Mechanistic Insights into the Sonochemical Activation of

Sep 11, 2015 - The gDCC mechanophores undergo a mechanically facilitated electrocyclic ring-opening to 2,3-dichloroalkene products as a result of ultr...
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Mechanistic Insights into the Sonochemical Activation of Multimechanophore Cyclopropanated Polybutadiene Polymers Jeremy M. Lenhardt,† Ashley L. Black Ramirez,‡ Bobin Lee,‡ Tatiana B. Kouznetsova,‡ and Stephen L. Craig*,‡ †

Materials Science Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States Department of Chemistry, Duke University, Durham, North Carolina 27708-0346, United States

‡

S Supporting Information *

ABSTRACT: Structure−activity relationships in the mechanochemistry of gem-dichlorocyclopropane (gDCC)-based polymer solutions triggered by pulsed ultrasound are reported. Insights into the flow-induced mechanochemical transformations of gDCC mechanophores into the corresponding 2,3dichloroalkenes are obtained by monitoring the mechanochemistry as a function of initial polymer molecular weight and sonication conditions. The competition between gDCC activation and polymer chain scission is invariant to sonication power, temperature, polymer concentration, and solvent but is sensitive to initial polymer molecular weight. The results have practical implications for the use of polymer sonochemistry as a tool for quantifying the relative mechanical strength of scissile polymers and conceptual implications for thinking about the nature of the force distributions experienced during sonochemical experiments.

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INTRODUCTION The proliferation of studies concerning mechanically activated functional groups, or mechanophores, along polymer chains has been fueled by the use of pulsed ultrasound as the de facto default technique for coupling a mechanical force to mechanophore reactions in solution. The mechanical nature of polymer ultrasound is now widely accepted,1 and the technique has found utility in inducing electrocyclic ringopening reactions,2−4 the activation of latent catalysts,5 trapping transition state structures and high-energy intermediates,6 dissociation of specific weak bonds along polymer chains,7 and a growing list of mechanically assisted transformations.8 Additionally, mechanophore activation by pulsed ultrasound provides initial insights into creating mechanically responsive polymeric materials,3,9 although a truly quantitative connection between solution and solid-state mechanophore activity is currently unavailable. As the number of mechanically activated species and their study grows, it is becoming apparent that a more extensive description of the factors that drive molecular reactivity under sonication conditions is required.10 While many of the fundamentals of polymer sonochemistry are known, quantitative experimental data regarding the magnitude and distribution of forces along the polymer backbone are rare. The mechanical effects of pulsed ultrasound derive from the formation, growth, and subsequent collapse of cavitation bubbles in solution. For mechanophore-laden polymers of sufficient molecular weight and proximity to the cavitation collapse, large elongational flows provide mechanical forces that stretch polymer chains and direct the embedded mechanophore reactivity. The magnitude of the associated stretching forces © XXXX American Chemical Society

reach the order of nN, sufficient to induce the dissociation of carbon−carbon bonds in the polymer backbone, leading to rupture of the polymer main chain and molecular weight degradation. While it has been generally accepted that the magnitude of force at the polymer midchain must reach the nN regime to induce carbon−carbon bond scission along the polymer chain (on the time scale of cavitation bubble collapse), not much experimental data are available regarding the distribution of force along that polymer chain. One description of this force distribution is based on the bead−rod model,11 from which the maximum force (Fmax) at the center of a (fully extended) polymer chain can be calculated using the viscosity of the solvent (hs), radius of the bead (a), length of the bead (b), the strain rate (ε), a bead shielding factor (S), and the number of beads along the contour length (N): Fmax = (3π /4)hsabεSN 2

(1)

From eq 1 it is straightforward to calculate the force distribution along a fully extended polymer chain. A theoretical treatment, for instance, of polybutadiene (PB) of ca. 250 kDa shows that peak forces of 5 nN (the approximate force necessary for a covalent carbon−carbon single bond to rupture on the μs time scale of the extensional flow12) are easily achieved by completely stretching the polymer chain in an Received: July 28, 2015 Revised: September 5, 2015

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Macromolecules extensional field created during cavitation collapse. Of interest here is the distribution of forces that extend out from the midchain, where the force peaks. As seen in Figure 1, in the

Figure 2. Synthesis of poly(gDCC-PB) and mechanical acceleration of gDCC ring-opening by pulsed ultrasound.

cyclopropane polymers, discussing the effects of varying sonochemical parameters and gDCC content on the formation of 2,3-dichloroalkene. The effects of sonication conditions on the absolute rates of sonomechanical activation have been reviewed previously,1c but a systematic study of their effects on the force distribution and dynamics of mechanophore activation along an extended polymer backbone are, to the best of our knowledge, unreported. We first present the results of the studies, organized by experimental variable, and then revisit these results and their implications in a separate Discussion section.

