StructureâProperty Relationships of Poly(glycolic acid) and Poly(2

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Structure−Property Relationships of Poly(glycolic acid) and Poly(2hydroxybutyrate) Yuji Sasanuma,* Hiromi Yamamoto, and Somin Choi Department of Applied Chemistry and Biotechnology, Graduate School and Faculty of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan Macromolecules Downloaded from pubs.acs.org by AUCKLAND UNIV OF TECHNOLOGY on 05/09/19. For personal use only.

S Supporting Information *

ABSTRACT: Conformational analysis of poly(glycolic acid) (PGA) and poly(2-hydroxybutyrate) (P2HB) has been carried out via molecular orbital (MO) calculations and NMR experiments on model compounds. The MO energies validated through comparison with the NMR data were introduced into the rotational isomeric state (RIS) scheme to yield the configurational properties of the two polymers. The spatial configuration of the P2HB chain with chiral centers was calculated by the RIS scheme combined with stochastic processes and expressed as a function of (S)/(R) or meso/ racemo ratio. The above results are compared with those obtained previously for poly(lactic acid) and discussed. The density functional theory calculations with a dispersion force correction were performed for PGA crystal under periodic boundary conditions and revealed the origin of its superior thermostability and mechanical strengths.

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chains form stereocomplexes,13,15 which are superior to the homocrystals in thermostability: T0m’s of PLA and P2HB stereocomplexes are 279 °C15 and 239.1 °C,16 respectively. As stated above, the three polyesters differ only in the sidechain length; however, the small differences are magnified to appear as their own distinguishing features in high-order structures and physical properties. From the point of view of molecular design for polymers, therefore, it is of especial interest to elucidate structure−property relationships of the three polyesters, which is the subject of the present study. The overall scheme of this study is illustrated in Scheme 1. The contents of this study may be divided into two main parts: (1) conformational analysis and evaluation of configurational properties of PGA and P2HB; (2) structural characterization and property evaluation of PGA crystal. In the former part, conformational analyses of PGA and P2HB were carried out via molecular orbital (MO) calculations and NMR experiments on model compounds: methyl 2-acetoxyacetate (MAA) for PGA and methyl 2-acetoxybutanoate (MAB) for P2HB (Figure 2). In the community of polymer science, the following principle has been accepted as established and demonstrated:17−19 configurational properties of polymers in the unperturbed state will be influenced only by short-range intramolecular interactions. The spatial configuration and thermodynamic functions of a given polymer can be evaluated from conformational energies obtained from small compound(s) with the same bond sequence as that of the polymeric chain. Based on the theory, this study has

INTRODUCTION Poly(glycolic acid) (PGA), poly(lactic acid) (PLA), and poly(2-hydroxybutyrate) (P2HB) belong to a family whose chemical formula can be expressed as [−O−CHR−C( O)−]x (R = H, CH3, and C2H5, see Figure 1); these three polyesters have the same backbone, differ from each other only in the side-chain length, and possess biodegradability in common. Of them, PLA has been most extensively investigated in terms of synthesis, structure, properties, processing, and biodegradability and the most mass-produced in chemical industries.1 Because PGA shows not only biodegradability but also high gas-barrier properties and mechanical strengths comparable to those of superengineering plastics, it has been used as sutures for surgical stitching, orthopedic parts for bone fixation, interlayers between thin films of poly(ethylene terephthalate) for bottles, and moving tools in wellbores for shale gas exploration.2,3 On the other hand, P2HB has rarely been used alone, and it is usually blended or copolymerized with PLA so as to adjust physical properties as desired.4−6 In the crystalline state, PGA adopts an all-trans structure,7 whose equilibrium melting point (T0m) was reported to be as high as 231.4 °C.8 In contrast to PGA, PLA and P2HB include asymmetric methine carbons, which render the repeating units either (S)- or (R)-isomer. The stable α-crystal of (S)-PLA forms trans, gauche+, and trans conformations in bonds a, b, and c, respectively (for the bond designation, see Figure 1),9,10 and its T0m is 207 °C.11,12 The similarity in X-ray diffraction pattern between PLA and P2HB suggests that (S)P2HB also crystallizes in a tg+t conformation,13 but it has a much lower T0m of 130.3 °C.14 If equimolar all (S)- and (R)chains of PLA or P2HB are cocrystallized, the two kinds of © XXXX American Chemical Society

Received: March 7, 2019 Revised: April 9, 2019

A

DOI: 10.1021/acs.macromol.9b00459 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

Figure 1. Aliphatic polyesters treated in this study (the poly(glycolic acid) family): (a) poly(glycolic acid) (PGA), (b) poly(lactic acid) (PLA), and (c) poly(2-hydroxybutyrate) (P2HB). The bonds are designated as indicated, and x is the degree of polymerization.

Scheme 1. Contents of This Study

Figure 2. Model compounds used in this study: (a) methyl 2acetoxyacetate (MAA and MAA-13C), monomeric model for PGA; (b) methyl (S)-2-acetoxybutanoate ((S)-MAB and (S)-MAB-13C), monomeric model for P2HB; (c) 2-methoxy-2-oxoethyl 2-acetoxyacetate (MOAA), dimeric model for PGA; (d) (S)-1-methoxy-1oxobutan-2-yl (S)-2-acetoxybutanoate ((S,S)-MOAB), dimeric model for P2HB. The bonds are designated as indicated, and the carbonyl carbon atoms of MAA-13C and MAB-13C were selectively labeled with 13C as shown.

tional energy of the two polymers. Inasmuch as P2HB has asymmetric carbon atoms, if the raw material is a mixture of (S)- and (R)-optical isomers, the synthesized P2HB chain may include a variety of stereosequences. In order to investigate the configurational properties of P2HB as a function of stereoregularity, two stochastic processes were employed: the Bernoulli trial to assemble atactic chains; the Markov chain to arrange isotactic, syndiotactic, and inbetween chains.22,23 The P2HB chains thus prepared also underwent the RIS calculations. Our previous study already dealt with the conformational analysis and RIS calculations on PLA,23 and the resulting data on PGA, PLA, and P2HB are compared and discussed herein.

determined conformational energies of PGA and P2HB from the monomeric and dimeric models. After the MO energies were validated through comparison with the NMR experiments, the MO data were introduced to the rotational isomeric state (RIS) scheme20,21 to yield configurational properties such as the characteristic ratios, configurational (conformational) entropies, and configuraB


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Macromolecules In the latter part, the density functional theory (DFT) calculations including a dispersion force correction (abbreviated as DFT-D) 24,25 under the periodic boundary condition26,27 were applied to the PGA crystal so as to reveal the sources of its high Tm0 and mechanical strengths comparable to those of superengineering plastics. The PGA crystal was structurally optimized at the B3LYP-D/6-31G(d,p) level and compared with that determined by X-ray diffraction.7 The interchain interaction (cohesive) energy was evaluated via the counterpoise (CP) method for the basis set superposition error (BSSE) correction28−30 and compared with those of other typical polymers. The stiffness and compliance tensors and Young’s moduli of PGA crystal were calculated and compared with those of other polymers. On the basis of the above data, the characteristics of PGA crystal are discussed, and the origins of its unique thermal and mechanical properties are elucidated. This study has aimed at revealing characteristics and uniqueness of not merely the single-chain conformations but also solid-state properties of the polyesters.

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Figure 3. Energy contour map of MAA as a function of dihedral angles of bonds b1 (φb) and c1 (φc). The electronic energies were calculated at the B3LYP/6-311+G(2d,p) level over −180° to +180° at intervals of 10° of φb and φc without the thermal correction and solvent effect.

