Molecular Design of Aromatic Polythionoesters.

As an example of molecular design of new polymers, structures and properties of poly(ethylene thionoterephthalate) (PET[S2]) and the related polymers have been predicted from calculations of ab initio molecular orbital (MO) theory, rotational isomeric state (RIS) scheme, and periodic density functional theory (DFT). The MO calculations were confirmed by NMR experiments and introduced to the RIS scheme for PET[S2] to yield its configurational properties, which are compared herein with those of analogous polyester, polythioester, and polydithioester. Configurational properties of randomly thiono-substituted poly(ethylene terephthalate) (PET), PET[S z O1-z ], were also evaluated as a function of sulfidity (z). On the assumption that the crystal of PET[S2] can be expressed as an isomorphic replacement of the PET crystal, the crystal structure was optimized by a periodic DFT simulation and its Young's moduli in the a-, b-, and c-axis directions were, respectively, evaluated to be Ea = 0.94(7.20) GPa, E b = 19.58(22.26) GPa, and E c = 142.1(182.4) GPa, where the parenthetic values are those of the PET crystal. There is a possibility that properties of PET[S z O1-z ] will be controlled between those of PET and PET[S2] by adjusting the sulfidity. The potential practical applications of the polythionoesters are also discussed herein. By purely theoretical computations, the structures and properties of the not-yet synthesized polymers were predicted quantitatively; that is, the theoretical molecular design of new polymers has been achieved.

Introduction

When the primary structure (constituent atoms and chemical bonds) of a new polymer is suggested, if one could predict its higher-order structures and physical properties, it would be considered to be a molecular design.[1] The present study has aimed at the realization of such a molecular design.

In previous studies, we investigated conformational characteristics and structure–property relationships of aromatic polyester and polythioesters expressed by chemical formulae given in Figure : X = Y = O, poly(ethylene terephthalate) (PET);[2] X = O and Y = S, poly(ethylene dithioterephthalate) (PETS2);[3−5] X = Y = S, poly(ethylene tetrathioterephthalate) (PETS4).[3−5] In Table , their conformational characteristics and configurational properties are summarized. These polymers, because of lack in side-chain motions, that is, poor in entropic advantages, are hardly soluble in common organic solvents. PETS2 in particular is insoluble in any solvent and decomposed at 346 °C without melting.[3] This is because its S–CH2–CH2–S spacer mostly lies in extremely stable conformations (g±tg∓) in both solid and liquid phases, where t, g+, and g– represent trans, gauche+, and gauche- conformations, respectively (for the Newman projections, see Figure ). This nature can be seen from the small configurational entropy (Sconf) and large characteristic ratio (⟨r2⟩0 /nl2) (Table ). Therefore, the rigid polythioester, even if melted or dissolved, would not acquire sufficient thermodynamic (entropic) benefit. PETS2 can be prepared by polycondensation of terephthaloyl dichloride and ethanedithiol (Scheme a), whereas PETS4 was difficult to synthesize (Scheme b). The monomer, tetrathioterephthalic acid protected with piperidinium reacts as it is with 1,2-dibromoethane to yield PETS4, which is decomposed at 220 °C.[3]

Figure 1

Polyester (X = Y = O, PET), polythioester (X = O and Y = S, PETS2), polydithioester (X = Y = S, PETS4), and polythionoester (X = S and Y = O, PET[S2]) with terephthaloyl or thionoterephthaloyl and ethylene groups. The Y–CH2–CH2–Y part is termed “spacer” herein. Poly(ester-thionoester) (X1 = O, X2 = S and Y = O, PET[SO]) and randomly thiono-substituted PET, PET[SO1–] (z, sulfidity), have also been treated here.

Table 1

Summary of Conformational Characteristics and Configurational Properties of Aromatic Polythionoester, Polyester, Polythioester, and Polydithioester with C(X)–Y–CH2–CH2–Y–C(X) Parta

	PET[S2]b	PETb	PETS2c	PETS4c
the most stable conformation in free state	tg±t	tg±t (∼tg±g±)	g±tg∓	g±tg∓
crystal conformation of model	ttt	ttt	g±tg∓	g±tg∓
number of states around benzene ring	2d	2d	2d	6e
⟨r2⟩0/nl2	2.05	2.47	16.7	5.20
dln⟨r2⟩0 /dT × 103 (K–1)	0.63	0.42	–4.83	0.35
Sconf (cal K–1 mol–1)	5.02	7.13	4.87	8.87
Uconf (kcal mol–1)	–1.84	–1.02	0.44	0.29

In a benzene environment (dielectric constant = 2.27) at 25 °C. See Figure .

From free energies at the MP2/6-311++G(3df,3pd)//B3LYP/6-311+G(2d,p) level.

From free energies at the MP2/6-311+G(2d,p)//B3LYP/6-311+G(2d,p) level.[3−5]

cis and trans.[3−5]

trans–trans, (trans–cis)±, (cis–trans)±, and cis–cis.[5]

Figure 10

Rotamers around the (a) O–CH2 and (b) CH2–CH2 bonds with definition of the coefficients (vicinal coupling constants) used in eqs , 7, and 8.

Scheme 1

Synthesis of (a) PETS2 and (b) PETS4. Adapted from refs (3) and (4) with Permission from The Royal Society of Chemistry

