values results mainly from the initial rate jump at zero conversion, e.g., as illustrated in Figure 9. The drop of x4 might be related to a viscosity reduction, but with a decrease from 9.2 to 1.7 Pa·s within the same temperature interval, the correlation holds qualitatively at best. The high value of the scaling exponent μ = x5 − ν ≈ 16 reflects consistently the rapid drop of the kinetic termination coefficient due to the suppression of translational mobility. However, conventional DSC instruments are too slow for monitoring reliably the rapid initial changes in the photopolymerization kinetics of liquid precursors.
5. CONCLUSIONS The important elements behind the kinetics of free radical polymerization have already been identified throughout the past decades. However, to the best of our knowledge, the present work reports for the first time a closed-form semiempirical expression for the polymerization rate as a function of conversion including non-steady-state behavior, termination control by center-of-mass diffusion and reaction diffusion, vitrification, and radical “deactivation” by trapping or similar mechanisms. Following scaling arguments common for the description of structural and dynamical features of polymers and polymer networks, we were able to couple the structurally driven kinetic factors to the chemical kinetics into a compact mathematical rate−conversion relation. Applied to J
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(3) Morawetz, H.; Rubin, I. Polymerization in the Crystalline State. II. Alkali Acrylates and Methacrylates. J. Polym. Sci. 1962, 57, 669− 686. (4) Morosoff, N.; Morawetz, H.; Post, B. Polymerization in the Crystalline State. VII. A Crystallographic Study of the RadiationInitiated Polymerization in Single Crystals of Vinyl Stearate. J. Am. Chem. Soc. 1965, 87, 3035−40. (5) Baysal, B. M.; Erten, H. N.; Ramelow, U. S. Solid-state Polymerization of Acrylamide and Some Acrylates, Initiated by Ultraviolet Radiation. J. Polym. Sci., Part A-1: Polym. Chem. 1971, 9, 581−587. (6) Mahdavian, A.-R.; Zandi, M. Kinetic Study of Radical Polymerization. II Solid-state Bulk Polymerization of Sodium Methacrylate by Differential Scanning Calorimetry. J. Appl. Polym. Sci. 2003, 90, 1648−1654. (7) Berchtold, K. A.; Hacioğlu, B.; Nie, J.; Cramer, N. B.; Stansbury, J. W.; Bowman, C. N. Rapid Solid-state Photopolymerization of Cyclic Acetal-containing Acrylates. Macromolecules 2009, 42, 2433− 2437. (8) Jian, Y.; He, Y.; Wang, J.; Xu, B.; Yang, W.; Nie, J. Rapid Photopolymerization of Octadecyl Methacrylate in the Solid State. New J. Chem. 2013, 37, 444−450. (9) Jian, Y.; He, Y.; Wang, J.; Yang, W.; Nie, J. Rapid Solid-State Photopolymerization of Octadecyl Acrylate: Low Shrinkage and Insensitivity to Oxygen. Polym. Int. 2013, 62, 1692−1697. (10) Allen, P. E. M.; Patrick, C. R. Kinetics and Mechanisms of Polymerization Reactions. Application of Physico-Chemical Principles; John Wiley and Sons: Chichester, 1974. (11) Odian, G. Principles of Polymerization; John Wiley and Sons: New York, 1991. (12) Li, W.-H.; Hamielec, A. E.; Crowe, C. M. Kinetics of the FreeRadical Copolymerization of Methyl Methacrylate/Ethylene Glycol Dimethacrylate: 1. Experimental Investigation. Polymer 1989, 30, 1513. (13) Zhu, S.; Tian, Y.; Hamielec, A. E.; Eaton, D. R. Radical Trapping and Termination in Free-Radical Polymerization of MMA. Macromolecules 1990, 23, 1144−1150. (14) Zhu, S.; Tian, Y.; Hamielec, A. E.; Eaton, D. R. Radical Trapping and Termination in Free-Radical Polymerization of MMA/ EGDMA. Polymer 1990, 31, 154−159. (15) Bowman, C. N.; Peppas, N. A. Coupling of Kinetics and Volume Relaxation during Polymerizations of Multiacrylates and Multimethacrylates. Macromolecules 1991, 24, 1914−1920. (16) Russell, G. T.; Gilbert, R. G.; Napper, D. H. Chain-lengthdependent Termination Rate Processes in Free-radical Polymerizations. 1. Theory. Macromolecules 1992, 25, 2459−69. (17) Anseth, K. S.; Wang, C. M.; Bowman, C. N. Reaction Behaviour and Kinetic Constants for Photopolymerizations of Multi(meth)acrylate Monomers. Polymer 1994, 35, 3243−3250. (18) Anseth, K. S.; Wang, C. M.; Bowman, C. N. Kinetic Evidence of Reaction Diffusion during the Polymerization of Multi(meth)acrylate Monomers. Macromolecules 1994, 27, 650−655. (19) Anseth, K. S.; Kline, L. M.; Walker, T. A.; Anderson, K. J.; Bowman, C. N. Reaction Kinetics and Volume Relaxation during Polymerizations of Multiethylene Glycol Dimethacrylates. Macromolecules 1995, 28, 2491−2499. (20) Guymon, C. A.; Bowman, C. N. Kinetic Analysis of Polymerization Rate Acceleration During the Formation of Polymer/Smectic Liquid Crystal Composites. Macromolecules 1997, 30, 5271−5278. (21) Cook, W. D. Thermal Aspects of the Kinetics of Dimethacrylate Photopolymerization. Polymer 1992, 33, 2152−2161. (22) Cook, W. D. Photopolymerization Kinetics of Oligo(ethylene oxide) and Oligo(methylene oxide) Dimethacrylates. J. Polym. Sci., Part A: Polym. Chem. 1993, 31, 1053−1067. (23) Buback, M.; Huckestein, B.; Russell, G. T. Modeling of Termination in Intermediate and High Conversion Free Radical Polymerizations. Macromol. Chem. Phys. 1994, 195, 539−554.