RESULTS AND DISCUSSION MO Calculations. The conformational energies ΔEk’s of PGA were determined as follows. In preliminary MO calculations on MAA, the following points were found: the C(O)−O bond is essentially fixed in the trans (t) state (the cis form has a very high energy, being negligible), the O−CH2 bond can adopt trans, gauche+ (g+), and gauche− (g−) states, and the CH2−C(O) bond lies in either a trans or a synperiplanar (s) state. For the definition of the conformations, see Figure 5. However, to search more systematically for the stable conformers, we repeated the MO calculations on MAA at the B3LYP/6-311+G(2d,p) level, changing dihedral angles of bonds b1 (φb) and c1 (φc) over −180° to +180° at intervals of 10°. At each (φb, φc) position, the structural optimization was conducted with the two parameters, φb and φc, fixed. The B3LYP electronic energies thus obtained are plotted as a function of (φb, φc) in Figure 3. It should be noted that the B3LYP energies include no thermal correction and differ from the MP2 energies given in Table 1. In the energy map, the central high mountain around (0°, 0°) represents strong repulsion between the CO and −O− groups, and the still higher mountains around (0°, ±180°) reflect close contact between two CO groups. The energy minima can be found as bottoms of the valleys at intersections (g±t and g±s) of the horizontal and vertical dotted lines. The tt (±180°, ± 180°) and ts (±180°, 0°) positions also have low energies but seem to be saddles (transition zone). The contour map in Figure 3 differs significantly from that of Llactyl residue ((S)-PLA) reported by Brant et al.;31 their map has four minima but no synperiplanar minimum. Of them, the two of lowest energy were assigned to g+t and g+g+. All possible conformers of MAA underwent the geometrical optimization at the B3LYP/6-311+G(2d,p) level, and only five conformers remained: ttt, tg±t, and tg±s. Here, for example, tg+s means that bonds a1, b1, and c1 lie in trans, gauche+, and synperiplanar states, respectively (see Figure 2a). To investigate effects of the neighboring bonds on the geometrical optimization, a dimer, 2-methoxy-2-oxoethyl 2acetoxyacetate (MOAA) (Figure 2c), was also subject to the geometrical optimization. As a result, an additional conformation, tts, converged on an energy local minimum. To

Table 1. Conformational Energies for PGA, Derived from MOAAa bondb

gas

DMSO

a

b

c

25 °C

mp

25 °C

mpc

t t t t

t t g± g±

t s t s

2.27 1.58 0.00 0.67

2.15 1.55 0.00 0.73

1.74 1.39 0.00 0.44

1.66 1.36 0.00 0.55

c

In kcal mol−1. bAbbreviations: t, trans; g, gauche; s, synperiplanar The thermochemical term at the equilibrium melting point, 231.4 °C,8 is included. a c

clarify the solvent effect on conformational energies, two extreme media have been assumed here: nonpolar gas, dielectric constant ϵ = 1; polar dimethyl sulfoxide (DMSO), ϵ = 46.7. The energies of the six states, ttt, tts, tg±t, and tg±s, of MOAA were determined from averages over conformations (represented by i) of bonds b1 (variable among t, g+, and g−) and c2 (variable between t and s) with conformations (k) of bonds c1, a2, and b2 being fixed: ΔEk =

∑i ΔEk(i) exp( −ΔEk(i)/RT ) ∑i exp( −ΔEk(i)/RT )

(1)

Here ΔEk is the averaged energy of conformation k, ΔEk(i) is the energy of conformations k and i, R is the gas constant, and T is the absolute temperature. Table 1 shows the average energies derived from MOAA. Under the RIS approximation, stable conformations of a model compound of (S)-P2HB, (S)-MAB, were searched for with bonds a1 and a2 being fixed in the trans state, and three rotamers were found in each rotatable bond: bond b1, t, g+, and g−; bond c1, t, s, and g−; bond d1, t, g+, and g− (Figure 2b). The conformational energies of (S)-P2HB were determined as follows. All possible conformers of (S)-MAB were subjected to the geometrical optimization, and only conformers with the g+ state in bond b1 were found to show C


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Macromolecules especially low energies. The other conformers have the energies higher than or close to 2 kcal mol−1. As the Boltzmann factor of 2 kcal mol−1 at 25 °C is equal to 0.034, only the stable conformations are influential in conformationdependent properties of P2HB. In the previous study on PLA,23 the conformational energies were found to depend somewhat on the chain length, namely, whether the model compound is monomeric, dimeric, or trimeric. Therefore, the energies of the stable conformations were also evaluated from a dimeric model, (S)-1-methoxy-1-oxobutan-2-yl (S)-2-acetoxybutanoate ((S,S)-MOAB, Figure 2d) according to eq 1; the conformations of bonds c1 (t, s, and g−) and d1 (t, g+, and g−) were assigned to i in eq 1, and those of bonds c2 (t, s, and g−) and d2 (t, g+, and g−) were treated as k with bonds a1, b1, a2, and b2 fixed in t, g+, t, and g+, respectively. To avoid the model-size effect, this study has adopted the internal energy that the MO calculations yielded instead of the Gibbs energy. For the details, refer to the section Molecular Orbital Calculations of Methods. Table 2 shows the conformational energies thus determined. Table 2. Conformational Energies for the (S)-Form of P2HBa ΔEk (kcal mol−1)

bond a

b

c

d

gas

DMSO

t t t t t t t t t t t t t

t t g+ g+ g+ g+ g+ g+ g+ g− g− g− g−

s g− t t t s s s g− t t g− g−

(t) (t) (t) (g+) (g−) (t) (g+) (g−) (t) (t) (g+) (t) (g+)

2.25 1.99 0.00 −0.76 −0.71 0.77 0.12 0.23 2.68 2.88 2.03 1.97 1.41

2.38 2.68 0.00 −0.55 −0.47 0.58 0.03 0.22 3.10 3.13 2.24 2.44 1.70

In kcal mol−1. The energies of the conformers with the g+ state in bond b were derived from (S,S)-MOAB with eq 1, and the other energies were obtained from (S)-MAB. This is because the structural optimization for (S,S)-MOAB always rendered the conformation of bond b gauche+ owing to its strong g+ preference, even though bond b was initially set in the t or g− conformation. a

NMR Experiments. Parts a and b of Figure 4 show 1H and 13C NMR spectra observed from MAA-13C. The spacing of the doublet in Figure 4a directly gives the vicinal coupling constant (3JCH) between the carbonyl carbon and methylene protons. The 13C NMR spectrum of the carbonyl carbon in Figure 4b also includes the vicinal coupling; a spectral simulation for the 13C NMR spectrum yielded the same 3JCH value. In Table 3, the 3JCH values are listed. Parts c−e of Figure 4 show 13C and 1H NMR spectra of MAB-13C. The spectral simulations yielded the coupling constant (3JCH) between the carbonyl carbon and methine proton and the coupling constants (3JAB and 3JAC) between the methine (A) and methylene (B and C) protons as listed in Table 4. For the hydrogen designation, see Figure 5. The vicinal coupling constants can be expressed as a function of the bond conformations of the centrally intervening bond as formulated in Table 5. In the NMR

Figure 4. Observed (above) and calculated (below) 1H and 13C NMR spectra of MAA-13C and MAB-13C: (a) 1H NMR, methylene protons of MAA-13C; (b) 13C NMR, 13C-labeled carbonyl carbon of MAA-13C; (c) 13C NMR, 13C-labeled carbonyl carbon of MAB-13C; (d) 1H NMR, methine proton of MAB-13C; (e) 1H NMR, methylene protons of the side chain of MAB-13C. The asterisk in part c indicates impurity signals. The solvent was (CD3)2SO, and the measurement temperature was 25 °C. The MAB-13C sample was a mixture of (S)and (R)-isomers.

experiment for MAB-13C, the sample was a mixture of (S)and (R)-isomers; however, because both optical isomers give D


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Macromolecules Table 3. Observed Vicinal MAA-13C solvent

13

C−1H Coupling Constants of

dielectric constant

temp (°C)

CD3OD

32.7

(CD3)2SO

46.7

D2O

78.3

15 25 35 45 55 25 35 45 55 15 25 35 45 55

Table 4. Observed Vicinal Constants of MAB-13Ca solvent

13

temp (°C)