Figure 1. Calculated force distribution for a 250 segment polymer at peak force of 5 nN. Dotted lines frame the portion of the polymer that experiences a >2 nN force necessary for gDCC ring-opening.

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case of a fully extended PB polymer chain, the calculation shows that forces of >3, 2, and 1 nN envelope approximately 63, 77, and 89% of the polymer backbone. Depending on the mechanophores, therefore covalent mechanochemistry occurs not only at the polymer midchain but also over a substantial portion of the polymer. The presence of a relatively broad force distribution has been shown experimentally by the Moore group in the context of off-center, site-specific activation of azolinkages along poly(ethylene glycol) polymers,7b in our previous work on gem-dihalocyclopropane mechanochemistry,4,6a,b and in the ability to form block copolymers from sonicated multimechanophore polymers.9e The extent of nonscissile mechanophore activation per chain scission event is a function of the relative rates of mechanochemical activation of the nonscissile mechanophores and the scissile bonds that break along the polymer main chain, a competition that we have recently used to characterize the relative strengths of various scissile “weak bonds” along a polymer backbone.12b That work complemented studies of more complicated reactions13 and showed that even for simple homolytic bond scission reactions, mechanical bond strength does not vary directly with thermodynamic bond strength. Perhaps more importantly, however, it demonstrated a new methodology for quantifying the relative mechanical strength of scissile bonds in polymer mechanochemistry. The aim of this paper is to quantify the effect of experimental parameters in a pulsed ultrasound experiment on the competition between nonscissile and scissile reactivity and to establish the extent to which the size of the nonscissile activation zone changes in response to variations in sonochemical parameters such as sonication power/amplitude, temperature, and polymer concentration. Our benchmark for addressing these questions is the gem-dichlorocyclopropane (gDCC) mechanophore, which is embedded multiple times within a polybutadiene (PB) polymer backbone. The gDCC mechanophores undergo a mechanically facilitated electrocyclic ring-opening to 2,3-dichloroalkene products as a result of ultrasonically generated flow fields (Figure 2).4 We focus on extending the solution mechanochemistry of gem-dichloro-

EXPERIMENTAL SECTION

Materials. Dry solvents were obtained from VWR. Grubbs catalyst, second generation (Grubbs II catalyst), and butylated hydroxytoluene (BHT) were purchased from Sigma-Aldrich. The gDCC−cyclooctadiene14 and Grubbs−pyridine complex15 were prepared according to procedures published previously. Unless otherwise stated, all reagents were used without further purification. Polymer Synthesis. gDCC−cyclooctadiene14 (1) was dissolved in anhydrous DCM (0.3 mL). A solution (100 μL) of the Grubbs− pyridine complex15 in dichloromethane (DCM) was added to initiate the polymerization. Monomer and catalyst ratios were chosen to target the desired molecular weights. After the reaction mixture was stirred at room temperature for 3 h, several drops of ethyl vinyl ether were added and stirred for 30 min at room temperature to stop the polymerization. The polymer solution was diluted in DCM and precipitated into methanol for three times. The polymer was collected by filtration and dried under high vacuum for 3 h to remove the methanol. Sonication. Ultrasound experiments were performed in the specified solvents on a Vibracell Model VCX500 operating at 20 kHz with a 13.1 mm replaceable titanium tip probe from Sonics and Materials. Solutions were prepared at the concentrations specified and transferred to a three-necked Suslick cell in an ice−water bath and degassed by nitrogen bubbling for 30 min prior to sonication. Unless otherwise stated, the polymer was dissolved in solvent (typically THF). The solutions were degassed at 6−9 °C for 30 min (for sonication at 25 °C, degassing was also performed at 25 °C). The sonication was performed at time intervals (typically 0, 2, 4, 6, 8, 16, and 30 min) with 8.5 W cm−2 (AMPL = 20%) used as the standard sonication power. Additional experiments were performed with the power set to 10.9 and 14.6 W cm−2, respectively. Unless otherwise specified, sonication was performed while maintaining a temperature of 6−9 °C (external ice bath) under nitrogen. The sonication pulse sequence was set to 1 s on/1 s off. Individual sonication experiments were performed for each time point. The solution (1 mL) was filtered via filter syringe for GPC analysis. The remainder was concentrated under reduced pressure and dissolved in CDCl3 for NMR analysis. Characterization. 1H NMR spectra were collected in CDCl3 on a 400 MHz Varian NMR. 13C NMR spectra were collected in CDCl3 on a 500 MHz Varian NMR. CDCl3 (δ = 7.26 ppm for 1H and 77.16 ppm for 13C NMR) was used as an internal chemical shift reference. All B