the solid-state photopolymerization of a semicrystalline acrylated urethane-based PEG oligomer, the overall rate− conversion behavior is closely approximated by a simplified expression containing no more than three adjustable parameters with a physicochemical ground. For a given initiation rate, the full kinetics can thus be established within the time domain starting from the set of parameters. When the initial physical state is liquid, the experimental conversion−rate profiles are well-approximated using an extended version taking into account translational degrees of freedom. The fairly simple expressions based on fundamental insights provide a useful tool to process experimental data and predict FRP kinetics in general, limited neither to acrylated oligomers nor to photoinduced free-radical polymerization. It can be anticipated that polymer chemists and material scientists will benefit substantially from this straightforward tool to characterize FRP kinetics with minor mathematical effort.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00706. SI-1: schematic representation of the synthesis and the structure of AUP; SI-2: crystallization and fusion thermograms; SI-3: spectrum of the Hg−Xe lamp (Hamamatsu LC8) used for the DPC experiments and molar attenutation coefficient of HCPK; SI-4: schematic representation of the FTIR photorheology coupling; SI5: active radical concentration corresponding to the data in Figure 1; SI-6: undistorted heat flow profiles after dynamic crystallization; SI-7: rate−conversion profiles for the photopolymerization of AUP in the solid state after isothermal crystallization at 20 °C (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (P.R.). ORCID
Patrice Roose: 0000-0003-2768-701X Annemie Houben: 0000-0001-8676-456X Sandra Van Vlierberghe: 0000-0001-7688-1682 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Thierry Lardot for conducting the photocalorimetry experiments, Frédéric Baudour for the assistance in the literature overview, and Stéphane Roose for the valuable discussions regarding deconvolution techniques.
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REFERENCES
(1) Houben, A.; Roose, P.; Van den Bergen, H.; Declercq, H.; Van Hoorick, J.; Gruber, P.; Ovsianikov, A.; Bontinck, D.; Van Vlierberghe, S.; Dubruel, P. Flexible Oligomer Spacers as the Key to Solid-State Photopolymerization of Hydrogel Precursors. Materials Today Chemistry 2017, 4, 84−89. (2) Houben, A.; Pien, N.; Lu, X.; Bisi, F.; Van Hoorick, J.; Boone, M. N.; Roose, P.; Van den Bergen, H.; Bontinck, D.; Bowden, T.; Dubruel, P.; Van Vlierberghe, S. Indirect Solid Freeform Fabrication of an Initiator-Free Photocrosslinkable Hydrogel Precursor for the Creation of Porous Scaffolds. Macromol. Biosci. 2016, 16, 1883−1894. K
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Macromolecules
(45) Abdi, H.; Williams, L. J. In Methods in Molecular Biology; Reisfeld, B., Mayeno, A. H., Eds.; Springer Science: New York, 2013; Vol. 930, p 549. (46) Aster, R. C.; Borchers, B.; Thurber, C. H. Parameter Estimation and Inverse Problems, 2nd ed.; Academic Press: Oxford, 2013; p 193. (47) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: Oxford, 2003. (48) De Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (49) Martin, J. E.; Adolf, D.; Wilcoxon, J. P. Viscoelasticity of NearCritical Gels. Phys. Rev. Lett. 1988, 61, 2620−2623. (50) Adolf, D.; Martin, J. E.; Wilcoxon, J. P. Evolution of Structure and Viscoelasticity in an Epoxy Near the Sol-Gel Transition. Macromolecules 1990, 23, 527−531. (51) Huang, L.; Li, Y.; Yang, J.; Chen, Y. Self-initiated Photopolymerization of Hyperbranched Acrylates. Polymer 2009, 50, 4325− 4333. (52) Lee, Y. L.; Roper, T. M.; Jonsson, E. S.; Kudyakov, I.; Viswanathan, K.; Nason, C.; Guymon, C. A.; Hoyle, C. E. The Kinetics of Vinyl Acrylate Photopolymerization. Polymer 2003, 44, 2859−2865. (53) Worthington, K. S.; Baguenard, C.; Forney, B. S.; Guymon, C. A. Photopolymerization Kinetics in and of Self-Assembling Lyotropic Liquid Crystal Templates. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 471−489.