C6D12

2.0

CDCl3

4.8

CD3OD

32.7

15 25 35 45 55 15 25 35 45 55 15 25 35 45 55 25 35 45 55

46.7

JCH (Hz) 6.01 5.99 5.93 5.91 5.89 6.01 5.98 5.95 5.92 5.70 5.69 5.67 5.66 5.63

C−1H and 1H−1H Coupling

dielectric constant

(CD3)2SO

3

3

3

3

2.65 2.69 2.71 2.71 2.73 2.71 2.72 2.74 2.78 2.79 2.60 2.60 2.64 2.68 2.68 2.62 2.62 2.65 2.69

7.71 7.71 7.72 7.73 7.73 7.71 7.71 7.71 7.70 7.70 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62

4.62 4.64 4.66 4.68 4.70 4.62 4.64 4.65 4.68 4.68 4.66 4.69 4.70 4.70 4.73 4.83 4.83 4.85 4.87

JCH

JAB

JAC

Figure 5. Rotational isomeric states around (a) bond b1 of MAA-13C and (b) bond b1, (c) bond c1, and (d) bond d1 of (S)-MAB-13C. The coupling constants, JT’s and JG’s, are defined as illustrated. For the bond designation, see Figure 2.

provides no information on the conformation of bond c1, the MO calculations indicate its trans preference, and the pt value decreases with increasing medium polarity and temperature. Because MAB is soluble in various solvents, the NMR solvents were nonpolar C6D12 (ϵ = 2.02) to polar (CD3)2SO. However, the bond conformations are found to depend slightly on solvent, and the temperature dependence is also insignificant. In bond b1, the pg− values are small, and the g+ conformation is dominant. In bond d1, the magnitude relation of pg+ > pg− ≫ pt always holds regardless of solvent and temperature. In Table 7, the MO calculations are also given, being in good agreement with the NMR data. As for bond c1, the MO calculations indicate a magnitude relation of pt > pg+ ≫ pg− and yielded the pt values of ∼0.7 close to those of MAA. Rotational Isomeric State (RIS) Calculation. The refined RIS calculations33 were carried out with homemade programs that were coded in FORTRAN and compiled with Intel FORTRAN Composer XE for Windows or Intel FORTRAN Compiler for Linux. The statistical weight matrices were formulated for PGA and P2HB, being given in Formulations A and B, respectively (Supporting Informa-

a

In Hz.

identical spectra, the (S)-isomer has been exclusively employed as the model for the NMR analysis (Figure 5, parts b−d). The coefficients (JT’s and JG’s) of the equations are also given in the fourth column of in Table 5, and their sources are explained in the footnotes. For bond b1 of (S)MAB-13C, two equations include three unknowns, thus being indefinite. The MO calculations suggest that the pt value of bond b1 is nearly null. On the assumption that pt = 0, the pg+ and pg− of this bond were evaluated. The bond conformations thus obtained are shown in Tables 6 (MAA) and 7 (MAB). Inasmuch as MAA is soluble only in polar solvents, CD3OD, (CD3)2SO, and D2O, were used as the NMR solvents. In every solvent, bond b1 of MAA-13C exhibits small pt values (0.01−0.10), namely, a strong gauche preference. In Table 6, the pt’s derived from the MO calculations are also given and show a slight increase with an increase in solvent polarity and temperature. These tendencies as well as the calculated pt values are in fully satisfactory agreement with those of the NMR data. Although the NMR experiment E


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Macromolecules Table 5. Vicinal Coupling Constants as a Function of Bond Conformations compound 13

MAA- C

equation

JT’s and JG’s (Hz)

figure

J CH =JG pt + [(JT′ + JG′ )/2]pg

JG = 1.75, (JT′ + JG′ )/2 = 6.05a

5a

JG′ = 2.32, JT′ = 8.01b

5b

5d

bond 3

b1:O−CH2

pt + pg = 1 (S)-MAB-13C

3

b1:O−CH

J CH =JG pt + JG′ pg + + JT′ pg −

pt + pg + + pg − = 1 pt ≈ 0 d1: CH−CH2 (side chain)

3

J AB =JG pt + JT′ pg + + JG″ pg −

JT = JT′ = 13.12

3

J AC =JT pt + JG′ pg + + JG‴pg −

JG = JG′ = 2.96, JG″ = JG‴ = 3.31c

pt + pg + + pg − = 1 a

From MO calculations on MAA at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311+G(2d,p) level (this study). bFrom MO calculations on (S)MAB at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311+G(2d,p) level (this study). cFrom cyclohexane-1,1,2,2,3,3,4,4-d8:32 Jaa = 13.12, Jee = 2.96, and Jae = 3.65 Hz. J″G = J‴ G = (2.96 + 3.65)/2 = 3.31 Hz.

previous data on isotactic (S)-PLA23 are also summarized in Table 10. The previous paper mainly dealt with the DFT data at the B3LYP/6-311+G(2d,p) level, which well reproduced the solution and melt properties of PLA; however, Table 10 is based on the ab initio energies at the MP2/6-311+G(2d,p) level for consistency with the current calculations on PGA and P2HB. The characteristic ratio in the gas phase at 25.0 °C were obtained in the magnitude order of isotactic PLA > isotactic P2HB > PGA. The isotactic (S)-PLA chain can adopt only four conformations: tg+t tg+s, tg−t, and tg−g−.23 Of them, the latter two have high energies of 4.72 and 2.91 kcal mol−1; therefore, the former two will influence the configurational properties of the PLA chain. This is the reason for the large ⟨r2⟩0/nl2 value of isotactic PLA. The configurational entropy (often termed conformational entropy) was calculated from12,34 Ä É d(ln Z) ÑÑÑÑ R ÅÅÅ Sconf = ÅÅÅln Z + T Ñ x ÅÅÇ dT ÑÑÑÖ (2)

Table 6. Trans Fractions of MAA, Evaluated from NMR experiments and MO calculations bond medium CD3OD

(CD3)2SO

D2O

gas

DMSO

temp (°C) NMR exptl 15 25 35 45 55 25 35 45 55 15 25 35 45 55 MO calcd 15 25 35 45 55 25 35 45 55

b1

c1

0.01 0.01 0.03 0.03 0.04 0.01 0.02 0.02 0.03 0.08 0.08 0.09 0.09 0.10 0.01 0.01 0.01 0.01 0.02 0.03 0.03 0.04 0.04

where x is the degree of polymerization. The partition function, Z, can be obtained from ij n − 1 yz j z Z = J *jjj∏ UjzzzJ jj zz k j {

0.75 0.74 0.74 0.73 0.72 0.73 0.72 0.72 0.71

(3)

where n is the number of skeletal bonds, J* is the row matrix whose first element is unity and the others are null, Uj is the statistical weight matrix of bond j, and J is the column matrix filled with unity. The restricted freedom of conformation of isotactic PLA leads to the small configurational entropy (Sconf) of 1.47 cal K−1 mol−1 at T0m. The small Sconf results in a small entropy of fusion (ΔSu) because Sconf is known to account for 46−90% of ΔSu.23,35 The equilibrium melting point T0m is given by

tion). The geometrical parameters of PGA (Table S1, Supporting Information) and (S)-repeating unit of P2HB (Table S2) were, respectively, taken from MOAA and (S)MAB, and the latter geometries were converted to those of the (R)-isomer by the symmetry operation explained in Formulation B (Supporting Information). As explained above, the conformational energies of PGA at 25.0 °C and T0m and (S)-P2HB at 25.0 °C were determined as in Tables 1 and 2, respectively, and the environments (media) were assumed to be the completely nonpolar (gas phase) and polar organic solvent (DMSO). The RIS data on PGA and isotactic (S)-P2HB are shown in Tables 8 and 9, respectively. For the sake of comparison, the

Tm0 =

ΔHu ΔSu

(4)

where ΔHu is the enthalpy of fusion. Therefore, T0m of isotactic PLA is as high as 207 °C.11,12 The electronegative oxygen atoms so strongly repel each other that bond b of (S)PLA is forced into the g+ conformation.23 The asymmetrical carbon of PLA distinguishes the g+ and g− states, whereas the F


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Macromolecules Table 7. Bond Conformations of (S)-MAB, Evaluated from NMR Experiments and MO Calculations main chain

side chain

bond b1 medium

temp (°C)

