Article pubs.acs.org/Macromolecules
Estimating Monomer Sequence Distributions in Tetrapolyacrylates Yavuz Caydamli, Yi Ding, Abhay Joijode, Shanshan Li, Jialong Shen, Jiadeng Zhu, and Alan E. Tonelli* Fiber & Polymer Science Program, North Carolina State University, Campus Box 8301, Raleigh, North Carolina 27695, United States S Supporting Information *
ABSTRACT: Recently Ting et al. [ACS Macro Lett. 2013, 2, 770−774] described the syntheses of acrylic tetrapolymers with controlled molecular weights and tetramonomer compositions. Relative reactivity ratios of all monomer pairs were determined and used in the Walling−Briggs terminal copolymerization model along with Skeist’s equations to address the expected compositional drift in the monomer feed ratios. The anticipated control of monomer incorporation based on this approach was verified experimentally on several tetrapolyacrylates synthesized by RAFT polymerization, which additionally controlled their molecular weights. Their “new and simple paradigm combining both predictive models provides complementary synthetic and predictive tools for designing macromolecular chemical architectures with hierarchical control over spatially dependent structure−property relationships for complex applications” is extended here to the derivation of expected monad compositions, and diad, triad, and tetrad monomer sequence distributions. These were obtained directly from the comonomer reactivity ratios determined experimentally by Ting et al. Our motivation was twofold: (i) The similar chemical structures of the four acrylate monomers they selected (methyl, 2-carboxyethyl, 2-hydroxypropyl, and 2-propylacetyl acrylate) render the experimental determination of sequence distributions in the resulting tetrapolyacrylates problematic. (ii) Because they are spatially dependent structural parameters, the sequence distributions of monomer diads, triads, tetrads, etc., in co-, tri-, tetrapolymers, etc., are generally expected to correlate more closely with their properties than their overall compositions.
■
INTRODUCTION A growing interest in architecturally tailored1 and sequencespecified2 macromolecules with enhanced properties has recently developed because structurally controlled polymers are of widespread importance across many diverse fields. Among these are statistical copolymers (SCPs) that contain two or more monomers with specific compositions and sequence distributions. Depending on their end use, the morphologies of SCPs can be tailored by knowing their relative reactivity ratios and controlling the monomer concentrations during their polymerization, which in turn helps control the properties of SCPs. Ting et al.3 have synthesized acrylic tetrapolymers that are expected to have properties similar to those of the hydroxypropyl methylcellulose acetate succinates (HPMCAS), which are used in drug delivery applications.4 Compared to small molecules, controlling the molecular architecture of SCPs is more complex because of the potentially large variety of macrostructures, i.e., types, quantities, and locations of their microstructures. As an example, for the Ting et al. tetrapolyacrylates containing just 100 monomers, there are potentially 4100 or ∼1060 chains with distinct monomer distributions. At least partial control of the chain architecture can be achieved by radical polymerization techniques, like nitroxidemediated polymerization (NMP),5 atom transfer radical polymerization (ATRP),6 and reversible addition−fragmentation chain transfer polymerization (RAFT).7 Among these controlled free radical polymerizations (FRP), Ting et al. have © 2014 American Chemical Society
identified RAFT as providing better control over the chain propagation kinetics8 and have used it to synthesize acrylic tetrapolymers with controlled compositions and molecular weights (see Figure 1). The focus of the investigation of Ting et al. was to “control the statistics” for multicomponent polymer systems (especially for systems containing more than two monomers) in order to create SCPs with microstructures having targeted length scales and intermolecular associations. Four acrylic monomers [1, methyl acrylate (MA = 1); 2, 2-carboxyethyl acrylate (CEA = 2); 3, 2-hydroxypropyl acrylate (HPA = 3); and 4, 2propylacetyl acrylate (PAA = 4)] were copolymerized using RAFT techniques.6 Pairwise reactivity ratios of all four monomers were obtained in copolymerizations conducted below 15% total monomer conversion and in the range of feed mole fractions ( f i) of 0.1−0.9. The resultant tetrapolymer compositions (Fi) were estimated using 1H NMR. The Mayo− Lewis relationship9 was employed to obtain nonlinear fits of Fi vs f i from which the reactivity ratios (rij) for all pairwise combinations between MA, CEA, HPA, and PAA were calculated.3 Ting et al. then used a four-component Walling−Briggs10 copolymerization model, which predicts the polymer chemical composition at low conversion by incorporating the monomer Received: September 17, 2014 Revised: November 28, 2014 Published: December 17, 2014 58
dx.doi.org/10.1021/ma5019268 | Macromolecules 2015, 48, 58−63
Macromolecules
Article
Figure 1. Synthesis of acrylic tetrapolymers (MA = 1, CEA = 2, HPA = 3, PAA = 4) by the RAFT technique.3
Figure 2. Plots of instantaneous and cumulative polymer compositions as a function of total monomer conversion.3