(24) Barth, J.; Buback, M.; Russell, G. T.; Smolne, S. Chain-LengthDependent Termination in Radical Polymerization of Acrylates. Macromol. Chem. Phys. 2011, 212, 1366−1378. (25) O’Neil, G. A.; Torkelson, J. M. Modeling Insight into the Diffusion-Limites Cause of the Gel Effect in Free Radical Polymerization. Macromolecules 1999, 32, 411−422. (26) Lovell, L. G.; Stansbury, J. W.; Syrpes, D. C.; Bowman, C. N. Effects of Composition and Reactivity on the Reaction Kinetics of Dimethacrylate/Dimethacrylate Copolymerizations. Macromolecules 1999, 32, 3913−3921. (27) Goodner, M. D.; Bowman, C. N. Modeling Primary Radical Termination and Its Effects on Autoacceleration in Photopolymerization Kinetics. Macromolecules 1999, 32, 6552−6559. (28) Berchtold, K. A.; Hacioglu, B.; Lovell, L.; Nie, J.; Bowman, C. N. Using Changes in Initiation and Chain Transfer Rates To Probe the Kinetics of Cross-Linking Photopolymerizations: Effects of Chain Length Dependent Termination. Macromolecules 2001, 34, 5103− 5111. (29) Jakubiak, J.; Rabek, J. F. Modeling of the Kinetics of Linear and Cross-Linking Photopolymerization. Part III. Polymery 2001, 46, 10− 22. (30) Andrzejewska, E. Photopolymerization Kinetics of Multifunctional Monomers. Prog. Polym. Sci. 2001, 26, 605−665. (31) Achilias, D. S. A Review of Modeling of Diffusion Controlled Polymerization Reactions. Macromol. Theory Simul. 2007, 16, 319− 347. (32) Zhang, Y.; Kranbuehl, D. E.; Sautereau, H.; Seytre, G.; Dupuy, J. Study of UV Cure Kinetics Resulting from a Changing Concentration of Mobile and Trapped Radicals. Macromolecules 2008, 41, 708−71. (33) Bowman, C. N.; Kloxin, C. J. Toward an Enhanced Understanding and Implementation of Photopolymerization Reactions. AIChE J. 2008, 54, 2775. (34) Wen, M.; McCormick, A. V. A Kinetic Model for Radical Trapping in Photopolymerization of Multifunctional Monomers. Macromolecules 2000, 33, 9247−9254. (35) Ibrahim, A.; Maurin, V.; Ley, C.; Allonas, X.; CroutxeBarghorn, C.; Jasinski, F. Investigation of Termination Reactions in Free Radical Photopolymerization of UV Powder Formulations. Eur. Polym. J. 2012, 48, 1475−1484. (36) Achilias, D. S.; Siafaka, P. I. Polymerization Kinetics of Poly(2hydroxyethyl methacrylate) Hydrogels and Nanocomposite Materials. Processes 2017, 5, 21−40. (37) Kamal, M. R.; Sourour, S. Kinetics and Thermal Characterization of Thermoset Cure. Polym. Eng. Sci. 1973, 13, 59−64. (38) Taki, K.; Watanabe, Y.; Ito, H.; Ohshima, M. Effect of Oxygen Inhibition on the Kinetic Constants of the UV-Radical Photopolymerization of Diurethane Dimethacrylate/Photoinitiator Systems. Macromolecules 2014, 47, 1906−1913. (39) Fouassier, J.-P.; Allonas, X.; Lalevée, J. In Macromolecular Engineering: Precise Synthesis, Materials Properties, Applications; Matyjaszewski, K., Gnanou, Y., Leibler, L., Eds.; Wiley-VCH Verlag: Weinheim, 2007; pp 643−671. (40) Winter, H. H.; Chambon, F. Analysis of Linear Viscoelasticity of a Crosslinking Polymer at the Gel Point. J. Rheol. 1986, 30, 367− 382. (41) Brandrup, J.; Immergut, E. H. Polymer Handbook, 3rd ed.; John Wiley and Sons: New York, 1989. (42) Dworak, C.; Koch, T.; Varga, F.; Liska, R. Photopolymerization of Biocompatible Phosphorus-Containing Vinyl Esters and Vinyl Carbamates. J. Polym. Sci., Part A: Polym. Chem. 2010, 48, 2916− 2924. (43) Flammersheim, H. J.; Eckardt, N.; Kunze, W. The Deconvolution of DSC-curves in the Experimental Time Domain. Thermochim. Acta 1991, 187, 269−274. (44) Moukhina, E.; Kaisersberger, E. Temperature Dependence of the Time Constants for Deconvolution of Heat Flow Curves. Thermochim. Acta 2009, 492, 101−109. L
DOI: 10.1021/acs.macromol.8b00706 Macromolecules XXXX, XXX, XXX−XXX