There are four possible combinations to position oxygen and sulfur at the X and Y sites. Of them, this study has dealt with the remaining polythionoester (X = S and Y = O, see Figure ); the polythionoester with the O–CH2–CH2–O sequence, being represented as PET[S2] herein, must also be difficult to synthesize, because a thione-thiol rearrangement will readily change the −C6H4–C(=S)–O– part to −C6H4–C(=O)–S–.[6−10] However, a SciFinder search for O,O-diphenyl benzene-1,4-bis(carbothioate) (C6H5–O–C(=S)–C6H4–C(=S)–O–C6H5)[11] gave a list of relevant studies, in which the thionoester was mostly prepared with Lawesson’s reagent[12] from diphenyl terephthalate. Therefore, it may be possible to prepare PET[S2] from PET using Lawesson’s reagent, Belleau’s reagent,[13] or a P4S10-pyridine complex.[14] Unfortunately, PET is insoluble in common thionation solvents, such as toluene, benzene, xylene, acetonitrile, and dimethyl sulfone. Therefore, solvent-free reactions using, for example, microwave heating may be usable for the thionation.[15,16] In actual fact, as illustrated in Scheme , a model compound of PET[S2], O,O’-(ethane-1,2-diyl)dibenzothioate (designated as model SS herein), was prepared by microwave radiation from ethylene glycol dibenzoate (EGDB), a model for PET;[17] however, the yield was very low (0.9%) and the major product (yield, 23%) was the mono-sulfurated compound, 2-((phenylcarbonothioyl)oxy)ethyl benzoate (termed model SO). Because of these experimental facts, the microwave heating would not provide fully sulfurated PET[S2] but partially, moreover, randomly sulfurated PET[SO1–] (z, sulfidity, 0 ≤ z ≤ 1).

Figure 2

Polythionoester (X1 = X2 = S, PET[S2]), poly(ester-thionoester) (X1 = O and X2 = S, PET[SO]), and polyester (X1 = X2 = O, PET), and randomly thiono-substituted PET, PET[SO1–] (z, sulfidity). The bonds are designated as indicated.

Scheme 2

Model Compounds Used in MO Calculations and NMR Experiments, Prepared by Microwave Heating from (a) Ethylene glycol dibenzoate-13C (EGDB-13C):[17] (b) 2-(Benzenecarbothioyloxy)ethyl benzenecarbothioate-13C (model SS-13C); Mono-sulfurated 2-(Benzenecarbothioyloxy)ethyl benzoate-13C ((c) Model SO-S-13C and (d) Model SO-O-13C)

The bonds are numbered so as to be consistent with those of polymers (Figure ). The concepts of (c) forward and (d) backward directions were employed in the rotational isomeric state (RIS) calculations on PET[SO1–] (See the Section “RIS calculation”).

As mentioned at the beginning, this study has aimed at the molecular design of new polymers; the objects are three polythionoesters: (1) PET[S2]; (2) PET[SO] in which −C(=S)– and −C(=O)– groups are arranged alternately; (3) PET[SO1–] in which −C(=S)– and −C(=O)– appear randomly. Conformational characteristics of PET[S2] and PET[SO] have been investigated via molecular orbital (MO) calculations and NMR experiments on models SS and SO, respectively. Configurational properties of PET[SO1–], including PET[S2] (z = 1) and PET (z = 0), have been evaluated as a function of z from the rotational isomeric state (RIS) calculations[18−20] with the Bernoulli trial.[21,22] Preliminary to the present study, crystal structures of models SS and SO were determined by single-crystal X-ray diffraction[17] and both molecules were found to lie in all-trans conformations. It was earlier found that PET[23] and its model, EGDB,[24] also crystallize in all-trans structures. On the basis of these facts, crystal structures of PET[S2] and PET[SO] were predicted via simulations of density functional theory (DFT) under periodic boundary conditions[25,26] and crystalline moduli were evaluated for the optimized structures.

Herein, the conformational characteristics, configurational properties, crystal structures, and physical properties of PET, PET[S2], PET[SO1–], PETS2, and PETS4 are compared with each other and the effects of oxygen and sulfur positioned at the X and Y sites on the structures and properties and, furthermore, potential practical applications of the not-yet synthesized polythionoesters are discussed to adduce evidence of the molecular design.

Results and Discussion

MO Calculations

Table lists Gibbs free energies of model SS, model SO, and EGDB. In model SS, the tg±t conformations are the most stable followed by tg±g± and g±g±g±, and all conformers including g±g∓ (so-called the pentane-effect-like)[18] sequences are missing. Model SO has six major conformers (tg±t, tg±g±, and tg±g∓), whose ΔG values are close to each other. Its g±g±t and g±g±g± conformers also show negative ΔG’s, and no g±g∓ pairs appear in bonds 5 and 6. For EGDB, most stable tg±t and tg±g± conformers have similar ΔG values. However, its ΔG’s shown in Table are a little different from our previous ΔG’s calculated at the MP2/6-311+G(2d,p)//B3LYP/6-311+G(2d,p) level[2] because the current study has employed a larger basis set of 6-311++G(3df,3pd) in the MP2 single-point calculations.

Table 2

Conformational Free Energies of Model SS, Model SO, and EGDBa

	spacer bond				ΔGk (kcal mol–1)
k	5	6	7	Mkb	gas	benzene	DMSOc
model SS and PET[S2]
1	t	t	t	1	0.00	0.00	0.00
2	t	t	g+	4	0.47	0.50	0.49
3	t	g+	t	2	–2.07	–2.26	–2.47
4	t	g+	g+	4	–1.13	–1.27	–1.52
5	t	g+	g–	4
6	g+	t	g+	2
7	g+	t	g–	2	–0.12	0.08	0.40
8	g+	g+	g+	2	–1.05	–0.94	–0.74
9	g+	g+	g–	4
10	g+	g–	g+	2
		cisd			0.03	0.02	–0.04
model SO and PET[SO]
1	t	t	t	1	0.00	0.00	0.00
2	t	t	g+	2	0.02	0.09	0.12
3	t	g+	t	2	–1.38	–1.58	–1.81
4	t	g+	g+	2	–1.42	–1.52	–1.72
5	t	g+	g–	2	–1.61	–1.67	–1.82
6	g+	t	t	2	0.75	0.79	0.77
7	g+	t	g+	2	2.70	2.86	2.94
8	g+	t	g–	2	0.34	0.58	0.91
9	g+	g+	t	2	–0.71	–0.84	–1.10
10	g+	g+	g+	2	–0.82	–0.69	–0.50
11	g+	g+	g–	2
12	g+	g–	t	2
13	g+	g–	g+	2
14	g+	g–	g–	2
		cisd			0.12	0.12	0.07
EGDB and PET
1	t	t	t	1	0.00	0.00	0.00
2	t	t	g+	4	0.33	0.42	0.44
3	t	g+	t	2	–1.10	–1.29	–1.58
4	t	g+	g+	4	–1.17	–1.26	–1.49
5	t	g+	g–	4	–0.80	–0.94	–1.16
6	g+	t	g+	2	0.86	0.94	0.74
7	g+	t	g–	2	0.05	0.34	0.66
8	g+	g+	g+	2	–1.20	–1.03	–0.84
9	g+	g+	g–	4	–0.89	–0.94	–1.20
10	g+	g–	g+	2
		cisd			0.08	0.06	0.03

At the MP2/6-311++G(3df,3pd)//B3LYP/6-311+G(2d,p) level; relative to ΔG of the all-trans conformation. The blank line represents the absence of the conformation.

