Atom Transfer Radical Polymerization in the Solid‐State

Abstract Poly(2‐vinylnaphthalene) was synthesized in the solid‐state by ball milling a mixture of the corresponding monomer, a Cu‐based catalyst, and an activated haloalkane as the polymerization initiator. Various reaction conditions, including milling time, milling frequency and added reductant to accelerate the polymerization were optimized. Monomer conversion and the evolution of polymer molecular weight were monitored over time using 1H NMR spectroscopy and size exclusion chromatography, respectively, and linear correlations were observed. While the polymer molecular weight was effectively tuned by changing the initial monomer‐to‐initiator ratio, the experimentally measured values were found to be lower than their theoretical values. The difference was attributed to premature mechanical decomposition and modeled to accurately account for the decrement. Random copolymers of two monomers with orthogonal solubilities, sodium styrene sulfonate and 2‐vinylnaphthalene, were also synthesized in the solid‐state. Inspection of the data revealed that the solid‐state polymerization reaction was controlled, followed a mechanism similar to that described for solution‐state atom transfer radical polymerizations, and may be used to prepare polymers that are inaccessible via solution‐state methods.


Introduction
Ball milling (BM) processes have garnered attention because they can provide efficient and environmentally-friendly alternatives to solution-based reactions. [1] Thee fficacy has been attributed to the high forces generated under BM conditions which effectively facilitate ab road range of chemistry,i ncluding organic [2] and organometallic transformations, [3] crystallization phenomena, [4] and other productive chemical processes. [5,6] Them ajority of BM reports entail small molecule reactions and, by comparison, synthetic polymerization reactions have been relatively unexplored. [7] An early example was disclosed by Swager,who demonstrated that BM facilitates the Gilch polymerization of 2-methoxy-5-2'-ethylhexyloxy phenylene vinylene in the solid-state (Scheme 1A). [7a] Them ethodology afforded the expected polymeric products in relatively high molecular weight (MW) ( % 40 kDa) and under mildly basic conditions when compared to analogous reactions that were performed in the solution-state.Borchardt subsequently described solvent-free methods based on BM for condensing diamines and dialdehydes to afford poly(azomethine)s (Scheme 1B). Thes olidstate methodology obviated the need for high reaction temperatures and toxic solvents (e.g., hexamethylphosphoramide) commonly utilized in solution-based processes for accessing the same polymeric products. [7b] Likewise,s olidstate polycondensations of dibromoarenes and dihalophenylboronic acid were found to proceed over shorter periods of time (0.5 h) when compared to analogous reactions performed in the solution-state (12 to 24 h) and afforded arange of different architectures,including linear and hyperbranched poly(phenylene)s,i ncomparable yield. [7c] Thea forementioned reports demonstrated that the advantages intrinsic to BM processes may be used to drive stepgrowth polymerizations and build upon analogous stoichiometric reactions that are promoted under similar conditions. Since BM has also been shown to promote various types of catalyzed transformations (e.g., olefin metathesis,c oupling reactions,click chemistry,etc.), [8] analogous methodology can be envisioned to enable chain-growth polymerizations.K im reported aB Mm ethod for facilitating the ring-opening polymerization of d-lactide in the presence of catalytic amount of an organic base (Scheme 1C). [7d] After 2h of milling, 81 %o ft he monomer was converted to high MW poly(lactic acid) (PLA). Moreover,t he polymer MW correlated with the initial monomer-to-initiator ratio ([M] 0 /[I] 0 ) and the distributions of polymer chains produced remained relatively low ( % 1.5). Di-and triblock copolymers containing PLA and various hydroxy functionalized macroinitiators,s uch as poly(ethylene oxide) and poly(e-caprolactone), were subsequently synthesized using similar methodology. [7e] Kim also reported that the polymerization of trimethylene carbonate in the solid-state was faster than analogous reactions performed in solution. Fore xample,t he polymerization reaction reached 93 %c onversion within 2h when performed in aB Mr eactor whereas a7 0% conversion was achieved in toluene after 24 h, even though both methods produced polymers of similar MW (9.2 kDa vs.7 .1 kDa, respectively). [7f] Although BM may be used to facilitate ar ange of solidstate polymerizations,the forces generated during the milling process have been reported to cause chain scission. [9] For example,t he aforementioned poly(phenyl vinylene)s underwent areduction in MW,from 160 kDa to ca. 40 kDa, within 30 min of BM. Similarly,high MW poly(methyl methacrylate) (255 kDa) became oligomeric (7.6 kDa) after being subjected to BM conditions for 10 h. [10] Thechain scission processes may proceed in ah omolytic fashion since radicals have been observed by electron spin resonance spectroscopy upon BM polymeric materials. [11] It was hypothesized that the radicals generated under such conditions may be harnessed to promote synthetic polymer chemistry.M oreover,i fthe steady-state concentration of radicals is sufficiently low,then radical-radical coupling should be suppressed and control over the polymerization reaction may be achieved.