Overall, Ting et al., using RAFT polymerizations and introducing a combined Walling−Briggs−Skeist approach, were able to obtain multicomponent SCPs (tetrapolyacrylates) with controlled compositions and molecular weights. These acrylic tetrapolymers may subsequently be used to systematically model and determine pairwise comonomer reactivity ratios, targeting specific polymer compositions and identifying compositional drift, as well as correlating their properties with their structures. The properties of copolymers, however, are not only affected by their comonomer compositions, but possibly even more so by the sequences of enchained monomers. To confirm this view of copolymer structure−property relations, we need go no further than to consider proteins. Clearly it is the sequences of amino acids or the primary structures of proteins and not their amino acid compositions that determine their biological functions. Sequence distributions of monomers in co-, tri-, tetrapolymers, etc., are likewise generally expected to correlate more closely with their properties than their overall compositions because they are in fact “spatially dependent structural parameters”. However, these were not addressed in the Ting et al. study. In addition, we do not expect NMR12 to be very helpful in determining local monomer sequences in the tetrapolyacrylates they synthesized. This is a consequence of
feed and comonomer reactivity ratios. Good agreement was observed between this model and the experimental copolymer compositions, but at higher conversions, this model may have limitations that were cited, such as monomer depletion and potential loss of end-group fidelity. It has been highlighted that in FRPs there is an inherent trade-off between compositional control and higher conversions. These issues can be solved using the Skeist11 equations, which respectively track and correlate compositional drift and monomer conversion to changes in the instantaneous polymer composition. Another suggested way to control compositional drift is to add monomers continuously, but this approach adds design and modeling complexity. Plots of instantaneous and cumulative polymer compositions observed as a function of total monomer conversion for [MA/CEA/HPA/PAA] = [0.60/0.25/0.10/ 0.05] feed ratios targeted by Ting et al.3 are illustrated in Figure 2. At low conversions, a preferential addition of MA and bias against PAA addition prevents the random distribution of monomers. Also, the reaction needs to be stopped before 60% conversion to maintain chemical homogeneity. Such plots offer a unique way to monitor monomer and polymer compositions in the syntheses of SCPs. 59
dx.doi.org/10.1021/ma5019268 | Macromolecules 2015, 48, 58−63
Macromolecules
Article
the similar chemical structures of those portions of their side chains nearest the backbones, which can potentially affect their conformations and resultant 13C NMR spectra (see Discussion section). For these reasons, we have used the reactivity ratios determined by Ting et al. for each monomer pair to estimate the probabilities/populations of tetrad−monomer sequences, from which we may easily derive overall monomer compositions, as well as diad and triad populations. The effects of employing different tetramonomer feed ratios were also explored.
■
THEORETICAL CALCULATIONS
We have utilized the comonomer reactivity ratios (16 rij in all, where i and j denote the monomer pairing) for the four acrylate monomers (1 = methyl acrylate, 2 = 2-carboxyethyl acrylate, 3 = 2-hydroxylpropyl acrylate, and 4 = 2-propylacetyl acrylate) determined by Ting et al. to obtain comonomer pair probabilities Pr(ij):
Figure 3. Relative diad populations for monomer feed ratios f1/f 2/f 3/ f4 = 0.25/0.25/0.25/0.25.
From these comonomer probabilities, the probability/population of tetrad sequences, Pr(ijkl), are simply given13,14 by Pr(ijkl) = Pr(ij)Pr(jk)Pr(kl), i.e., a product of the comonomer probabilities for each of the three diads in each tetrad sequence. Then from the tetrad sequence probabilities, we may derive the diad and triad monomer sequence probabilities and monomer compositions in the following manner. For each of the 256 distinct tetrad sequences, the types and numbers of monads, and diad, and triad sequences contained therein were determined and were weighted by the tetrad probability to which they belong. For example, in the 2214 tetrad, there are the 221 and 214 triads; the 22, 21, and 14 diads, and two 2 monads and one each of the 1 and 4 monads. Consequently Pr(2214) was added to the sum of probabilities for the 221 and 214 triads; the 22, 21, and 14 diads, and 1 and 4 monads, while 2 × Pr(2214) was added to the sum of monad 2 probabilities. This procedure was repeated for all 256 tetrads, and the sum of probabilities obtained this way for all 64 triads, 16 diads, and 4 monomers or monads were used to normalize their individual probabilities and obtain fractional probabilities or populations. In an attempt to account for unequal tetramonomer feeds, as assumed above, each tetrad probability Pr(ijkl) was multiplied by the appropriate product of tetramonomer feed ratios. For example, suppose f1, f 2, f 3, f4 = 0.10, 0.60, 0.25, 0.05. Then if i, j, k, l = 2, 1, 1, 4, i.e., the 2114 monomer tetrad, then its probability is given by 0.60 × 0.102 × 0.05 × Pr(2114).