C6D12

CDCl3

CD3OD

(CD3)2SO

gas

DMSO

pt

pg+

15 25 35 45 55 15 25 35 45 55 15 25 35 45 55 25 35 45 55

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

0.94 0.94 0.93 0.93 0.93 0.93 0.93 0.93 0.92 0.92 0.95 0.95 0.94 0.94 0.94 0.95 0.95 0.94 0.94

15 25 35 45 55 25 35 45 55

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.98

bond c1 pg−

pt

NMR exptl 0.06 0.06 0.07 0.07 0.07 0.07 0.07 0.07 0.08 0.08 0.05 0.05 0.06 0.06 0.06 0.05 0.05 0.06 0.06 MO calcd 0.02 0.71 0.02 0.70 0.02 0.69 0.02 0.68 0.02 0.68 0.02 0.71 0.02 0.70 0.02 0.69 0.02 0.68

ps

bond d1 pg−

0.28 0.28 0.29 0.30 0.30 0.28 0.29 0.30 0.30

0.01 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.02

pt

pg+

pg−

0.15 0.15 0.15 0.15 0.16 0.15 0.15 0.16 0.16 0.16 0.15 0.16 0.16 0.16 0.16 0.17 0.17 0.17 0.17

0.45 0.45 0.46 0.46 0.46 0.45 0.45 0.45 0.45 0.45 0.45 0.44 0.44 0.44 0.44 0.45 0.45 0.45 0.45

0.40 0.40 0.39 0.39 0.38 0.40 0.40 0.39 0.39 0.39 0.40 0.40 0.40 0.40 0.40 0.38 0.38 0.38 0.38

0.15 0.15 0.16 0.16 0.17 0.20 0.21 0.21 0.22

0.44 0.44 0.43 0.43 0.43 0.45 0.44 0.44 0.43

0.41 0.41 0.41 0.41 0.40 0.35 0.35 0.35 0.35

Table 8. Configurational Properties of PGA, Evaluated from RIS Calculations energy parameter gas ⟨r ⟩0/nl d[ln⟨r2⟩0]/dT × 103 b (K−1) Sconfc (cal K−1 mol−1) Uconfd (kcal mol−1) 2

2b

DMSO

25.0 °C

231.4 °Ca

5.31 −0.082 2.74 −2.06

5.34 −0.050 3.15 −1.76

25.0 °C

231.4 °Ca

5.14 −0.042 2.96 −1.53 pte

5.27 −0.039 3.28 −1.30

bond medium gas DMSO

temp (°C)

b

c

25.0 231.4 25.0 231.4

0.04 0.10 0.05 0.12

0.74 0.64 0.66 0.61

The equilibrium melting point.8 bFor x → ∞. From the intercept at x−1 = 0 of the ⟨r2⟩0/nl2 (d[ln⟨r2⟩0]/dT) vs x−1 plot. cFrom eq 2. dFrom eq 5. Relative to the crystal conformation, the all-trans form. epg = 1 − pt

a

The isotactic P2HB chain has a relatively large Sconf of 3.67 cal K−1 mol−1 (in the gas phase at T0m) and a much lower T0m of 130.3 °C.14 These results are natural and easy to understand because P2HB has another conformational freedom in the side chain (bond d). The statistical weight matrix Uc of bond c includes conformations of bonds c and d; therefore, fractions of the couples can be calculated as given in

PGA chain is achiral and hence enabled to adopt six conformations: ttt, tts, tg±t, and tg±s. Inasmuch as the latter four have low energies, the Sconf value of PGA is comparatively large (3.15 cal K−1 mol−1 in the gas phase at T0m. Nevertheless, its T0m is 231.4 °C,8 still higher than that of isotactic PLA. According to eq 4, its high T0m would be due to a large ΔHu. This problem will be discussed later. G


Article

Macromolecules Table 9. Configurational Properties of isotactic (S)-P2HB, Evaluated from RIS Calculations energy parameter gas ⟨r ⟩0/nl d[ln⟨r2⟩0]/dT × 103 b (K−1) Sconf c (cal K−1 mol−1) Uconfd (kcal mol−1) 2b

2

medium

DMSO

25.0 °C

130.3 °C

6.44 −5.1 3.15 0.34

4.35 −2.7 3.67 0.52

temp (°C)

gas

gas

25.0 130.3 25.0 130.3

DMSO

gas

25.0 130.3 25.0 130.3

DMSO

130.3 °Ca

4.74 −3.0 3.37 0.33 conformation

t bond b 0.00 0.02 0.01 0.01 bond c 0.80 0.71 0.73 0.67 bond d (side chain) 0.14 0.20 0.18 0.22 bond c (d)

25.0 130.3 25.0 130.3

DMSO

25.0 °C

a

3.77 −1.6 3.74 0.46

g+ (s)

g−

0.98 0.94 0.98 0.95

0.02 0.04 0.01 0.04

0.18 0.24 0.26 0.30

0.02 0.05 0.01 0.03

0.46 0.43 0.45 0.43

0.40 0.37 0.37 0.35

conformation medium gas DMSO

temp (°C)

t(t)

t(g+)

t(g−)

s(t)

s(g+)

s(g−)

g−(t)

g−(g+)

g−(g−)

25.0 130.3 25.0 130.3

0.10 0.12 0.13 0.14

0.37 0.31 0.32 0.28

0.33 0.28 0.28 0.25

0.03 0.05 0.05 0.07

0.08 0.10 0.12 0.13

0.07 0.09 0.09 0.10

0.01 0.03 0.00 0.01

0.01 0.02 0.01 0.02

0.00 0.00 0.00 0.00

The equilibrium melting point.14 bFor x → ∞. From the intercept at x−1 = 0 of the ⟨r2⟩0/nl2 (d[ln⟨r2⟩0]/dT) vs x−1 plot. cFrom eq 2. dFrom eq 5. Relative to the tg+t (g+) conformation.

a

such as isotactic and syndiotactic or include a variety of stereosequences as an atactic chain and, consequently, show its own higher-order structure, spacial configuration, and physical properties. In order to investigate the relationship between configurational properties and stereoregularity of P2HB, its stereosequences were generated according to two kinds of stochastic processes, namely, the Bernoulli trial and the Markov chain, 22,23,36 and subjected to the RIS calculations. The atactic chain can be prepared by Bernoulli trials, in which the (S)- or (R)-unit will appear at a given (S)-ratio (PS) independently of the precedent trial. The (R)-ratio is calculated from PR = 1 − PS. In the Markov chain, the transition probability matrix P is defined as23,36

the lower part of Table 9. The variation in the two conformations renders the P2HB chain flexible, notwithstanding that bond b of (S)-unit ((R)-unit) is almost fixed in the g+ (g−) state. The configurational energy Uconf corresponds to the internal energy difference between in the crystal and in the unperturbed state (melt, amorphous state, and Θ solutions), being calculated from23 Uconf =

RT 2 d(ln Z) x dT

(5)

The positive Uconf means that the crystal conformation is more stable by −Uconf than the unperturbed state. The (S)-PLA and the backbone of (S)-P2HB crystallize in the most stable tg+t conformation,9,10,13 whereas PGA crystallizes in the all-trans structure7 with a higher energy by about 2 kcal mol−1 than tgt. Therefore, the Uconf value of PGA is negative (−1.3 to −2.1 kcal mol−1), and hence the all-trans crystallization seems to be unnatural. This problem will also be discussed later. Dependence of Configurational Properties of P2HB on Stereoregularity. Because of the asymmetrical carbon of P2HB, there is a possibility that the monomer may be selected from either (S)- or (R)-isomer or mixtures of the two. The synthesized polymer, depending on the polymerization method and catalyst, will possess well-defined stereoregularity

where, for example, PSR is the S → R transition probability that an (R)-unit will be attached as the ith monomer to the growing end of an (S)-unit formed in the (i − 1)th trial, and the other transition probabilities are defined similarly. By definition, these probabilities fulfill PSS + PSR = 1 and PRS + PRR = 1. Both extremes, PSS = PRR = 1 (PSR = PRS = 0) and PSS = PRR = 0 (PSR = PRS = 1), correspond to isotacticity and H