Multiplicity.

Dimethyl sulfoxide.

Calculated for model compounds shown in Figure . Relative to ΔG of the trans orientation around the benzene ring.

Figure 3

(a) Trans and (b) cis orientations between C=X1 and C=X2 groups around the benzene ring. The model compounds are termed model S–Bz–S (X1 = X2 = S), model S–Bz–O (X1 = S (O) and X2 = O (S)), and model O–Bz–O (X1 = X2 = O).

From the ΔG values, bond conformations of the three model compounds were calculated and only trans fractions (pt’s) are given in Table because the gauche fractions can be readily derived from pg+ = pg– = (1 – pt)/2. The pt value around the C(=S)O–CH2 bond of model SS (model SO) ranges from 0.71(0.80) to 0.83(0.88), where the data on model SO are bracketed. The CH2–OC(=O) bond of EGDB (model SO) shows the pt values of 0.39–0.47(0.31–0.40). On the other hand, all three models exhibit marked gauche preferences (pt = 0.02–0.07) in the central CH2–CH2 bonds, whose pt values tend to decrease with solvent polarity because all conformers with gauche CH2–CH2 bonds except g±g±g± become still more stable in polar media.

Table 3

Trans Fractions of Model Compounds and the Corresponding Polymersa

		X1 = X2 = S bond			X1 = O, X2 = S bond				X1 = X2 = Ob bond
medium	temp (°C)	3 (b)	5 (d)	6 (e)	3 (b)	5 (d)	6 (e)	7 (f)	3 (b)	5 (d)	6 (e)
NMR Expt
C6D6	15		0.69	0.05		0.70	0.06	0.44		0.45	0.03
	25		0.69	0.05		0.70	0.06	0.44		0.44	0.04
	35		0.69	0.05		0.69	0.07	0.44		0.43	0.05
	45		0.70	0.07		0.69	0.08	0.44		0.42	0.05
	55		0.70	0.07		0.69	0.08	0.44		0.42	0.06
CDCl3	15		0.71	0.05		0.71	0.06	0.42
	25		0.71	0.05		0.70	0.06	0.43
	35		0.71	0.06		0.70	0.07	0.43
	45		0.71	0.06		0.70	0.07	0.44
	55		0.71	0.06		0.70	0.09	0.44
DMSO-d6	25		0.69	0.02		0.70	0.04	0.46		0.45	0.02
	35		0.68	0.02		0.70	0.04	0.46		0.45	0.02
	45		0.66	0.02		0.70	0.05	0.46		0.44	0.03
	55		0.66	0.03		0.70	0.05	0.46		0.42	0.04
MOc and RIS Calc
gas	15	0.51	0.75	0.04	0.55	0.83	0.05	0.31	0.53	0.39	0.05
	25	0.51	0.74	0.05	0.55	0.82	0.05	0.31	0.53	0.39	0.06
	35	0.51	0.73	0.05	0.55	0.82	0.05	0.32	0.53	0.39	0.06
	45	0.51	0.72	0.06	0.55	0.81	0.06	0.32	0.53	0.39	0.07
	55	0.51	0.71	0.06	0.55	0.80	0.06	0.32	0.53	0.39	0.07
benzene	15	0.50	0.80	0.03	0.54	0.86	0.03	0.36	0.53	0.44	0.04
	25	0.50	0.79	0.03	0.54	0.85	0.04	0.36	0.53	0.43	0.04
	35	0.50	0.78	0.04	0.54	0.84	0.04	0.36	0.53	0.43	0.05
	45	0.50	0.77	0.04	0.54	0.84	0.04	0.36	0.52	0.43	0.05
	55	0.50	0.76	0.04	0.54	0.83	0.05	0.36	0.52	0.43	0.05
DMSO	25	0.51	0.83	0.02	0.55	0.88	0.02	0.40	0.51	0.47	0.03
	35	0.51	0.82	0.02	0.55	0.87	0.03	0.40	0.51	0.47	0.03
	45	0.51	0.80	0.03	0.55	0.86	0.03	0.40	0.51	0.46	0.03
	55	0.51	0.79	0.03	0.54	0.85	0.03	0.40	0.51	0.46	0.04

For the molecular structures and bond designations, see Figure .

The NMR data on EGDB-13C (X1 = X2 = O) are quoted from our previous paper.[2]

At the MP2/6-311++G(3df,3pd)//B3LYP/6-311+G(2d,p) level.

Figure illustrates trans and cis orientations between two C=X (X = S or O) groups bonded to the same benzene ring. Compared with the cis orientation, the trans state is, in principle, only slightly more stable, but the ΔGcis values are so small (less than 0.1 kcal mol–1) that both orientations are almost equally populated (pt = 0.50–0.55).