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Figure 3. An increase in pulsed ultrasound power from 8.5 to 14.6 W cm−2 leads to faster rates of molecular weight degradation (left) with increasing applied power. Normalizing the data to the polymer scission cycle leads to a collapse of the data onto an activation profile consistent with ϕ1 = 0.69 ± 0.02, as determined by linear fits to the data (fits constrained to the origin).

Figure 4. Ultrasonic activation of poly(gDCC-PB) as a function of the solvent. The rates of molecular weight degradation varied across the series (left), but ϕ1 stayed relatively constant. Fit is the best linear fit constrained to the origin, ϕ1 = 0.69 ± 0.01.

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RESULTS The impact of various sonication parameters, examined previously in the context of rates16 or side products,17 was tested on poly(gDCC-PB) synthesized in a single polymerization, Mn = 92 kDa and PDI = 1.625. The competition between gDCC ring-opening and polymer scission is reported as ϕ1, the extent of ring-opening extrapolated to one scission cycle. Sonication Power. Changes in sonication power are known to affect the overall rate of mechanically induced polymer chain scission.18 The effects of increasing power are attributed to changes in the size and number of cavitation bubbles per time that form during ultrasound: an increase in power leads to an increase in both the size and density of the cavitation bubbles in solution.19 As a result, cavitation collapse is more violent, leading to higher rates of molecular weight degradation and a lower limiting molecular weight. The applied power during pulsed ultrasound was varied from 8.5 to 14.6 W cm−2, and as expected, the rates of both molecular weight degradation and ring-opening increased with power (Figure 3). Normalizing the ring-opening data, however, revealed that ϕ1 was constant across the series at ϕ1 = 0.69 ± 0.02. Solvent. Pulsed ultrasound conducted in different solvents affects mechanochemical rates of chain scission by altering (i) changes in cavitation and (ii) the polymer−solvent interaction, including viscosity and the conformational preferences of the polymer in solution.20 Cavitation is affected by the solvent

chemical shifts are given in ppm (δ) and coupling constants (J) in Hz as singlet (s), doublet (d), triplet (t), quartet (q), multiplet (m), or broad (br). Column (flash) chromatography was performed using Silicycle F60 (230−400 mesh) silica gel. Gel permeation chromatography (GPC) was performed on double columns (Agilent Technology PL gel, #179911GP-504504 (104 Å) and #179911GP-503 (103 Å)) using stabilized THF (non-UV, HPLC grade, 99.7+%, stabilized with 250 ppm BHT) as mobile phase at 4 mL min−1 at room temperature. The flow rate was set using a Varian Prostar Model 210 pump, and molecular weights were calculated using an inline Wyatt Dawn EOS multiangle light scattering (MALS) detector and a Wyatt Optilab DSP interferometric refractometer (RI). The dn/dc values for each polymer were determined from the integrated inline RI response, assuming 100% mass recovery based on known injection mass. The fraction of ring-opened gDCC mechanophores, ϕ = [dichloroalkene]/([dichloroalkene + gDCC]), was determined by 1 H NMR as previously reported.4 The scission of polymer chains was followed by changes in molecular weight as determined by GPCMALS and reported by polymer scission cycle (SC). The scission cycle is calculated from the number-averaged molecular weight at timed intervals during sonication according to eq 2; MN(0) is the initial number-averaged molecular weight, and MN(t) is the number-averaged molecular weight at a sonication time interval t. SC can be regarded as a measure of the generation of the daughter polymers produced by scission of the initial parent: the average parent is split into two daughters at SC = 1, they are split into four granddaughters at SC = 2, etc.