■
Figure 4. Relative diad populations for monomer feed ratios f1/f 2/f 3/ f4 = 0.60/0.25/0.10/0.05.
RESULTS
Plots of expected diad and triad sequence populations calculated for three different tetramonomer feed ratios are presented in Figures 3−6.
Figure 5. Relative diad populations for monomer feed ratios f1/f 2/f 3/ f4 = 0.10/0.60/0.25/0.05. 60
dx.doi.org/10.1021/ma5019268 | Macromolecules 2015, 48, 58−63
Macromolecules
Article
than the value for random additions, i.e., all Pr(ij) = rij = 1 (p = 1/256 = 0.003906). However, once different feed ratios come into play, the sequence probabilities/populations are dependent upon both the comonomer feed and reactivity ratios. Dividing the populations that account for the difference in comonomer reactivity by those that assume all Pr(ij) = rij = 1, somewhat separates the effects of feed ratios from comonomer reactivity ratios and shows that diads 14 and 23 are more populated than other diads if equal feed ratios were used. On the other hand, it also demonstrates that by changing the feed ratios the populations of comonomer sequences can be effectively changed. The tetra-substituted cellulose polymers (HPMCAS)s are known4 to be effective in preventing hydrophobic drug molecules from aggregating and crystallizing in aqueous solution, which reduces their availability to be absorbed and delivered. It was concluded that their hydrophobicity, to attract hydrophobic drugs, and their amphilicity, which can reduce their agglomeration, are both critical attributes. This means that the sequence of substitutions on the cellulose chains is critical to their making hydrophobic drugs deliverable in aqueous media. Pockets of consecutive acetate and methyoxy substituted glucose units could attract and bind hydrophobic drugs, while randomly placed and negatively charged succinate substituted glucose units could prevent aggregation of HPMCASs. As a result, the compositions of HPMCAS samples are likely not as relevant to their ability to deliver drugs as the sequence distribution of their four differently substituted glucose rings. Similarly for the Ting et al. tetra-polyacrylates, compositional information is likely insufficient to understand their behaviors. For example, compare the populations of all tetrads containing only hydrophobic units (1 and/or 4) and only hydrogen-bonding or charged units (2 and/or 3) (see Figure 1) obtained directly from the tetrad sequence probabilities generated here (see Supporting Information) and those obtained from the tetrad monomer compositions, as presented below. The populations of tetrads 1111 + 1114 + 4111 + 1141 + 1411 + 1144 + 4411 + 1414 + 4141 + 1441 + 4114 + 4444 + 4441 + 1444 + 4414 + 4144 for equal 25/25/25/25 feed ratios, using Ting copolymer reactivity rations rij and assuming all rij = 1 are respectively 0.1213 and 0.0625, which differ by a factor of 2. Similarly for tetrads containing only hydrogen-bonding (2) or charged (3) side-chains the sum of probabilities are 0.1029 and again 0.0625, when Ting et al. copolymer reactivity ratios rij are used or assuming all rij = 1. Clearly for equal comonomer feed ratios the actual tetrad comonomer sequence populations containing only hydrophobic or only hydrogen-bonding or charged acrylate units are both much larger than the sum of their 16 equally populated tetrads, i.e., 16/256 = 0.0625, based on their comonomer compositions. Ting et al. presented an approach to control both the molecular weights and monomer compositions of tetrapolyacrylates by using reversible-fragmentation chain transfer freeradical polymerization,5 performed under certain experimental conditions and monomer conversions, the Walling−Briggs model,10 and Skeist’s equations.11 However, the Walling− Briggs−Skeist approach they used only predicts the monomer compositions of a tetrapolymer without specifying the precise sequences of enchained monomers, of which the latter are likely more important for understanding polymer properties. In order to achieve “designing macromolecular chemical architectures
Figure 6. Diad populations for various monomer feed ratios. Points indicate diad populations, while lines are drawn merely to aid the eye.