In our previous study on poly(ethylene oxide) (PEO, [−CH2–CH2–O−]) and poly(ethylene sulfide) (PES, [−CH2–CH2–S−]),[27] the natural bond orbital (NBO) analysis[28,29] was carried out and their conformational characteristics were interpreted in terms of vicinal bond–antibond (σ → σ*) and lone pair–antibond (n → σ*) interactions. As a result, it was found that the central CH2–CH2 bonds of both O–CH2–CH2–O and S–CH2–CH2–S parts essentially possess gauche preferences due to the σC–H → σC–X* (X = O or S) interaction. However, the steric repulsion between sulfur atoms of the S–CH2–CH2–S part forces the CH2–CH2 bond into the trans conformation. The sums of the σ → σ* and n → σ* stabilization energies of the ttt and ttg± conformations were estimated to be in the order of ttt > ttg± (O–CH2–CH2–O) or ttt < ttg± (S–CH2–CH2–S). Consequently, tg±t are more stable than ttt and ttg± in O–CH2–CH2–O, whereas g±tg± and g±tg∓ are dominant over ttt in S–CH2–CH2–S. In addition, the interaction between dipole moments formed in the C–S–C bonds stabilizes g±tg∓ more than g±tg±. For all of the above reasons, the tg±t conformations are the most stable in O–CH2–CH2–O’s of PET, PET[S2], and PEO and g±tg∓ has the lowest free energy in S–CH2–CH2–S’s of PETS2, PETS4, and PES.

NMR Experiment

Figure shows 1H and 13C NMR spectra observed from models SS and SS-13C along with the corresponding simulations, which yielded vicinal coupling constants, 3JC(S)H, 3JHH, and 3JHH′ (see Table ). In Figure , measured NMR spectra of models SO, SO–S-13C, and SO-O-13C are compared with the simulations, from which four vicinal coupling constants 3JC(S)H, 3JC(O)H, 3JHH, and 3JHH′ were obtained as in Table . Here, 3JC(X)H represents the vicinal 13C–1H coupling through the 13C(=X)–O–CH2 (X = S or O) bond sequence.

Figure 4

Observed (above) and calculated (below) NMR spectra of model SS: 1H NMR satellite spectra of CH2 protons of (a) model SS and (b) model SS-13C; (c) 13C NMR spectra of 13C=S carbon of model SS-13C. For the molecular structure of model SS-13C, see Scheme .

Table 4

Observed Vicinal 1H–1H and 13C–1H Coupling Constants of Model Compoundsa

solvent	temp (°C)	3JHH	3JHH′	3JC(S)H	3JC(O)H
Models SS and SS-13C
C6D6	15	6.46	2.65	3.08
	25	6.52	2.76	3.08
	35	6.52	2.76	3.08
	45	6.55	2.89	3.05
	55	6.55	2.89	3.05
CDCl3	15	6.40	2.70	3.01
	25	6.40	2.70	3.01
	35	6.45	2.75	3.00
	45	6.45	2.75	3.00
	55	6.45	2.75	3.00
DMSO-d6	25	6.29	2.29	3.10
	35	6.30	2.30	3.15
	45	6.37	2.30	3.22
	55	6.41	2.45	3.24
Models SO, SO-S-13C, and SO-O-13C
C6D6	15	6.57	2.79	3.04	3.04
	25	6.57	2.79	3.05	3.05
	35	6.48	2.89	3.06	3.07
	45	6.48	2.99	3.07	3.07
	55	6.48	3.06	3.07	3.07
CDCl3	15	6.57	2.86	2.99	3.11
	25	6.55	2.85	3.03	3.08
	35	6.52	2.94	3.03	3.08
	45	6.52	2.98	3.05	3.05
	55	6.48	3.12	3.05	3.04
DMSO-d6	25	6.45	2.56	3.04	3.00
	35	6.45	2.56	3.04	2.99
	45	6.47	2.68	3.05	2.99
	55	6.47	2.68	3.05	2.99

In Hz.

Figure 5

Observed (above) and calculated (below) NMR spectra of model SO: 1H NMR spectra of HA and HA′ protons of (a) model SO and (b) model SO–13C; (c) 13C NMR spectra of 13C=S carbon of model SO-S-13C; 1H NMR spectra of HB and HB′ protons of (d) model SO and (e) model SO–13C; (f) 13C NMR spectra of 13C=O carbon of model SO-O-13C. Model SO-13C is a mixture of model SO-S-13C and model SO-O-13C. For the molecular structures of the models, see Scheme .

According to the procedures described in the section “NMR Experiment and Analysis”, the bond conformations of the spacers of models SS and SO were derived from the vicinal coupling constants and the obtained pt values are given for the individual solvents and temperatures in Table . The pt values of the CH2–CH2 bonds of all models are in exact agreement with the MO data, and those for C(=X)O–CH2 bonds are also consistent with the MO calculations.

It has been well established that conformational characteristics of polymers depend on relatively short-range intramolecular interactions between atoms or groups separated by up to several bonds and that configurational properties of a given polymer in the unperturbed state (without the excluded-volume effect) will be evaluated from RIS calculations using the short-range intramolecular interaction energies that can be derived from small model compounds with the same bond sequences as those the polymer includes.[18,19] It has been proven above that the MO energies of model SS, model SO, and EGDB are reliable enough to be applied to the RIS calculations on PET[S2], PET[SO1–], and PET.

Configurational Properties of PET[S2]

In Table , configurational properties of PET[S2] are compared with those of PET, PETS2, and PETS4. Of them, PET[S2] and PET have the O–CH2–CH2–O spacer, in which the tg±t conformations are the lowest in ΔG (Table ): PET[S2], −2.1 to −2.5 kcal mol–1; PET, −1.1 to −1,6 kcal mol–1. Nevertheless, model SS,[17] EGDB,[24] and PET[23] crystallize in all-trans conformations. The S–CH2–CH2–S spacers of PETS2 and PETS4 are most stabilized in g±tg∓ conformations,[3,4] which are also crystal conformations of these two polythioesters and their model compounds.[30,31] The marked g±tg∓ stability of PETS2 results in a large 0/nl2 of 16.7 and a small Sconf of 4.87 cal K–1 mol–1. This is the reason why its melting point would be higher than the decomposition temperature of 346 °C.[3] Around the benzene ring (virtual bond), PET[S2], PET, and PETS2 adopt either trans or cis orientation coplanar with the benzene plane, whereas PETS4 is forced by steric hindrance between sulfur atoms to lie in one of six out-of-plane orientations with similar free energies, and the orientational flexibility, namely, quasi-free rotation around the benzene ring leads to a large Sconf of 8.9 cal K–1 mol–1.