Article

Macromolecules Table 10. Configurational Properties of isotactic (S)-PLA, Evaluated from RIS Calculations energy parametera gas 25.0 °C ⟨r ⟩0/nl d[ln⟨r2⟩0]/dT × 103 c (K−1) Sconf d (cal K−1 mol−1) Uconfe (kcal mol−1) 2

2c

medium gas CHCl3

gas CHCl3

temp (°C) 25.0 207 25.0 207 25.0 207 25.0 207

9.01 −3.6 1.17 0.18

CHCl3

207 °Cb

25.0 °C

6.17 7.26 −1.3 −2.7 1.47 1.27 0.30 0.17 conformation t

bond b 0.00 0.00 0.00 0.00 bond c 0.75 0.66 0.71 0.63

207 °Cb 5.49 −1.0 1.53 0.28

g+ (s)f

g−

0.99 0.98 0.99 0.98

0.01 0.02 0.01 0.02

0.24 0.32 0.28 0.35

0.01 0.02 0.01 0.02

Figure 6. Characteristic ratio of the P2HB ensemble of nc = 50 and x = 200 at 25 ◦C as a function of the probability (PS) of (S)monomeric unit, calculated with the gas (○) and DMSO (□) energy sets.

with respect to the vertical line of PS = 0.5. As PS is increased from 0, the ⟨r2⟩0/nl2 ratio decreases and reaches the bottom at PS = 0.5, where ⟨r2⟩0/nl2 = 2.17 (gas) or 2.38 (DMSO). In Figure 7, the characteristic ratio calculated with the Markov process under PSS = PRR = Pmeso (= 1 − Pracemo) is

a

At the MP2/6-311+G(2d,p)//B3LYP/6-311+G(2d,p) level. In the previous paper,23 the RIS calculations with the B3LYP/6-311+G(2d,p) energies that yielded results consistent with the solutions and melt properties of PLA were mainly discussed; however, those from the MP2/6-311+G(2d,p) energies are shown herein so as to be compared with the current data on PGA and P2HB. bThe equilibrium melting point.11,12 cFor x → ∞. From the intercept at x−1 = 0 of the ⟨r2⟩0]/nl2 (d[ln⟨r2⟩0]/dT) vs x−1 plot. dFrom eq 2. Per lactic acid unit (−O−CH(CH3)−C(O)−) . eFrom eq 5. Relative to the tg+t conformation. Per lactic acid unit. fIn the previous paper, the rotational states of bond c were termed t, g+, and g−; however, because the dihedral angle of the g+ state is very close to that of the synperiplanar position, the conformation is designated as synperiplanar (abbreviated as s) herein.

syndiotacticity, respectively. When the intermediate conditions of 0 < PSS < 1 and 0 < PRR < 1 are indicated, the polymeric chain will be arranged with the aid of a random number generation, which can be performed by subroutines such as random_seed and random_number implemented in the FORTRAN compiler. In order to generate random numbers uniformly between zero and unity, it is preferable that the trial should be repeated as many times as possible. If the polymer ensemble is assumed to comprise nc chains of x degree of polymerization, the trial will be repeated x × nc times. The uniformity may be checked by the average of the generated random numbers; if the random numbers are perfectly uniform, the mean value must be the absolute half, 0.500000000.... However, as a result of trial and error, the practical choice was determined as nc = 50 and x = 200 (x × nc = 10000), and the averages were found in a narrow range of 0.495−0.505 (1% margin of error), and the difference in ⟨r2⟩0/nl2 between x = 200 and x → ∞ also stayed within 1%. Therefore, all the RIS calculations to investigated the stereoregularity dependence were carried out with nc = 50 and x = 200. Figure 6 shows the characteristic ratio of poly((R)-2HBran-(S)-2HB) at 25 °C as a function of the (S)-unit fraction, PS (=1 − PR). Both extremes, PS = 0 (PR = 1) and PS = 1 (PR = 0), correspond to isotactic poly((R)-2HB) and poly((S)2HB), respectively. The ⟨r2⟩0/nl2 vs PS curve is symmetrical

Figure 7. Characteristic ratio of the P2HB ensemble of nc = 50 and x = 200 at 25 °C as a function of the meso probability (Pmeso), calculated with the gas (○) and DMSO (□) energy sets under Pmeso = PSS = PRR. For example, Pmeso = 0 corresponds to syndiotacticity and Pmeso = 1 to isotacticity.

plotted as a function of Pmeso. Both ends, Pmeso = 0 and Pmeso = 1, correspond to the perfectly syndiotactic and isotactic chains, respectively. The ⟨r2⟩0/nl2 value is maximized at Pmeso = 1 and decreases considerably toward Pmeso = 0, where ⟨r2⟩0/ nl2 becomes as small as 0.91 (gas) or 1.33 (DMSO). The characteristic ratio smaller than unity seems to be extraordinary. Such a behavior of the ⟨r2⟩0/nl2 vs Pmeso curve was reported for alternating copolymers of L- and D-alanines.37 As Pmeso is decreased, the ⟨r2⟩0/nl2 value decreases and finally reaches a value smaller than unity at Pmeso = 0. The unusually small ⟨r2⟩0/nl2 value results from the alternating symmetry of the preferred conformations; if the L- and D-residues adopt the preferred conformations consistently, a helix of essentially zero pitch is generated. Similarly, in the poly((S)-2HB-alt-(R)2HB) chain, dihedral angles of bonds a−c of the (R)-unit will be opposite in sign to those of the (S)-unit, and, consequently, the chain extent will be reduced considerably. I


Article

Macromolecules In addition, early studies on polymeric sulfur [−S−]x and polymeric selenium [−Se−]x reported such examples.38,39 These polymers are known to have two RISs (±ϕ) in each bond, and the statistical weight matrix of the bond j may be expressed as

Table 11. Comparison between Optimized and Experimental Crystal Structures of PGAa Lattice Constant (Å) experimentalb

optimized a

b

5.154

5.951

c

a

7.032 5.22 ΔLC = 0.0551 (%)c Fractional Coordinates

σ = exp( −ΔEσ /RT )

C C O O H

(8)

with ΔEσ = −0.24 kcal mol−1 for [−S−]x or −0.41 kcal mol−1 for [−Se−]x.20,38,39 The negative ΔEσ indicates the σ value larger than unity and that the alternate (+ϕ, −ϕ) and (−ϕ, +ϕ) pairs occur more frequently than the same (+ϕ, +ϕ) and (−ϕ, −ϕ) couples. For the syndiotactic chain, eq 6 can be rewritten as

x/a

y/b

0.351 0.337 0.201 0.571 0.473

0.250 0.250 0.250 0.250 0.399

z/c

x/a

0.188 0.348 0.523 0.326 0.359 0.194 0.532 0.557 0.181 0.464 ΔCHO = 1.45 × 10−4 d Geometrical Parameters (Å, deg)