Herein, avariant of atom transfer radical polymerization (ATRP), [12] which is an efficient reversible-deactivation radical polymerization method, [13] was used to facilitate as eries of solid-state BM polymerizations.2 -Vinylnaphthalene (2-VN) was selected as the monomer (Scheme 1D) because it is asolid (mp 64-68 8 8C) and structurally similar to styrene,amonomer that is commonly polymerized in the solution-state using ATRP,a nd thus was envisioned to serve as am odel substrate.I nitiators and catalysts typically employed in solution based ATRP reactions were used. As will be described below,t he polymerizations were found to proceed in acontrolled manner as determined by acorrelation between the initial monomer-to-catalyst ratio ([M] 0 /[I] 0 )a nd the MW of the polymer produced as well as aseries of chain extension experiments.H owever,t he MWs of the polymer products were lower than their theoretical values due to chain scission. To quantify the decomposition processes,m odels were created to accurately predict polymer MW as afunction of milling time.F inally,i tw ill be shown how the technique may be used to prepare copolymers comprised of monomers that exhibit different solubilities and thus be used to circumvent fundamental challenges commonly encountered with the synthesis of such types of materials.

Results and Discussion
In ap reliminary experiment, az irconium dioxide milling jar was charged with a50:1:1molar ratio of 2-VN,phenylethyl bromide (PE-Br) (initiator), and Cu I Br/tris(2-pyridylmethyl)amine (TPMA) (catalyst) under nitrogen (N 2 ). After adding a1 0mmd iameter zirconium dioxide ball and sealing the vessel under N 2 ,the mixture was subjected to vibrational BM at 30 Hz for 6h. [14] Samples were periodically withdrawn from the vessel and analyzed by size exclusion chromatography (SEC) to monitor the evolution of polymer MW over time or spiked with as tandard (anisole) and analyzed by 1 HNMR spectroscopy to calculate monomer consumption. [15] As shown in Figure 1A,t he distribution of polymer chains was determined to be relatively broad during the early stages of the reaction, although the polydispersity decreased over time.
Asemi-logarithmic plot of the monomer concentration versus time was found to be linear and the conversion of the polymerization reaction reached 97 %a fter 6h( Figure 1B). Alinear correlation between the polymer MW and monomer conversion was also observed ( Figure 1C), although the experimentally determined number average MW (M n,SEC ) was lower than its theoretical value (M n,Theory ), [16] and attributed to premature mechanical degradation (see below). Collectively,t hese and other results (see Table 1f or as ummary) indicated that the solid-state polymerization reaction was proceeding in am anner consistent with those described for the solution-state ATRP and other controlled radical polymerization reactions. [12b] It has been previously shown that the addition of reductants (e.g.,C u 0 )c an accelerate ATRPs without compromising reaction performance or control in part because the additive functions as as upplemental activation and reducing agent. [17] To determine if such additives would also promote analogous polymerizations in the solid-state,C u 0 powder (20 equiv relative to the initiator) was added to amixture that was prepared as described above and subjected to the BM conditions.I na ccord with results obtained in solution, [17] af aster polymerization reaction was observed (97 %c onversion in 3h)w hile the relationship between the monomer conversion and the number average MW of the polymer produced remained linear and control over the reaction was achieved ( Figures 1D-F). Considering the advantages bestowed by adding the Cu 0 ,s ubsequent experiments utilized this additive.