SC = [ln(MN(o)) − ln(MN(t ))]/ln(2)

(2) C

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Macromolecules vapor pressure; increasing vapor pressure leads to increasing vaporization into a forming cavitation bubble. The vapor inside the cavitation bubble subsequently “cushions” the collapse, leading to decreased solvent strain rates around a polymer, slower molecular weight degradation rates, and higher limiting molecular weights.18,21 The choice of solvent has also been reported to influence mechanochemistry through the solvent quality. If the polymer− solvent interaction leads to a more extended polymer conformation in solution, the coil−stretch transition becomes more facile and the rate of molecular weight degradation will increase.22 Poly(gDCC-PB) was dissolved in varying solvents and subjected to pulsed ultrasound (8.5 W cm−2, 6−9 °C, N2), resulting in molecular weight degradation and cis-gDCC ringopening. Pulsed ultrasound in dichloromethane led to slower molecular weight degradation than that observed during pulsed ultrasound in toluene, chloroform, and THF (Figure 4). The variation in molecular weight degradation had little effect on ϕ1, however, because the rate of ring-opening slowed proportionally, leading to a relatively constant value of ϕ1 = 0.69 ± 0.01. Polymer Concentration. The formation and size of cavitation bubbles in solution are inversely correlated with polymer concentration.18 This is attributed to both an increase in solution viscosity that raises the cavitation threshold and to the solution volume available for cavitation bubbles to form. For example, sonication of polystyrene was shown to proceed much more rapidly at polymer solution concentrations below the critical overlap concentration of polystyrene,18 a value indicating the point at which the polymer volume is equivalent to the solution volume. As a result, rates of molecular weight degradation decrease with increasing polymer concentration, while values of the apparent limiting molecular weight increase. The polymer overlap concentration (c*) was calculated23 for 92 kDa poly(gDCC-PB) from the polymer radius of gyration (Rg = 11.6 nm; obtained by MALS) to be c* = 23 mg mL−1. Pulsed ultrasound of polymer solutions at a range of concentrations both near (5.0, 10 mg mL−1) and more than 1 order of magnitude below (0.5, 1, and 2 mg mL−1) c* revealed the expected slower rates of molecular weight degradation and larger values of the limiting molecular weight as polymer concentration increased. Normalizing the extent of gDCC ringopening to the polymer scission cycle gave ϕ1 = 0.68 ± 0.01 across this series of sonication experiments (Figure 5). Temperature. An increase in solution temperature during sonochemical degradation of polymers leads to a decrease in the rate of molecular weight degradation.18,24 The effects of increasing temperature are associated with an increase in the amount of solvent vaporization into a forming cavitation bubble. The presence of an increasing concentration of solvent vapor “cushions” the bubble collapse and leads to a decrease in force from the solvent shear field, decreasing rates of chain scission and leading to higher values of the polymer limiting molecular weight. Pulsed ultrasound of poly(gDCC-PB) was conducted at 6−9 °C (ice/water bath) and at room temperature, ca. 22−26 °C (room temperature water bath). The degradation behavior at the two temperatures differed as expected, although normalization to the polymer scission cycle revealed indistinguishable values of ϕ1 = 0.70 ± 0.01 (Figure 6). Molecular Weight Effects. It has been well documented that the initial molecular weight of a polymer has a dramatic effect on its rate of mechanochemical polymer scission,25 as

Figure 5. Pulsed ultrasound (THF, 8.5 W cm−2, 6−9 °C, N2) of poly(gDCC-PB) as a function of polymer concentration leads to varying rates of molecular weight degradation (top). Normalizing the data to the polymer scission cycle leads to a master curve for all concentrations with ϕ1 = 0.68 ± 0.01.

ultrasonic scission is more rapid for higher molecular weight polymers. Below the so-called limiting molecular weight (ML), the strain rates around a collapsing cavitation bubble are insufficient to lead to substantial amounts of C−C bond scission over the time during which the ultrasound is applied. We wondered if sonication of poly(gDCC-PB) of varying initial molecular weight would result in a change in the extent of ringopening activation. The effects of initial polymer molecular weight were first examined by sonicating poly(gDCC-PB) of the following initial molecular weights: 59, 92, and 169 kDa. Pulsed ultrasound led to the expected, higher rates of molecular weight degradation with initial molecular weight (Figure 7),25a but unlike the variations observed in all of the studies reported above, in this case data normalization to the polymer scission cycle generated a subsequent increase in ϕ1 for decreasing initial molecular weight, with values of ϕ1 = 0.92, 0.69, and 0.51 for initial MW = 59, 92, and 169 kDa, respectively. We note that ϕ1 = 0.92 is an extrapolated value; sonication of the 59 kDa polymer reached only SC = 0.5 after 30 min of sonication.