Dependence of Configurational Properties of PET[SO1–] on Sulfidity

In Figure , the characteristic ratio (⟨r2⟩0 /nl2) and its temperature coefficient (dln⟨r2⟩0/dT) and configurational entropy (Sconf) of PET[SO1–] are plotted against the sulfidity (z). Both ends, z = 0 and 1, correspond to pure homopolymers, PET and PET[S2], respectively. The ⟨r2⟩0/nl2 value monotonously decreases with increasing z. The chain dimension was calculated with a virtual bond (bond b) (Figure ), thus being comparable only with those of polymers including a benzene ring in the repeating unit, such as PET, PET[S2], PETS2, and PET4. The configurational entropy markedly decreases as z increases. This can be explained as follows: the spacer of PET is allowed to adopt a number of conformations with similar ΔG’s, such as tg±t, tg±g±, tg±g∓, g±g±g±, and g±g±g∓, whereas PET[S2] falls in two very stable states, tg±t (Table ) and hence its degree of conformational freedom is restricted, which results in the small Sconf value and, furthermore, suggests its high equilibrium melting point[32] and poor solubility.

Figure 6

(a) Characteristic ratio (⟨r2⟩0 /nl2), (b) its temperature coefficient (dln0/dT), and (c) configurational entropy (Sconf) of PET[SO1–] at 25 °C as a function of sulfidity (z), calculated by the RIS scheme with different Gibbs free energies: circle, gas; square, benzene; triangle; DMSO. z = 1 corresponds to PET[S2], and z = 0 to PET.

On the other hand, the temperature coefficient tends to increase with z. The dln⟨r2⟩0/dT value was found to be related to the rubberlike property as[33−39]where f is the tension (f) of a given elastomer and composed of two terms due to internal-energy (U) and entropy (S) changeswhereandwith T, V, and L being the absolute temperature, volume, and length, respectively. Therefore, a large positive Tdln0/dT value, that is, a significantly positive f/f suggests that the polymer may behave like a rubber because f is always positive. The energy term (fU) reinforces the entropic elasticity (fS). As the polymeric chain is extended (ΔL > 0), the conformational distribution will be shifted from the stable tg±t conformations to, for example, a unstable and extended ttt state (ΔU > 0); thus, ΔU/ΔL ≈ (∂U/∂L) = f > 0. The nature is reflected by a positive dln0/dT. The PET[S2] chain shows an fU/f value of 0.19, which is comparable to those of cis-1,4-polybutadiene (0.10–0.17), polydimethylsiloxane (0.13–0.30), and natural rubber (0.12–0.18).[22,36] It is also suggested that even PET, if it forms a completely amorphous network, has a comparatively large f/f value of 0.13. Therefore, it is expected that the amorphous PET[SO1–] network would become more elastic with increasing sulfidity. In a polar environment, however, this effect may be weakened as the DMSO data indicate (Figure b).

Periodic DFT Calculation

Preliminary to the current study, we determined crystal structures of models SS and SO by X-ray diffraction.[17]Figure shows the two crystallized molecules, together with EGDB.[24] As shown in Table , in the gas phase and solutions, the tg±t states of model SS, model SO, and EGDB are much lower in free energy than ttt, but nevertheless, all three models crystallize in all-trans conformations. The crystallized PET chain also lies in an all-trans conformation, being packed in a triclinic lattice of space group P1̅.[23] On the basis of the above facts, we have made a hypothesis that the crystal structure of PET[S2] corresponds to an isomorphic replacement of the PET crystal: the PET[S2] chain also keeps all-trans in a triclinc P1̅ lattice. On the other hand, the C=S and C=O groups of model SO are not regularly arranged in the crystal and each is randomly placed at either of two equivalent C=X sites of the molecule (see Figure b).[17] For the sake of comparison, however, the PET[SO] chain was arranged with one-dimensional periodicity of [-C(=O)C6H4C(=S)OCH2CH2O-] and packed as an isomorphic replacement of PET; however, the asymmetric unit corresponds to the monomeric one and hence the space group has been assumed to be P1.

Figure 7

Molecular structures of (a) model SS, (b) model SO, and (c) EGDB in the crystalline state. (a, b) Displacement ellipsoids are drawn at the 50% probability level. Reproduced from ref (17) with permission of the International Union of Crystallography. (c) Drawn on the basis of ref (24) with the Mercury 4.13 program.[40] The three molecules lie in all-trans conformations.

The lattice constants and atomic coordinates of PET being set initially, the PET[S2] and PET[SO] crystals were subjected to the structural optimization. Consequently, the lattice energies of both polymer crystals were fully converged. The crystal structures thus determined are depicted in Figure , the lattice constants are given in the figure caption, and the fractional atomic coordinates are listed in Tables S3 and S4 (Supporting Information). The intermolecular close contacts that were detected by the PLATON program[41] are explained in the caption of Figure . The length of the a axis corresponds to the π···π distance: PET[S2], 5.750 Å; PET[SO], 4.639 Å; PET, 4.45 Å.[42] The sulfur atom with a large van der Waals radius seems to extend the chain spacing.

Figure 8

Crystal structures optimized at the B3LYP-D/6-31(d,p) level: (a) PET[S2]; (b) PET[SO]. The crystal lattices are as follows: (a) triclinic cell of space group P1̅, a = 5.750 Å, b = 6.509 Å, c = 10.726 Å, α = 96.25°, β = 123.25°, and γ = 120.73°; (b) triclinic cell of space group P1, a = 4.639 Å, b = 6.283 Å, c = 10.779 Å, α = 96.98°, β = 118.15°, and γ = 116.50°. Intermolecular close contacts detected by the PLATON program:[41] (a) π···π (Cg···Cg = 5.750 Å), C–S···π (S···π = 3.636 Å), and C–H···S (C···S = 3.839 Å); (b) π···π (Cg···Cg = 4.639 Å), C–O···π (O···π = 3.498 Å), C–S···π (S···π = 3.625 Å), C–H···O (C···O = 3.357 Å), and C–H···S (C···S = 3.509 and 3.799Å). Cg is the centroid of the benzene ring. For the atomic positions, see Tables S3 and S4 (Supporting Information).