To further optimize the BM methodology,t he milling frequency was varied. As eries of polymerization reactions were independently performed at 10, 20, or 30 Hz for 6h using a50:1:1molar ratio of monomer,initiator, and catalyst in the presence of Cu 0 (20 equiv). At low frequency,n o significant polymerization was observed. However,increasing the frequency to 20 Hz resulted in the formation of apolymer with a M n,SEC of 16.0 kDa albeit with am odest monomer conversion (50 %) and relatively broad polydispersity ( of 3.23). The M n,Theory ,asbased on the monomer conversion, was calculated to be lower (4.0 kDa) than the SEC-derived value, which indicated that the initiation efficiency may be restricted. While the use of ah igher milling frequency( 30 Hz) resulted in ah igh monomer conversion (99 %) and afforded ap olymer with ar elatively low MW (M n,SEC of 4.6 kDa) and narrow polydispersity ( of 1.49), the MW of the polymer produced was found to be lower than its theoretical value (7.8 kDa) and attributed to mechanical degradation during the BM reaction. Aseries of controls were also performed in parallel with the aforementioned experiments.F or example, conducting apolymerization in aball-less BM vessel resulted in am onomer conversion of 16 %a nd afforded ap olymer with a M n,SEC of 1.0 kDa and of 2.27. Likewise,n eat polymerizations at 40 8 8Cr esulted in al ow monomer conversion (38 %) and gave polymers with relatively low MW and high polydispersity index values (M n,SEC of 3.3 kDa and of 1.69) (see Figure S1).
Next, efforts were directed toward verifying that the aforementioned solid-state polymerizations proceeded in ac ontrolled manner.A ss ummarized in Table 1, ap ositive correlation between the [M] 0 /[I] 0 and the polymer MW was observed. While such ar elationship reflects ac ontrolled polymerization process,anability to extend growing polymer chains upon exposure to an additional monomer is ak ey criterion. To test the latter, low MW macroinitiators were first   (20 equiv), and then subjected to BM (30 Hz). Aliquots were withdrawn from the reaction vessel over time and analyzed using 1 HNMR spectroscopy and SEC which collectively showed that the monomer was consumed (ca. 80 %) concomitantly with an increase in polymer MW ( Figure 2). However,t he final products obtained appeared to consist of mainly two distributions of polymer chains:o ne from the chain extension and one from unreacted macroinitiator.
Deconvoluting the corresponding SEC data revealed that the quantity of unreacted macroinitiator was approximately 30 %ofthe total mixture, [18] which may be due to aloss of the halogen end-groups during the macroinitiator synthesis or chain extension.
To quantify the apparent loss in end-group functionality over time,alow MW polymer was synthesized using the BM methodology described above . After 2h,5 3% of the monomer was converted to polymer,asdetermined by analyzing the product mixture using 1 HNMR spectroscopy.Based on the monomer conversion value and assuming full initiation, the M n,Theory of the polymer produced was calculated to be 4.3 kDa. Further inspection of the NMR data revealed diagnostic signals at d 4.5 ppm and over the range of 2.7 to 0.5 ppm (CDCl 3 ), which were assigned to the terminal bromomethine groups and hydrogens in the polymer backbone,r espectively.U sing the relative intensities of the aforementioned NMR signals,t he number average MW of the polymer (M n,NMR )was calculated to be 6.7 kDa (see Figure S2). Thed ifference between the M n,Theory and M n,NMR values indicated that approximately 33 % of the chain termini became non-functional during the polymerization reaction. Forc omparison, approximately 8% of the end-groups lose their functionality during the solution phase ATRP of styrene at similar conversions (48 %). [19] Ah allmark of solution-state ATRP reactions is that they proceed through radical pathways as determined in part through trapping experiments with scavengers (e.g., 2,2,6,6tetramethyl-1-piperidinyloxy (TEMPO) free radical). [20] To determine if radicals were also generated during the afore-  Figure S4). Similarly,n op olymerization was observed when only the monomer or the monomer and at ypical free radical initiator (e.g.,a zobisisobutyronitrile; AIBN) were separately subjected to the BM conditions (see Table 1). Collectively,t hese results indicated that the solidstate ATRP reactions initiated rapidly and proceeded in amanner similar to those that are performed in solution, and that the catalyst was key to not only generating radicals but also maintaining their concentrations at asteady state.