■
DISCUSSION Initially for f1 = f 2 = f 3 = f4 = 0.25, it seems surprising that the monomer populations obtained with actual and equal (all rij = 1) comonomer reactivity ratios are so similar and close to 0.25. The sums of Pr(ij) for monomers j, as obtained by adding all P(rij) (Supporting Information), dividing by 4, and then dividing by the sum of their sums are monomer j ⟨Pr(ij)⟩ 1 0.203 2 0.213 3 0.283 4 0.301 If we also sum Pr(ij) over all monomers i (Supporting Information), divide by 4, and then divide by their sum, we get monomer i ⟨Pr(ij)⟩ 1 0.290 2 0.303 3 0.206 4 0.201 So when we add the ⟨Pr(ij)⟩s and ⟨Pr(ij)⟩s, we find that their sum, which should be a measure of monomer populations, is quite similar: ⟨Pr(ij)⟩s + ⟨Pr(ij)⟩s → 1 = 0.493; 2 = 0.516; 3 = 0.489; and 4 = 0.502 or after normalization 1 = 0.2516; 2 = 0.2635; 3 = 0.2500; and 4 = 0.2567. With equal feed ratios (f1/f 2/f 3/f4 = 0.25/0.25/0.25/0.25), diads 14 (p = 0.129) and 23 (p = 0.150) in particular are more populated (p = fractional population) than if we assume the comonomer addition is random, i.e., all Pr(ij) = rij = 1 (p = 1/ 16 = 0.0625). This is not surprising considering the large Pr(ij)s for the 14 and 23 comonomer pairs, 3.3 and 3.8, respectively. Similar predictions based on the comonomer reactivity ratios measured by Ting et al. are also seen for triads (Supporting Information). For example, triads 123 (p = 0.045), 141 (p = 0.043), 234 (p = 0.040), 314 (p = 0.038), 323 (p = 0.040), 414 (p = 0.030), and 423 (p = 0.028) are significantly more populated than a random comonomer addition would produce, i.e., all Pr(ij) = rij = 1 (p = 1/64 = 0.01563). Also as expected (see Supporting Information), tetrad populations calculated for 1414 (p = 0.027984), 1423 (p = 0.024482), 2314 (p = 0.025547), and 2323 (p = 0.024901) tetrads are much larger 61
dx.doi.org/10.1021/ma5019268 | Macromolecules 2015, 48, 58−63
Macromolecules
Article
monomer sequence distributions in the Ting et al. tetrapolyacrylates, as is the case also for the HPMACSs. 13 C NMR could potentially yield comonomer diad populations. If the 13C NMR spectra of the homopolyacrylates show backbone methylene and/or methine carbon resonances that are distinct from each other, then in the tetraacrylate polymers at least some diad monomer sequences should be identifiable. However, this does not seem likely, because each acrylate comonomer side chain is attached to the methine backbone carbon (CH) by the following identical structure:
with hierarchical control over spatially dependent structure− property relationships for complex applications”, the overall goal of Ting et al., monomer sequence distributions need to be determined. As shown here, these can be estimated from monomer feed ratios and comonomer reactivity ratios, and they need to be considered in modeling the specific properties of complex macromolecules like, for instance, the HPMCASs. According to Ting et al., “This new and simple paradigm combining both predictive models provides complementary synthetic and predictive tools for designing macromolecular chemical architectures with hierarchical control over spatially dependent structure-property relationships for complex applications such as oral drug delivery.” However, they only demonstrated control over the molecular weight and monomer composition over a majority of the tetrapolymerization, i.e., from 0 to ∼60% total monomer conversion. As demonstrated here, from the comonomer reactivity ratios they determined, we can easily estimate the probabilities/populations expected in their tetrapolyacrylates for sequences of four consecutive monomers. Ting et al. also studied the RAFT homopolymerization kinetics of their four monomers (MA, CEA, HPA, and PAA) based on the same tetrapolymer synthesis procedure described in their Supporting Information. Monomers CEA, HPA, and PAA had similar initiation rates, while MA had a relatively slow RAFT pre-equilibration (see Figure 7). However, RAFT pre-
Independent of monomer sequences, the backbone methine carbons of each tetramonomer repeat unit have identical α-, β-, and γ-substituents and the ester bonds are trans, while all their backbone methylene carbons have identical α-, β-, γ-, and δsubstituents. This likely means that the backbone conformations are also independent of monomer sequences. Taken together, we expect12 virtually identical 13C resonance frequencies or chemical shifts for the backbone carbons of all four acrylate repeat units.