The stiffness (C) and compliance (S) tensors of the PET[S2] and PET[SO] crystals are given in Appendix B (Supporting Information). From the S tensors, Young’s moduli in the a- (E), b- (E), and c-axis (E) directions were calculated as follows: PET[S2], E = 0.94 GPa, E = 19.58 GPa, and E = 142.1 GPa; PET[SO], E = 2.67 GPa, E = 21.83 GPa, and E = 173.1 GPa; PET, E = 7.20 GPa, E = 22.26 GPa, and E = 182.4 GPa.[42] In general, the O → S replacement tends to reduce the crystalline moduli in all three axis directions because the larger van der Waals radius of sulfur expands the crystal lattice and hence interatomic interactions are weakened. The stiffness along the fiber axis, E, which is, in principle, the largest Young’s modulus of the polymer, was evaluated in the order of PET (182.4 GPa) > PET[SO] (173.1 GPa) > PET[S2] (142.1 GPa). Figure shows Young’s modulus distributions on the plane perpendicular to the c axis. All three plots are seen to form crosses, which exhibit the maximum in the molecular plane and its normal directions. The cross shapes are seen to become well-defined and sharp in the order PET < PET[SO] < PET[S2] because Young’s modulus in the a′ direction tends to be markedly reduced in this order, that is, as the a-axis length increases.

Figure 9

Young’s modulus distributions on the plane normal to the c axis of (a) PET[S2], (b) PET[SO], and (c) PET. The a’ and b’ vectors represent the orthogonal projections on the plane. The grid spacing corresponds to 10 GPa.

Possible Applications

As described above, PET[S2] may not be so stiff as PET. This is because the sulfur atom with a large van der Waals radius expands the crystal lattice and weakens interchain attractions, especially the π/π interaction. This can be seen from the large a-axis length of 5.750 Å and the small E value of 0.94 GPa. PET[S2] strongly prefers the tg±t conformations; the −Uconf value of 1.84 kcal mol–1 suggests that the crystalline state is of higher energy by −Uconf than the free (amorphous and molten) state (cf. −Uconf of PET is 1.02 kcal mol–1).

As mentioned in the Introduction, it is difficult to synthesize pure PET[S2] in solutions. Instead, solid-state thionation of PET by microwave radiation with Lawesson’s reagent[15,16] enables us to prepare partly thiono-substituted PET, that is, PET[SO1–]. If the amorphous phase is susceptible to the thionation, carbonyl-rich (PET crystallites) and thiocarbonyl-rich (sulfurated amorphous) domains are formed in the PET[SO1–] material.

As illustrated in Scheme , the thiocarbonyl unit, C=S, may act as a cross-linking site.[8] If a radical species attacks and bonds to the sulfur atom, a carbonyl double bond, C=O, will be formed via a thione-thiol rearrangement, and, simultaneously, the fragment terminated by a methylene radical will be left.[8,10] If the methylene radical attacks another C=S group or combines with a different radical species, an interchain cross-linking will be formed. If sulfur is added together with a vulcanization accelerator, vulcanized networks may be formed. If the amorphous phase can be plasticized properly and, consequently, the glass transition temperature could be reduced as needed, the material will behave as an elastomer because PET[S2] has the potential ability to behave as a rubber (the large positive f/f of 0.19). Such PET[SO1–] materials as are composed of PET-rich (hard), and rubberlike (soft) domains are expected to be superior in impact resistance.[43] Furthermore, the polythionoesters exhibit a characteristic reddish color. The optical property will be either an advantage or a disadvantage, depending on the usage.

Scheme 3

Mechanism of Cross-Linking Formation via the Thiocarbonyl Group

Conclusions

Structures and properties of PET[S2], PET[SO], and PET[SO1–] have been predicted from the MO, RIS, and periodic DFT calculations. The spacer, O–CH2–CH2–O, of PET[S2] strongly prefers tg±t conformations, which results in a small chain dimension (0/nl2 = 2.05), a low degree of conformational freedom (Sconf = 5.02 cal K–1 mol–1), and potential rubberlike properties (fU/f = 0.19). As the sulfidity, z, decreases, the configurational properties of PET[SO1–] approach those of PET: 0/nl2 = 2.47; Sconf = 7.13 cal K–1 mol–1; fU/f = 0.13. The crystal structure of PET[S2], assuming to be an isomorphic replacement of the PET crystal, was simulated from periodic DFT calculations to be a triclinic lattice of the space group P1̅, a = 5.750 Å, b = 6.509 Å, c = 10.726 Å, α = 96.25°, β = 123.25°, γ = 120.73°, and density = 1.533 g cm3. The sulfur atom with a large van der Waals radius (1.80 Å) expands the crystal cell especially in the a- and b-axis directions. From the compliance tensor of PET[S2], Young’s moduli along the a, b, c axes were evaluated to be E = 0.94 GPa, E = 19.58 GPa, and E = 142.1 GPa, respectively, being smaller than those of PET: E = 7.20 GPa, E = 22.26 GPa, and E = 182.4 GPa. The physical properties of PET[SO1–] will be controlled between those of PET[S2] and PET by adjusting the sulfidity. On the basis of the information thus obtained, the practical applicability of the polymers has also been discussed. Here, the structures and properties of the not-yet synthesized polymers, PET[S2], PET[SO], and PET[SO1–], were predicted by the purely theoretical scheme; therefore, the theoretical molecular design for new polymers has been accomplished.

Methods

Molecular Orbital Calculation

Molecular orbital calculations on model SS, model SO, and EGDB were carried out with the Gaussian09 program.[44] For each of all conformers that can be enumerated under the RIS approximation, the geometrical parameters were optimized and the thermochemical energies at 1 atm and 25 °C were evaluated by the density functional theory (DFT) calculations at the B3LYP/6-311+G(2d,p) level. For the optimized structure, the electronic energy was calculated at the MP2/6-311++G(3df,3pd) level. From the MP2 electronic and B3LYP thermochemical energies, the Gibbs free energy was calculated for each conformer.