Since various stimuli (e.g., photochemical, [21] electrochemical, [22] and sonochemical [23] )h ave been used to effectively switch ATRP reactions between "on" (active) and "off"  Figure 3, the rate of the polymerization was multiply switched between "on" and "off" states over the course of 78 hb ya lternating the milling frequency. While chain growth occurred only during the "on" states,t he resulting the polymer exhibited arelatively broad polydispersity ( of 1.88), presumably due to the chain-end deactivation processes described above and/ or mechanical degradation. As noted above,the MWs of the polymers produced were measured to be lower than their theoretical values and attributed to chain scission (e.g., see Figure S5 for plots of key data obtained from Table 1). As such, the phenomenon was modeled to gain adeeper understanding of the decomposition mechanism and to predict the loss in polymer MW.A s summarized in Equation (1), the decomposition rate can be expressed in terms of the change in polymer MW over time and the corresponding rate constant (k d )c an thus be determined from the semi-logarithmic relationship described in Equation (2). An integrated form of the latter, Equaln M n;0 À M n;1 M n;t À M n;1 tion (3), indicates that the polymer MW at any given time M n;t ¼ M n;0 À M n;1 ÀÁ e Àkdt þ M n;1 ð3Þ (M n,t )s hould exponentially decrease from its initial state (M n,0 )a nd approach al imiting value (M n,1 ). [9,11] Assuming that ap olymerization reaction affords ap olymer with its theoretical MW (M n,Theory )ifthere was no decomposition, the M n,0 can be equated to M n,Theory and thus the loss in polymer MW (M n,Loss )can be determined as afunction of milling time, as shown in Equation (4). M n;Loss ¼ M n;Theroy À M n;1 ÀÁ e Àkdt þ M n;1 ð4Þ where t, R d , M n,0 , M n,t , M n,Loss ,a nd M n,Theory are the milling time,t he rate of decomposition, the initial polymer molecular weight, the polymer molecular weight at time t, the predicted loss in polymer molecular weight due to mechanical degradation, and the theoretical molecular weight, respectively.
To test the aforementioned model, as eries of decomposition studies were conducted by separately BM poly(2-VN) with different initial MWs (M n,0 = 95.9, 25.7, or 18.3 kDa). After 12 h, the MWs of the polymers measured for each experiment approached al imiting M n,1 value of 3.2 kDa ( Figure 4A). [9] The k d values measured from the semi-logarithmic plots of the change in MW versus milling time were found to be similar and an average of 0.33 AE 0.054 h À1 was calculated ( Figure 4B). Inputting the k d value into Equation (4) resulted in al inear correlation between Figure 3. Summary of polymerization kineticsd ata that were recorded over time. (A) As emi-logarithmic plot of the monomer concentration vs. time. Note that the areas labeled as "on" or "off"state refer to periods wherein the BM frequency was varied between 30 Hz and 0Hz, respectively.(B) Size exclusion chromatograms and corresponding data as recorded over time (indicated). Note:the chromatograml abeled as "Purified" refers to data that were recorded for ap olymer that was passed through acolumn of neutral alumina and then precipitatedf rom methanol.    Figure 4C). Theg ood fit indicates that the model not only effectively rationalizes the difference between M n,Theory and M n,SEC but provides am eans to predict polymer MW as afunction of BM time.