C(O)−O O−CH2 CH2−C(O) CO C−H ∠C(O)−O−CH2 ∠O−CH2−C(O) ∠CH2−C(O)−O

The similarity between eqs 7 and 9 indicates that the alternate (S)- and (R)-units render the syndiotactic chain contracted considerably. The alternation of the conformations f requently happens in [−S−]x and [−Se−]x, and that of chiralities always occurs in the syndiotactic P2HB. The RIS calculations here express so-called phantom chains without the excludedvolume effect;17,20 the syndiotactic P2HB chain will be shrunk in molten and amorphous states but nevertheless may be expanded by good solvents and dissolved in them. If the syndiotactic chains should crystallize well so that the (S)-unit faces the (R)-unit of the adjacent chain, the stereocomplex may be formed. Otherwise, they will stay completely amorphous. Periodic Density Functional Calculations on PGA Crystal. As we have shown above, bond b of PGA strongly prefers the gauche conformation. Nevertheless, PGA crystallizes in the all-trans structure,7 which has a higher energy by about 2 kcal mol−1 than tgt. In contrast, (S)-PLA and, probably, (S)-P2HB crystallize in the stable tg+t conformation.9,10,13 In this study, the all-trans PGA crystal underwent structural optimization at the B3LYP-D/6-31G(d,p) level under boundary periodic conditions, and the optimized structure is compared with that determined by X-ray diffraction in Table 11 and illustrated in Figure 8. The differences between the DFT-D calculation and X-ray experiment in lattice constants and atomic fractional coordinates are as slight as ΔLC = 0.0551% and ΔCHO = 1.45 × 10−4, where ΔLC and ΔCHO are defined in the footnotes of Table 11. The fully small differences prove the reliability of both X-ray experiment and DFT-D computations. The crystallographic software PLATON40 did not detect any classical hydrogen bond in the optimized structure but reported a close contact: C−H···O (C−H = 1.09 Å, H···O = 2.41 Å, C···O = 3.4959 Å, and ∠C−H···O = 173°). Our previous studies on polyethers have estimated the interaction energies of such weak C−H···O attractions to be about −1 kcal mol−1.41−47 Therefore, some more attractions would be formed in the all-trans crystal. For example, a short distance of 3.038 Å can also be found between interchain carbonyl Cδ+

c 7.02

experimentalb

optimized

where

b 6.19

1.345 1.433 1.510 1.211 1.091 115.97 107.63 108.84

y/b

z/c

0.250 0.250 0.250 0.250 0.395

0.193 0.521 0.361 0.535 0.195

1.32 1.43 1.51 1.21 114 109 111.5

An orthorhombic cell of space group Pcmn. bBy Chatani et al.7 É1/2 ÅÄÅ 2 2 2Ñ Ñ 1 Åi acalc − aexpt y c zz + ijj bcalc − bexpt yzz + ijj ccalc − cexpt yzz ÑÑÑÑ × 100 (%). ΔLC = 3 ÅÅÅÅjjj a z j z j z Ñ b c k expt { k expt { ÑÑÑÖ ÅÅÅÇk expt { Ä ÉÑ2 ÄÅ ÉÑ2 l oÅÅÅ x ÑÑ Å ÑÑ y 1 x d Å Ñ + ÅÅÅ y ÑÑ + Å Ñ ΔCHO = N ∑atom o − − m ÅÅ b calc o a expt Ñ b expt Ñ ÑÑÖ ÑÑÖ oÅÅÅÇ a calc atom Å Ç n ÄÅ ÉÑ2 |1/2 ÅÅ z ÑÑ o z ÅÅ Ñ o where Natom is the number of atoms in the ÅÅ c calc − c expt ÑÑÑ } o ÅÇ ÑÖ o ~ asymmetric unit. a

()

()

()

()

()

()

and Oδ− atoms. This is probably due to an electrostatic interaction as explained below. The short contacts are depicted by dotted lines in Figure 8. The Born effective charges, which have been accepted as real especially in periodic systems and appropriate for expressing molecular polarizations and dipole moments in crystals,48,49 were also calculated for the PGA crystal (in the unit of e): CH2, + 0.422; CH2, + 0.088; CO, + 1.626; CO, − 1.029; −O−, −1.195. However, the electric charges maintain the neutrality: the sum of the charges is null. The atomic Born charge tensors are written in Table S3 (Supporting Information). The dipole moment (μ⃗mono) per monomeric unit, −O− CH2C(O)−, can be calculated from μ⃗mono =

∑ monomeric unit

⎯⎯⎯→

qm rm

(10)

where qm and r⃗m are the electrical charge and position of atom m, respectively. The dipole moment was obtained as μ⃗mono = (μa, μb, μc) = (±8.180, 0.000, ±10.630) in D, where μa, μb, and μc are the components along the orthogonal a, b, and c axes; therefore, μmono = |μ⃗mono | = 13.413 D, and the μ⃗mono vectors make angles of ±52.42° and ±127.58° with the a axis (see Figure 8). The large dipole moments come from the maldistributed electron density owing to the two electroJ


Article

Macromolecules

Intermolecular Interaction Energy of PGA Crystal. In our previous studies,30,50 the counterpoise (CP) method28,29 to correct for the basis set superposition error (BSSE) of polymer crystals was developed to evaluate interchain interaction energies. Here, the methodology has also been applied to the PGA crystal. The BSSE of a single polymer chain surrounded by ng ghost chains, BSSE(ng), may be written as BSSE(ng ) = E SC{Domain}(ng ) − E SC{SC}

(11)

SC{Domain}

Here E (ng) is the energy of a single chain (SC) positioned at the center of a domain where ng ghost chains are arranged as in the crystal, and ESC{SC} is the energy of the single isolated chain. The curly braces express the extent of basis sets, and the ghost chain is unsubstantial but supplies its basis set. The interchain interaction energy corrected for the BSSE by the CP method, ΔECP, is expressed as

Crystal ji E zy ΔE CP = jjj − E SC{SC}+ Dzzz − BSSE(∞) j Z z (12) k { Crystal where E is the total energy of the crystal cell, Z is the number of repeating units in the cell, and ESC{SC}+D is the SC energy with the dispersion force correction.24,25 The BSSE (∞) may be evaluated from extrapolation (ng → ∞) of the BSSE (ng) vs ng plot. Figure 9 shows the BSSE (ng) vs ng plot. As expected, the magnitude of BSSE (ng) increases with ng but becomes nearly

Figure 9. Basis set superposition error (BSSE) as a function of the number (ng) of ghost chains. The calculated data (●) were fitted by an exponential function, − 9.306 + 9.306 exp(−2.293 ng) (dotted line). Therefore, it follows that BSSE(∞) = −9.31 kcal mol−1.

constant over ng = 12. An exponential function A + B exp (− Cng) (A, B, and C: adjustable parameters) was fitted to the data points, and the A value (−9.31 kcal mol−1) corresponds to BSSE (∞). The (ECrystal/Z − ESC{SC}+D) term of eq 12 was calculated to be −24.78 kcal mol−1; therefore, ΔECP was determined to be −15.47 kcal mol−1. For the sake of comparison, the ΔECP values of other polymers that we have investigated are also listed in Table 12.30,50 Because the repeating units of the polymers are different in chemical species and formula weight, the ΔECP values are recalculated in the units of kcal (mole of skeletal bond)−1 and cal g−1. The poly(methylene oxide) (PMO) chains are packed in either an orthorhombic51 or a trigonal lattice.52−55 In the former crystal, the PMO chain forms a 2/1 helical structure, and in the latter, it adopts a 9/5 helix. The

Figure 8. Crystal structure of PGA, optimized by the DFT-D calculations at the B3LYP-D/6-31G(d,p) level under periodic boundary conditions with a dispersion force correction. The arrows schematically illustrate dipole moments per monomeric unit. The dotted lines express the interchain close contacts of C+0.422−H+0.088··· O−1.195 and CO−1.029···C+1.626(O).

negative oxygen atoms, interact effectively with each other, and lower the enthalpy in the crystal, but counterbalance each other; hence, both electronic charges and dipole moments, if summed up over the crystalline lattice, become null. K


Article

Macromolecules Table 12. Interchain Interaction Energies of Some Polymers, Evaluated from the DFT-D Calculations under the Periodic Boundary Condition interchain interaction energya crystalline polymer PGA nylon 4 nylon-6 PMOf

form α α γ 9/5 helix 2/1 helix

per T0mb (°C)

monomerc

bondd

weighte

231 265 225

−15.47 −17.90 −21.25 −20.50 −3.17 −3.38

−5.16 −3.58 −3.04 −2.93 −1.59 −1.69

−267 −210 −188 −181 −106 −113

206

a

At the B3LYP-D/6-31G(d,p) level. At 0 K. bThe equilibrium melting point. cIn kcal mol−1. dIn kcal (mole of bond)−1. eIn cal g−1. f Poly(methylene oxide).