It is known that the MP2 method occasionally overestimates π/π attractions between aromatic groups.[45] When we investigated conformational characteristics of poly(trimethylene terephthalate) (PTT) and poly(butylene terephthalate) (PBT),[46] half of the MP3 term was added to the MP2 energy to compensate the overestimated π/π attractions.[47,48] Inasmuch as the benzene rings of PTT and PBT are connected by −O–(CH2)3–O– and −O–(CH2)4–O– chains, respectively, their adjacent benzene rings can approach and attractively interact with each other. In contrast, PET has shorter −O–(CH2)2–O– chains, and hence its benzene rings cannot come close to each other. Therefore, the above correction is unnecessary for PET. The PET[S2] and PET[SO] chains and their model compounds include the same −O–(CH2)2–O– part, being free from the close contacts of benzene rings. Therefore, their conformational energies were calculated at the MP2/6-311++G(3df,3pd)//B3LYP/6-311+G(2d,p) level.

The solvent effects on the MP2 electronic energy were assessed by the polarizable continuum model using the integral equation formalism variant (IEF-PCM).[49] The vicinal coupling constants required for NMR analysis were also calculated at the B3LYP/6-311++G(3df,3pd) level.[50]

Synthesis of Models SS-13C and SO-13C

Models SS and SO were synthesized from EGDB and Lawesson’s reagent by microwave irradiation at 500 W for 3.0 min, as described elsewhere.[17] Models SS-13C, SO-S-13C, and SO-O-13C were similarly synthesized as illustrated in Scheme ; EGDB-13C that had been prepared previously[2] was used as the starting material. Because models SO-S-13C and SO–O-13C could not be isolated, the mixture (model SO-13C) underwent the following NMR measurements.

NMR Experiment and Analysis

1H and 13C NMR of models SS, SS-13C, SO, and SO-13C were measured at 500 MHz (126 MHz) with a JEOL JNM-ECA500 spectrometer in the Center for Analytical Instrumentation. Each model compound was dissolved in benzene-d6, chloroform-d, or dimethyl-d6 sulfoxide (DMSO-d6) placed in a 5 mm glass tube at a concentration of 0.06 M (model SS’s) or 0.12 M (model SO’s), and the probe temperature was set at 15, 25, 35, 45, or 55 °C. The pulse width, flip angle, and relaxation delay were set equal to 7.25 μs (3.78 μs) and 45° (30°) and 5.0 s (2.0 s), respectively. The 32 (128) free induction decays (FIDs) were accumulated for model SS’s, zero-filled, and subjected to a Fourier transform. For models SO’s, the FIDs were added up 128 (256) times. Here, the values with and without parentheses represent the 13C and 1H NMR parameters, respectively. The NMR spectra thus obtained underwent the gNMR simulation[51] to yield chemical shifts and scalar coupling constants.

model SS: 1H NMR (500 MHz, CDCl3, δ) 5.14 (s, 4H), 7.37–7.40 (m, 4H), 7.53–7.56 (m, 2H), 8.20–8.22 (s, 4H).

model SO: 1H NMR (500 MHz, CDCl3, δ) 4.79-4.82 (quin, 2H), 4.99–5.02 (quin, 2H), 7.36–7.40 (m, 2H), 7.43–7.46 (m, 2H), 7.52–7.59 (m, 2H), 8.06–8.09 (m, 2H), 8.19–8.22 (m, 2H).

model SS-13C: 1H NMR (500 MHz, CDCl3, δ) 5.14 (d, 4H), 7.37–7.40 (m, 4H), 7.53–7.56 (m, 2H), 8.20–8.22 (m, 4H).

model SO-13C: 1H NMR (500 MHz, CDCl3, δ) 4.79-4.82 (m, 2H), 4.99–5.02 (m, 2H), 7.36–7.40 (m, 2H), 7.43–7.46 (m, 2H), 7.52–7.59 (m, 2H), 8.06–8.09 (m, 2H), 8.19-8.22 (m, 2H).

The vicinal 13C–1H coupling constants (3JC(X)H’s) observed from models SS-13C and SO-13C can be expressed as a function of trans (pt) and gauche (pg) fractions around the C(=X)O–CH2 (X = S or O) bond[52]where the coefficients, JG, JT′, and JG′ (see Figure ), were calculated from MO calculations at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311+G(2d,p) level to be 1.71, 7.51, and 4.81 Hz for model SS and 1.71, 7.57, and 4.62 Hz for model SO, respectively. By definition, the bond conformations must fulfill

Two vicinal 1H–1H coupling constants (3JHH and 3JHH′) observed from two methylene units, CHAHA′ and CHBHB′ (for the hydrogen designation, see Scheme and Figure ), are related to pt and pg of the CHAHA′–CHBHB′ bond:andwhere the coefficients were adopted from those often used for the O–CH2–CH2–O bond sequences of ethers and esters: JG = JG′ = JG″ = 2.3 Hz and JT = JT′ = 11.4 Hz.[53] The sum of pt and pg that eqs and 8 directly gave were slightly different from unity. Then, the two values were divided by the sum to satisfy eq .

RIS Calculation

The computer program for the refined RIS calculations[18−20] on PET[SO1–] (0 ≤ z ≤ 1) was homemade, coded in FORTRAN, and compiled with Intel FORTRAN Composer XE. The statistical weight matrices were formulated as written in Appendix A (Supporting Information). The geometrical parameters were extracted from the optimized conformers of models SS and SO (Tables S1 and S2, Supporting Information) and EGDB,[2] and the Gibbs free energies of Table were used for the conformational energies.