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DISCUSSION Sonochemical Conditions. The mechanochemical ringopening reactions of gDCC mechanophores are independent of variations in ultrasound amplitude, solvent composition, polymer concentration, and temperature when scaled to the extent of polymer chain scission. Adjusting these sonochemical parameters is observed to alter the rates of molecular weight D

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Figure 7. Change in MN vs sonication time (top) and extent of ringopening vs scission cycle (bottom) for poly(gDCC-PB) of different initial molecular weight.

Figure 6. Degradation of poly(gDCC-PB) (top) is dependent on the temperature of the sonication bath. Normalizing the extent of ringopening during sonication to chain scission gave ϕ1 values in the range of 0.70 ± 0.01. Shown at the bottom is the best linear fit constrained to the origin.

The results are therefore inconsistent with a picture in which variations in sonochemical conditions, and a subsequent change in molecular weight degradation rates, have a substantive effect on the distribution of forces felt along the polymer during cavitation collapse. Instead, these results are consistent with a picture in which the typical mechanochemical event is characterized by polymer extension and force that increase until the chain breaks, a process that is limited by the effective strength of the bonds in the polymer backbone and not by the sonication conditions (within the experimental range examined here). The fact that the ϕ vs SC plots are linear even at low conversion suggests that the majority of ring-opening reactions occur during an activation event that culminates in chain scission, a suggestion supported by modeling (see below). In this picture, sonochemical parameters affect the frequency of activating high force events but have only a minimal effect on the actual distribution of forces within the activation force window (forces between that necessary for ring-opening and that necessary for chain scission on the time scale of the event). Within that limit, we can consider what should occur when a polymer breaks. The midchain force on the polymer undergoing scission on the time scale of the ultrasound experiment (μs) is very high, ca. 5 nN,12a and so any gDCC at a site near the position of peak force along the polymer chain will undergo a very rapid ring-opening reaction prior to breaking of the polymer midchain C−C bond. For example, single molecule force spectroscopy was previously used to determine the rate of cis-gDCC ring-opening along polybutadiene polymers.27,28 The reaction rate increased ∼13 orders of magnitude to ca. 102 s−1

degradation, though a determination of the fraction of ringopening after the first polymer scission cycle results in values of ϕ1 that are confined to a narrow range of 0.69 ± 0.02. Parameters that alter mechanochemical rates of polymer scission, or C−C bond dissociation reactions, have no effect on the relative extent of mechanophore ring-opening reactions. The observed consistency in ϕ1 is initially counterintuitive because the relative rates of ring-opening and bond scission almost certainly have very different force dependencies. To begin our discussion, we note that the force at a polymer midchain during sonochemically induced scission (C−C bond homolysis) accumulates to several nN11,26applied forces that overcome the >80 kcal mol−1 C−C bond energy on the time scale of cavitation bubble collapse. By comparison, the activation barrier to gDCC ring-opening, 2 nN necessary for ring-opening to occur, the fraction that were on a chain that experienced a force of >5 nN necessary for chain scission. Distribution calculated using eq 1.

most of the ring-opening occurs when a polymer breaks. Obviously, the probability of nonscissile ring-opening will depend on sonication conditions. As the polymer molecular weight decreases, for example, it becomes increasingly likely that a chain could experience a force large enough for ringopening to occur but not so great as to trigger chain scission. Because ϕ1 is relatively invariant across the range of conditions explored here, we conclude that the variations in experimental conditions do not substantially alter the relative probability of a chain experiencing forces necessary for ring-opening (∼2 nN) and experiencing forces necessary for chain scission (∼5 nN). The existence of a “constant ϕ1” zone is supported also by the high N tail of Figure 9. As polymer contour length increases, the relative probability of ring-opening with and without chain scission levels off. In this regime, the relative probability of ringopening and chain scission, and therefore ϕ1, should have similarly limited sensitivity to changes in experimental parameters, as observed here. Molecular Weight Effects. One parameter that has a substantial effect on ϕ1 is the initial polymer molecular weight. With decreasing initial molecular weight, an increase to ϕ1 = 0.83 occurs when the initial polymer molecular weight is close to that of the limiting molecular weight, a term that indicates the minimum size of a polymer that will undergo flow-induced scission during pulsed ultrasound. As discussed previously, this may result from some gDCC ring-opening occurring without chain scission, and previous authors have shown that it is possible to work in this regime almost exclusively.2 In addition, high molecular weight polymers are likely to undergo multiple scissions per chain, and the “activation zone” of a second or third scission event that originating from a single parent polymer would overlap with the activation zone from a prior event. Because each gDCC mechanophore can only be activated once, multiple scission events per initial polymer would lead to a decrease in ϕ1.