From the S tensor, Young’s moduli along the a, b, and c axes were evaluated as given in Table 13.76 Of them, the c axis

PMO chain has no well-defined interchain attraction but nevertheless shows a small Sconf value,35,56−58 which leads to a small ΔSu and, consequently, a high T0m of 206 °C.12 The α form of nylons 4 and 6 includes all-trans chains that are bridged by the classical CO···H−N hydrogen bond,59,60 which causes comparatively large negative ΔECP’s and ΔHu’s and, furthermore, high T0m’s.12,61,62 Of the polymers in Table 12, PGA exhibits the largest negative ΔECP (in cal g−1) although it forms no classical hydrogen bond. The all-trans crystallization is probably due mainly to the electrostatic and dipole−dipole attractions and partly to the weak C−H···O hydrogen bond,41−47,63 and these attractions are more effective in the all-trans structure than in the tgt conformation. The stabilization due to such dipole−dipole interactions was also found in the crystal of poly(ethylene sulfide),45,64,65 whose T0m is as high as 216 °C66 (cf. T0m of poly(ethylene oxide) is 68 or 80 °C).66,67 Solid-state 1H NMR experiments on highly drawn PGA fiber have found three phases in the solid PGA:68 rigid crystalline phase with a long relaxation time; semirigid noncrystalline phase (mesophase) with an intermediate relaxation time; highly mobile noncrystalline phase with the shortest relaxation time. Solid-echo 1H NMR and 13C crosspolarization NMR measurements on PGA fibers have also detected three components:69,70 well-oriented, poorly oriented (mesophase), and isotropic amorphous components. It is wellknown that poly(ethylene terephthalate) (PET) also forms the mesophase during crystallization.71−73 Both PGA and PET are forced to crystallize in the unstable all-trans conformation,74 in which favorable interchain interactions are formed: the electrostatic and dipole−dipole attractions of PGA and π−π stacking between the benzene rings of PET. Compared with the most stable conformation, the all-trans structure is as high in energy as about 2 kcal mol−1 (PGA) or 1 kcal mol−1 (PET).75 In the crystallization, the polymeric chains, even if being aggregated densely, partly stay non-all-trans until the interchain attractions are attained. Such noncrystalline states may be observed as the mesophase. Crystalline Modulus. The stiffness (C) and compliance (S) tensors of the PGA crystal at 0 K were calculated at the B3LYP-D/6-31G(d,p) level:

Table 13. Crystalline Moduli of Some Polymer Crystals, Evaluated from Periodic DFT-D Calculationsa polymerb PGA PE nylon 4 nylon 6 PET PMO PBT PTT

form

α α γ 9/5 helix 2/1 helix α

Ea

Eb

Ec

conformation

26.5 10.9 53.6 44.5 25.4 7.2 17.3 13.7 4.8 6.9

29.3 7.8 334 316 120 22.3 17.3 12.0 11.6 18.4

451 333 16.8 19.4 38.1 182 115 82.9 20.8 7.1

all-trans all-trans all-trans all-trans partly distortedc pseudo all-transd all-gauche all-gauche g+g+tg−g− tggt

a

In GPa. At the B3LYP-D/6-31G(d,p) level. At 0 K. Ea, Eb, and Ec are Young’s moduli in the a, b, and c axis directions, respectively. Boldfaced values represent Young’s modulus parallel to or nearly parallel to the chain axis. bAbbreviations: PE, polyethylene; PET, poly(ethylene terephthalate); PBT, poly(butylene terephthalate); PTT, poly(trimethylene terephthalate). cDihedral angles: HN−CH2 = 111.8° and CH2−C(O) = 117.5°.30 dDihedral angle: O−CH2 = 141.9°.77

direction parallel to the molecular axis exhibits a very large modulus of 451 GPa. Figure 10 shows Young’s modulus distribution on the ab plane perpendicular to the molecular axis; the moduli along the a and b axes are 26.5 and 29.3 GPa, respectively. In Table 13, Young’s moduli of other polymers, calculated so far at the same B3LYP-D/6-31G(d,p) level, are also included.30,50,77 The boldfaced value represents the Young’s modulus parallel to or nearly parallel to the molecular axis, and the magnitude can be seen to depend significantly on the crystal conformation. Poly(trimethylene terephthalate) (PTT) lies in a bent conformation (tggt)78,79 and has the smallest Ec of 7.1 GPa, and the α form of poly(butylene terephthalate) (PBT), being forced in a twisted structure of g+g+tg−g−,80−82 exhibits a somewhat small Ec of 20.8 GPa. Poly(methylene oxide) adopts a 9/552−55 (115 GPa) or 2/151 (82.9 GPa) helical structure of all-gauche conformation. Poly(ethylene terephthalate) (PET) with an Ec of 182 GPa lies in a pseudo all-trans state,74,77 and the γ form of nylon-6 lying in a partly distorted structure30,83 has an Eb of 120 GPa. The all-trans chains show much larger moduli: 316 GPa (α L


Article

Macromolecules

being only the difference among the three polymers, is the very origin of all their distinguishing features in higher-order structures and physical properties. This is a true thrill of polymer science.

■

SUMMARY Conformational characteristics of PGA and P2HB have been investigated via MO calculations and NMR experiments on model compounds and compared with those of PLA. All of the three polymers tend to exclusively adopt either a trans− gauche−trans or a trans−gauche−synperiplanar conformation in the C(O)−O−CHR−C(O) bonds of the main chain, and the CH−CH2 bond of the P2HB side chain prefers the gauche conformations. The conformational energies and geometrical parameters derived from the MO calculations on the model compounds at the MP2/6-311+G(2d,p)//B3LYP/6-311+G(2d,p) level were applied to the RIS scheme to yield the configurational properties of the polyesters. The characteristic ratios of PGA, isotactic PLA, and isotactic P2HB at 25 °C were obtained as follows: PGA, 5.31 (in the gas phase) and 5.14 (in DMSO); PLA, 9.01 (gas) and 7.26 (CHCl3); 6.44 (gas) and 4.74 (DMSO). Compared with isotactic PLA, the achiral PGA chain is rather flexible because of the equivalency of the gauche+ and gauche− conformations, and isotactic P2HB is also somewhat flexible owing to another CH−CH2 rotation of the side chain. The P2HB chains including various stereosequences of the (S)- and (R)-monomeric units were generated by the Bernoulli and Markov stochastic processes and subjected to RIS calculations; the characteristic ratio of the completely random atactic copolymer is 2.17 (gas phase) or 2.38 (DMSO), and that of the syndiotactic chain is as small as it can be close to unity: 0.91 (gas phase) or 1.33 (DMSO). The regular alternation of the (S)- and (R)-units renders the syndiotactic chain considerably contracted. The DFT-D calculations at the B3LYP-D/6-31G(d,p) level were carried out under periodic boundary conditions for PGA crystal and accurately reproduced the crystal structure determined by X-ray diffraction. The atomic Born effective charges calculated for the optimized structure show that electrostatic and dipole−dipole interactions compel the PGA chain to crystallize in the intrinsically unstable all-trans structure. The interchain cohesive energy and the Young’s modulus in the chain axis direction were, respectively, evaluated to be −267 cal g−1 and 451 GPa, much larger than those of ordinary polymers. These are reasons why the PGA crystal exhibits the high melting point and extraordinary mechanical strengths.