The polymeric chain of x degree of polymerization was imaginarily produced, and its C(=X) sites were assumed to be randomly sulfurated by Bernoulli trials[21,22] so as to fulfill a given sulfidity z0: the random numbers distributed uniformly between 0 and 1 were generated by the subroutine random_number. If the value was smaller than or equal to z0, the site was assumed to be sulfurated (C=S); otherwise, a C=O group was put there. These procedures were repeated for all nc chains included in the ensemble. As the number of trials, 2x × nc, increases (a repeating unit has two C=X sites), the sulfidity (z) generated by the software approaches z0. When x = 200 and nc = 100 were chosen, the discrepancies between z0 and z, defined as |z – z0|/z0 × 100 (%), were found to stay smaller than 0.5%; therefore, x = 200 and nc = 100 were set in all computations. The cis energy and the geometrical parameters around the benzene ring depend on the combination of X1 and X2 (see Figures and 11): X1 = X2 = S, model S–Bz–S; X1 = S (O); and X2 = O (S), model S–Bz–O; X1 = X2 = O, model O–Bz–O. The energy and geometrical parameters of the spacer were chosen, depending on the X2 and X3 pair: X2 = X3 = S, from model SS; X2 = S and X3 = O, from model SO (forward direction, see Scheme ); X2 = O and X3 = S, from model SO (backward direction); X2 = X3 = O, from EGDB. In such a way, the energy and geometrical parameters of the models were assigned to all x × nc monomeric units and the super generator matrices were assembled and multiplied successively from one end to the other to yield the configurational properties as a function of z.[20]

Figure 11

Polymer architecture for the RIS calculations on PET[SO1–] (z, sulfidity) and definition of X1, X2, and X3.

The configurational entropy can be obtained from[32,54]Here, the partition function, Z, is calculated fromwhere n is the number of skeletal bonds, J* is the row matrix whose first element is unity and the others are null, U is the statistical weight matrix of bond j, and J is the column matrix filled with unity. The configurational energy Uconf corresponds to the difference in internal energy between the crystalline and unperturbed states, derived from[2]The positive (negative) Uconf means that the crystal conformation is more stable (unstable) by −Uconf than the unperturbed state (melt, amorphous, and Θ solutions).

Periodic DFT Calculation

Density functional theory calculations with a dispersion force correction were carried out under periodic boundary conditions using the CRYSTAL17 program.[25,26] The Hamiltonian used here was B3LYP with a dispersion force correction (DFC). The DFC term (Edisp) is based on Grimme’s D2 formula[55,56]where s6 is the global scaling factor, Nat is the number of atoms included in the system, C6 is the dispersion coefficient for atom pair ij, given by C6 = (C6C6)1/2, and R is the distance between atoms i and j. Here, the damping factor is defined aswhere d represents the steepness of the damping function and R is the sum of van der Waals radii (RvdW) of atoms i and j. All above parameters except RvdW’s were based on Grimme’s original.[55] As Milani et al. pointed out,[57,58] however, the following RvdW’s are more suitable than Grimme’s for, at least, polymer crystals: H, 1.3013 Å; C, 1.70 Å; O, 1.52 Å. Our previous studies[42,59−61] have also confirmed Milani’s suggestion. Of the RvdW values, those of carbon and oxygen are equal to Bondi’s RvdW’s.[62] Therefore, we first examined which RvdW is more appropriate for sulfur in polymer crystals, i.e., Grimme’s 1.683 Å[55] or Bondi’s 1.80 Å.[62] As the object of study, we have chosen poly(ethylene sulfide) (PES, [−CH2–CH2–S−]Figure ) because its simple asymmetric unit includes only four atoms (S, C, and H2) and hence the RvdW value of sulfur must affect the optimized structure significantly. The lattice constants and atomic positions that were determined by X-ray diffraction[63] were set as the initial structure and optimized by minimizing the total lattice energy. In Table , the crystal structures due to RvdW’s of 1.683 and 1.80 Å are given and the discrepancy from the experiment was quantified by two parameters: ΔLC for lattice constants and ΔSC for atomic positions, which are defined in the footnotes of Table . The RvdW of 1.683 Å yielded ΔLC = 0.94% and ΔSC = 0.011 and that of 1.80 Å gave somewhat better results, ΔLC = 0.74% and ΔSC = 0.011. The crystal densities were calculated to be 1.432 g cm–3 (1.683 Å) and 1.405 g cm–3 (1.80 Å); the latter is closer to the experimental value (1.410 g cm–3). In general, the RvdW of 1.80 Å yielded more favorable results and hence has been used for sulfur throughout this study.

Figure 12

Crystal structure of poly(ethylene sulfide) (PES) optimized with RvdW of sulfur = 1.80 Å. As in the PETS2 and PETS4 crystals, the spacer of PES also adopts g±tg∓ conformations that are the most stable in the free state.[27]

Table 5

Optimized and Experimental Crystal Structures of Poly(ethylene sulfide)a

Lattice Constants (Å)
	optimized				experimentalb
RvdW	a	b	c	ΔLCc (%)	a	b	c
1.683	8.419	4.851	6.816	0.94	8.50	4.95	6.70
1.80	8.457	4.908	6.832	0.74

An orthorhombic cell of space group Pbcn.

Reported by Takahashi et al.[63]

which was calculated for sulfur and carbon atoms.

The crystal structures of PET[S2] and PET[SO] were simulated by isomorphic replacement for the PET crystal: The repeating unit of PET, whose one (PET[SO]) or two (PET[S2]) −C=O– oxygen atoms were replaced with sulfur, was initially set as in the PET crystal[23] triclinic cell of space group P1 (PET[SO]) or P1̅ (PET[S2]) and optimized at the B3LYP/6-31G(d,p) level with a modified Broyden method under default conditions except for a Fock/Kohn-Sham matrix mixing of 80% and a shrinking factor of 4.[26]

The stiffness (S) and compliance (C) tensors were derived from the ELASTCON routine[64,65] included in the CRYSTAL17 program. The number of points to derive the second derivative of the crystalline energy and the strain-step size were 5 and 5×10–3, respectively. The Young’s modulus E(l1, l2, l3) in an arbitrary direction represented with the unit vector (l1, l2, l3) can be calculated from[66]where s (u and v = 1–6, Voigt’s notation) is the element of the compliance tensor.