■
CONCLUSIONS We have shown that it is possible to utilize experimental comonomer reactivity ratios along with selected monomer feed ratios to estimate the distributions of monomer sequences in tetrapolymers like the tetrapolyacrylates examined by Ting et al.3 This permits the development of structure−property relations based on “macromolecular chemical architectures with hierarchical control” and to predict “spatially dependent structure−property relationships for complex applications”.
■
ASSOCIATED CONTENT
S Supporting Information *
Tables of monad, diad, triad, and tetrad populations and charts showing triad and diad populations referred to in the text. This material is available free of charge via the Internet at http:// pubs.acs.org.
■
Figure 7. Initial RAFT homopolymerization kinetics of MA, CEA, HPA, and PAA monomers.3
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (A.E.T.). Notes
The authors declare no competing financial interest.
equilibration is not a key factor affecting the chemical compositions of the tetrapolymers. Even though CEA, HPA, and PAA had higher initiation rates, it is only the propagation processes, i.e, the comonomer reactivity ratios (rijs) and monomer feed ratios ( f1/f 2/f 3/f4), which control monomer composition. In other words, monomer initiation has little effect on the overall chemical composition of the tetrapolymers because after initiation all four MA, CEA, HPA, and PAA monomers are added according to their monomer feed and comonomer reactivity ratios. Further study of RAFT preequilibration effects on chemical composition may not therefore be necessary. Unlike the tetrasubstituted celluloses (HPMCAS), which are characterized by heterogeneous chain lengths and molecular weights,15 the Ting et al. tetrapolyacrylates are largely homogeneous in this regard; however, as noted in the Introduction, it may be difficult to experimentally determine
■
REFERENCES
(1) Bates, F. S.; Hillmyer, M. A.; Lodge, T. P.; Bates, C. M.; Delaney, K. T.; Fredrickson, G. H. Science 2012, 336, 434−440. (2) (a) Badi, N.; Lutz, J. Chem. Soc. Rev. 2009, 38, 3383−3390. (b) Lutz, J. Polym. Chem. 2010, 1, 55−62. (c) Ganesan, V.; Kumar, N. A.; Pryamitsyn, V. Macromolecules 2012, 45, 6281−6297. (d) Powers, W.; Ryu, C. Y.; Jhon, Y. K.; Strickland, L. A.; Hall, C. K. ACS Macro Lett. 2012, 1, 1128−1133. (3) Ting, J. M.; Navale, T. S.; Bates, F. S.; Reineke, T. M. ACS Macro Lett. 2013, 2, 770−774. (4) (a) Friesen, D. T.; Shanker, R.; Crew, M.; Smithey, D. T.; Curatolo, W. J.; Nightingale, J. A. S. Mol. Pharmaceutics 2008, 5, 1003−1019. (b) Ilevbare, G.; Liu, H.; Edgar, K. J.; Taylor, L. S. Cryst. Growth Des. 2012, 12, 3133−3143. (5) Hawker, C. J.; Bosman, A. W.; Harth, E. Chem. Rev. 2001, 101, 3661−3688. 62
dx.doi.org/10.1021/ma5019268 | Macromolecules 2015, 48, 58−63
Macromolecules
Article
(6) Wang, J. S.; Matyjaszewski, K. J. Am. Chem. Soc. 1995, 117, 5614−5615. (7) Moad, G.; Rizzardo, E.; Thang, S. H. Aust. J. Chem. 2009, 62, 1402−1472. (8) Matyjaszewski, K. Macromolecules 2002, 35, 6773−6781. (9) Mayo, F. R.; Lewis, F. M. J. Am. Chem. Soc. 1944, 66, 1594−1601. (10) Walling, C.; Briggs, E. R. J. Am. Chem. Soc. 1945, 67, 1774− 1778. (11) Skeist, I. J. Am. Chem. Soc. 1946, 68, 1781−1784. (12) Tonelli, A. E. NMR Spectroscopy and Polymer Microstructure: The Conformational Connection; VCH: New York, 1989. (13) Frisch, H. L.; Mallows, C. L.; Bovey, F. A. J. Chem. Phys. 1966, 45, 1565−1577. (14) Bovey, F. A. Chain Structure and Conformation of Macromolecules; Academic Press: London, 1982, Chapters 3 and 5. (15) Chen, R.; Ilasi, N.; Sekulic, S. S. J. Pharm. Biomed. Anal. 2011, 56, 743−748.
63
dx.doi.org/10.1021/ma5019268 | Macromolecules 2015, 48, 58−63