Figure 10. Young modulus distribution on the ab plane perpendicular to the molecular axis of PGA crystal. The spacing of the grid lines corresponds to 10 GPa.

form of nylon-6); 334 GPa (α form of nylon 4); 333 GPa (polyethylene, PE). Compared with these data, the Ec value of PGA is remarkable. Montes de Oca and Ward84 have theoretically calculated the Ec value of PGA at 0 K using the COMPASS force field85 to be 294 GPa and, furthermore, conducted X-ray diffraction experiments to obtain the Ec values of 77 GPa at 20 °C and 113 GPa at −50 °C. The underestimates of the X-ray method were suggested to be due to the hypothesis employed there, that is, the homogeneous stress assumption that both amorphous and crystalline phases undergo the same stress. Lee et al.86 have also estimated the Ec values of PGA by X-ray diffraction on the homogeneous stress assumption to be 104 GPa at 300 K and 145 GPa at 13 K, and the lateral moduli perpendicular to the chain axis at 300 K were obtained as 7.3 and 5.8 GPa from the (110) and (020) reflections, respectively. They suggested that the PGA skeleton would not be fully extended but possess a contracted conformation in the crystal and yield the Ec value smaller than that of PE. The flexural strength of PGA was estimated to be approximately 200 MPa, double that of PET, about 1.6 times as much as that of nylon-6, and somewhat larger than that of poly[ether ether ketone] (PEEK).3 Because the crystalline modulus along the chain axis at 0 K is the ultimate stiffness that the polymer can exhibit, the Ec value of PGA at 0 K must be larger than those of PET, nylon-6, and PEEK. The structural optimization here gave the all-trans extended structure consistent with that determined by Chatani et al.7 Therefore, the present value of 451 GPa should be acceptable. As has been shown above, supported by the electrostatic and dipole−dipole interactions, the PGA chain crystallizes in the all-trans structure7 and shows the superior thermal and mechanical properties, even though the all-trans conformation is in itself an unstable state for the isolated PGA chain. In contrast, isotactic PLA and P2HB are allowed to adopt their inherently stable tg+t conformation ((S)-isomer) even in the crystal,9,10,13 and equimolar mixtures of all (S)- and (R)chains of PLA and P2HB can form the stereocomplexes,13,15 which exhibit melting points higher than the homopolymers. The side-chain length, namely, whether H, CH3, or C2H5,

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METHODS

Materials. MAA-13C.87,88 Acetyl-1-13C chloride (1.0 g, 12.6 mmol) was added to methyl 2-hydroxyacetate (1.14 g, 12.6 mmol) under nitrogen atmosphere. The solution was stirred at room temperature for 1 h, heated gradually up to 120 °C, and kept there for 2 h. The reaction mixture was thrice washed with saturated saline solution, and the separated organic layer was identified by 1H and 13C NMR as MAA-13C (yield, 0.40 g, 24%). MAB-13C.89 A mixture of (S)- and (R)-2-chlorobutanoic acids (5.13 g, 41.9 mmol) was stirred at 60 °C for 15 min, and sodium hydroxide solution (6.29 mol L−1, about 12.7 g) was added so that the pH value of the solution would stay between 7 and 9. After being cooled to room temperature and kept nearly neutral, the solution was condensed on a rotary evaporator. M


Article

Macromolecules

The crystal structure determined by X-ray diffraction7 was set initially and optimized under the following conditions: DFT, B3LYP combined with Grimme’s dispersion force expression (B3LYPD)24,25 and Milani’s parameters;93 basis set, 6-31G(d,p); space group, Pcmn; self-consistent field (SCF) convergence threshold, 10−8; truncation criteria for bielectronic integrals, 10−7, 10−7, 10−7, 10−7, and 10−14; integration grid, 75 radial and 974 angular points; Fock/ Kohn−Sham matrix mixing, 80%; shrinking factor, 4; using the modified Broyden method. The Born effective charge tensors were derived from the frequency calculations.94,95 The stiffness and compliance tensors were calculated with the ELASTCON routine96,97 implemented in the CRYSTAL14 program under a rigid threshold (10−8) for the SCF convergence. The number of points to derive the numerical second derivative was 5, and the strain-step size was 0.005.

The residue (2-hydroxybutanoic acid) as unpurified was dissolved in methanol (11.1 g, 0.35 mol) and sulfuric acid (0.06 g), heated up to 80 °C, and kept there for 2 h. The reaction mixture was cooled to room temperature, mixed with sodium carbonate (0.04 g, 0.38 mmol), stirred for 10 min, and evaporated. The residue was confirmed by 1H NMR to be methyl 2-hydroxybutanoate. Acetyl-1-13C chloride (1.0 g, 12.6 mmol) was added to the methyl 2-hydroxybutanoate prepared as above (1.47 g, 12.4 mmol), stirred at room temperature for 1 h, heated up to 120 °C, and kept there for 2 h. The reaction mixture was washed thrice with saturated saline solution, and the extracted organic layer was identified by 1H and 13C NMR as MAB-13C (yield 1.31 g). NMR. The model compounds were dissolved at about 500 mM in each deuterated solvent (C6D12, CDCl3, CD3OD, (CD3)2SO, or D2O) and put in a 5 mm NMR tube. 1H (13C) NMR spectra were measured at 500 (125) MHz on a JEOL JNM-ECA500 spectrometer equipped with a variable temperature control unit in the Center for Analytical Instrumentation of Chiba University. The typical measurement conditions were as follows: scan, 32 (64); 90° pulse width, 12 (10) μs; acquisition time, 7.0 (3.5) s; recycle delay, 1.0 (2.0) s; temperature range, from 15 or 25 °C to 45 or 55 °C; temperature interval, 10 °C. Here, the parenthesized values represent the 13C NMR conditions. The free induction decay was fully zero-filled prior to the Fourier transform so as to yield sufficient digital resolution for the gNMR spectrum simulation,90 from which chemical shifts and coupling constants were derived. Molecular Orbital Calculations. Molecular orbital calculations on the model compounds were carried out with the Gaussian09 program91 on a HITACHI SR1600 computer installed in The Institute of Management and Information Technologies of Chiba University or an HPC 5000-XBW216TS-Silent computer in our laboratory. For each conformer, the molecular geometry was fully optimized at the B3LYP/6-311+G(2d,p) level, and the frequency calculation at the same level yielded thermochemical data. For each optimized geometry, the single-point calculation was conducted at the MP2/6-311+G(2d,p) level. From the MP2 electronic energy and B3LYP thermochemical term, the internal energy relative to a reference conformer was evaluated and adopted as the conformational energy, being expressed herein as ΔEk (k, conformer). The solvent effect on the electronic energy was evaluated by the integral equation formalism of the polarizable continuum (IEF-PC) model.92 In most of our previous studies, we have evaluated conformational energies of polymers from Gibbs free energies of their small model compounds. This is because the conformational equilibrium depends on differences in free energy between conformations. However, when we treated model compounds with bulky substituents or large polarizations, the Gibbs energies occasionally exhibited unnatural values. In the MO calculation, the Gibbs energy is derived from the electronic and thermochemical energies. The latter includes the entropy term calculated from molecular vibrational frequencies. Because the vibrational motions are influenced by the bulkiness, polarity, and chain length, the Gibbs energy may sometimes be perturbed by such molecular characteristics. The molecular-size effect on the Gibbs energy, namely, the dependence on whether the used model is monomeric, dimeric, or trimeric, was found for PLA models;23 therefore, in this study, the conformational energies were derived from the internal energies (without the entropy term). Although the internal energy includes the vibrational one, the conformational energy obtained therefrom depends less on the molecular size. According to our experiences, differences in internal energy between conformations (relative internal energies, ΔEk’s) are usually very close to those (ΔGk’s) in free energy. In Table S4 (Supporting Information), internal energies of major conformations of the monomeric and dimeric models for P2HB are compared. It can be seen from the table that both models give similar energies within allowable tolerances. Density Functional Theory Calculations under Periodic Boundary Conditions. Periodic density functional theory (DFT) calculations on PGA crystal were conducted using the CRYSTAL14 program26,27 installed in an HPC 5000-XBW216TS-Silent computer.

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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.9b00459.

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Formulation A, statistical weight matrices of PGA; formulation B, statistical weight matrices of P2HB; Table S1, geometrical parameters of PGA; Table S2, geometrical parameters of (S)-monomeric unit of P2HB; Table S3, atomic Born charge tensors of PGA crystal; and Table S4, internal energies of representative (stable) conformers of (S)-MAB and (S,S)-MOAB (PDF)

AUTHOR INFORMATION

Corresponding Author

*(Y.S.) E-mail: [email protected]. Telephone: +81 (0)43 290 3394. Fax: +81 (0)43 290 3394. ORCID

Yuji Sasanuma: 0000-0003-0374-0621 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was partially supported by a Grant-in-Aid for Scientific Research (C) (16K05906) from the Japan Society for the Promotion of Science.

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REFERENCES

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