To realize the potential of the aforementioned methodology,e fforts were directed toward the synthesis of random copolymers comprised of charged and neutral monomers. Such copolymers,which are often termed polyelectrolytes, [24] have found utility in applications that range from nanoparticle encapsulation [25] to drug delivery, [26] yet are challenging to prepare because the two types of monomers typically exhibit orthogonal solubilities. [27] As ar esult, relatively sophisticated synthetic schemes that often entail multiple protection-deprotection steps are required, [28] even when controlled radical polymerizations are used. [29] Thesolid-state BM ATRP method described above employs as ingle phase and thus effectively circumvents these fundamental and practical drawbacks.T om aintain continuity with the aforementioned studies,2 -VN was selected as am onomer along with sodium styrene sulfonate (NaSS), acharged species that is often paired with neutral monomers in the synthesis of copolymers. [30] As summarized in Table 2, various mixtures of 2-VN and NaSS were combined with the initiator,c atalyst, and reductant described above,and then ball milled at 30 Hz. Aliquots were periodically withdrawn from the reaction vessel and dissolved in either CDCl 3 (for 2-VN) or D 2 O( for NaSS), spiked with aknown quantity of an external standard (anisole or DMF,r espectively) and analyzed by 1 HNMR spectroscopy to ascertain monomer conversion (see Figure S6). As expected, the solubilities of the copolymer products depended on their compositions.C opolymers with relatively high molar compositions of 2-VN (e.g., poly(2-VN) 28 -ran-poly(NaSS) 7 )w ere soluble in organic solvents whereas copolymers rich in NaSS (e.g., poly(2-VN) 10 -ranpoly(NaSS) 36 )w ere soluble in aqueous media. Copolymers with near equimolar monomer compositions (e.g., poly(2-VN) 25 -ran-poly(NaSS) 18 )w ere insoluble in THF as well as aqueous media and could only be dissolved in DMSO at elevated temperatures.The solubility differential required the development of anovel suite of techniques to characterize the copolymers.S EC was used to determine the M n and the polydispersity of the copolymers that were soluble in either THF or aqueous media. However,t of acilitate au niversal comparison, dynamic light scattering (DLS) was used in conjunction with the specific refractive index increment (dn/ dc) of the copolymers,w hich was found to be linearly correlated with the monomer composition in DMSO (see Figure S7) and was used to determine the absolute weight average MWs (M w,absol. )o ft he copolymers.C ollectively,t he MWs and polydispersities of the copolymers were typical of controlled polymerizations and, in abroader perspective,the results demonstrated that the solid-state methodology may facilitate access to copolymers that are inaccessible or challenging to prepare via solution-state approaches. [31]

Conclusion
In conclusion, aseries of ATRP reactions were performed in the solid-state.BMmixtures that consisted of initiators and catalysts commonly employed in solution-state ATRP reactions along with solid monomers resulted in controlled polymerizations,a nd the addition of Cu 0 accelerated the reactions without detriment. Radicals were generated during the process,a sc onfirmed by trapping experiments,a nd appeared to reach as teady state within as hort period time. Moreover,t he polymerization reaction was effectively switched between active and inactive states by alternating the applied frequency over time.W hile losses in end-group functionality were observed and the molecular weights of the polymers produced were lower than their theoretical values, the differences,w hich were attributed to mechanically induced chain scission, were successfully modeled and an accurate prediction of the polymer MW over time was realized. In abroader context, these results demonstrate that radicals generated in the solid-state may be harnessed in as imilar manner to those formed in solution. Moreover, copolymers that are inaccessible or challenging to obtain via solution-state polymerization methods were also synthesized. As such, the solid-state chemistry described herein may effectively obviate the need for solvents in other types of radical-based, synthetic transformations (e.g., Kharasch additions,r eversible addition-fragmentation chain-transfer (RAFT), etc.) and expedite access to exotic polymeric materials that exhibit limited solubilities in organic solvents or aqueous media.