Figure 8. Polymer molecular weight as a function of sonication time. Symbols indicate experimental data, and the line gives the results of simulations with time scaled to give the best fit to the experimental data.

do not know the rate or density of bubble formation, the time axis in the simulations is arbitrary and is scaled to provide the best fit to the experimental data. Nonetheless, the agreement between the relative chain scission profiles supports the validity of the models to our systems. We next asked the following questions: What is the relative probability of a polymer chain experiencing a force large enough to open a ring on the time scale of cavitation collapse (taken as 2 nN, based on extrapolation from our previously published force spectroscopy studies), versus the probability of F

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Macromolecules Alternatively, the variation in ϕ1 values with initial molecular weight may be indicative of a fundamental change in the conformation of the polymer undergoing extension. In the high molecular weight regime, it is possible for the midchain to be the predominant site of polymer scission31 even if polymer rupture occurs when the chain is not fully extended.32 Chu et al.33 have reported the observation of five separate polymer conformations during the stretching of DNA polymers in sudden elongational flow; these molecules adopt conformations that are not completely “stretched out” in the flow, but instead adopt shapes such as dumbbells and half-dumbbells, that are folded, kinked, and coiled. One possibility, therefore, is that the relative fraction of the polymer that constitutes the “mechanically active zone” in gDCC-PB polymers decreases with increasing initial molecular weight because large molecular weight polymers are not fully extended (e.g., dumbbell/halfdumbbell) prior to polymer chain rupture, while small molecular weight gDCC-PB polymers adopt increasing stretched conformations prior to polymer main chain homolysis. There must be limits where such dynamics come into play, because the force on the midchain grows as the polymer uncoils, and so if the force gets high enough for the chain to break at a rate comparable to the strain rate, incomplete uncoiling of one form or another will result. In addition, because the elongational strain rate drops with distance from the center of the bubble collapse, polymers of large contour length might extend into regions where the strain rate is not high enough to overcome internal rotational relaxation time scales, preventing full extension of the polymer.

be general for polymer sonochemistry, we note the specific conclusions are limited to linear polymers, and the consequences for multimechanophore activation in star polymers34 and other branched polymer architectures might be much more subtle and rich. From a mechanistic standpoint, the most telling outcome of this study is that care should be taken when using casual language to the effect that “force increases with sonication power, decreases with temperature, etc.”, at least under conditions where chain scission is observed. While the probability per time of a given polymer chain does change with these parameters, the maximum force experienced by a polymer is the force necessary to break it changes negligibly the distribution of forces that is actually responsible for observed sonochemical polymer mechanochemistry are fairly invariant across a fairly wide range of sonication conditions, at least among those examined here.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01677. Additional details of polymer syntheses, characterization, and sonochemical experiments (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (S.L.C.).

CONCLUSION These results are consistent with a picture in which the distribution of peak forces that are experienced by polymers under the range of sonication conditions employed is less reflective of the conditions involved, but instead limited by the force at which the polymer chain breaks. Calculations show that such a regime exists, and we therefore conclude that the conditions employed here rest in that regime. The observed value of ϕ1 is sensitive to initial molecular weight, presumably because of either the relative contributions of secondary chain scission events or chain relaxation dynamics, both of which should have significant molecular weight dependencies. Regardless of mechanism of the latter case, these results have important practical applications in the context of quantifying polymer mechanochemistry using pulsed sonication techniques. We have previously reported that the relative strength of scissile mechanophores can be ascertained either by measuring ϕ as a function of SC or by characterizing the molecular weight of polymers with high scissile mechanophore content at long sonication times. The latter approach is simpler to implement, but the so-called “effective limiting molecular weight” will depend on sonication power, temperature, solvent, and polymer concentration. These factors might vary as either a matter of necessity (polymer solubility) or convenience from one system or one lab to another, complicating direct comparisons of data taken at different times or in different locations. On the other hand, the use of ϕ vs SC is shown here to be much more robust. The exception is seen in the initial molecular weight of the polymers employed, which is pleasantly complementary in that it does not impact the long-time sonication molecular weight (as long as initial molecular weight distribution exceeds the long-time sonication molecular weight). Although we expect that the general physics should

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge financial support from the National Science Foundation under Grant CHE-1508566 and thank Duke University for additional support.

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REFERENCES

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DOI: 10.1021/acs.macromol.5b01677 Macromolecules XXXX, XXX, XXX−XXX