Hydrogen-Bonding Interactions in Hard Segments of Shape Memory

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Hydrogen-Bonding Interactions in Hard Segments of Shape Memory Polyurethane: Toluene Diisocyanates and 1,6Hexamethylene Diisocyanate –A Theoretical and Comparative Study Cuili Zhang, Jinlian Hu, Xun Li, You Wu, and Jianping Han J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp508817v • Publication Date (Web): 28 Nov 2014 Downloaded from http://pubs.acs.org on December 12, 2014

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The Journal of Physical Chemistry

Hydrogen-Bonding Interactions in Hard Segments of Shape Memory Polyurethane: Toluene Diisocyanates and 1,6Hexamethylene Diisocyanate –A Theoretical and Comparative Study Cuili Zhang a,b,c · Jinlian Hu a,b * · Xun Li c You Wu a,b Jianping Han a,b a

Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China;

b

The Hong Kong Polytechnic University Shenzhen Base, Shenzhen, China.

c

Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China

* Corresponding author. Tel.: +852 27666437; fax: +852 2775 1432. E-mail address: [email protected] (J.L. Hu).

1 ACS Paragon Plus Environment


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ABSTRACT: In this study, the hydrogen–bonding interactions of three widely used diisocyanate based hard–segment (HS) models in polyurethane, 2,4-toluene diisocyanate-methanol (2,4-TDIMeOH),

2,6-toluene

diisocyanate-methanol

(2,6-TDI-MeOH),

and

1,6-hexamethylene

diisocyanate-methanol (HDI-MeOH), were investigated theoretically by density functional theory (DFT). The B3LYP/6-31G* method was used to calculate the equilibrium structures, Mulliken charges, hydrogen–bonding energies, and infrared (IR) spectra, in good agreement with previous experimental data. The HS models with benzene ring have much longer hydrogen bonds (HB), due to steric hindrance of benzene ring, while the aliphatic model form much shorter hydrogen bonds. Different positions of methyl group on benzene ring for 2,4-TDI-MeOH and 2,6-TDI-MeOH result in different types of hydrogen bonds with various strengths. The style of hydrogen bonding for HDI-MeOH is more flexible due to simple aliphatic chemical structure without benzene ring. The charge transfer on atoms N, H and O involved in hydrogen bonding occurs with the forming of hydrogen bond. The hydrogen bonding of 2,4-TDI-MeOH is much stronger than the others, and 2,6-TDI-MeOH froms the weakest hydrogen bonds. This study can supply guidance for the selection of hard segment in design of polyurethane and in-depth understanding of the hydrogen–bonding mechanism in the hard segments of polyurethane.

Keywords: Density functional theory (DFT), hydrogen–bonding interactions, diisocyanate based hard–segment, 2,4-toluene diisocyanate-methanol, 2,6-toluene diisocyanate-methanol, 1,6hexamethylene diisocyanate-methanol


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1. INTRODUCTION Shape memory polymer (SMP) is a kind of material that is able to remember and recovery its permanent shape under certain external stimulus, such as heat 1, light 2, electricity 3, water 4 or solvent 5 etc, which spans various areas of everyday life

6-9

. Generally, an SMP consists of two

components, the crosslinkages (hard segments) determining the permanent shape, and the switching segments (soft segments) fixing the temporary shape at temperatures below the transition temperature (Ttrans), which is either the glass transition or melting temperature of the switching segments. Segmented polyurethanes (PUs) are an important class of shape memory materials, where the hard segments (HSs) are based on diisocyanate and diol, and polyols or polyethers act as the soft segments (SSs) 10-13, see Figure 1. For hard segments, 2,4- and 2,6-toluene diisocyanate (2,4TDI, 2,6-TDI) 14-17 are two of the most important aromatic isocyanates, while 1,6-hexamethylene diisocyanate (HDI)

7,18-20

is a commonly used aliphatic diisocyanate in practical applications.

The hard segments can both serve as hydrogen–bonding acceptors (C═O and –O–) and donor (N–H). The hydrogen bonding-induced microphase separation of the hard domains and soft domains allows the materials to possess better mechanical properties

21

. Improved phase

separation in polyurethanes also leads to stronger hydrogen bonding in the hard segments and usually better physical properties 22. Also, due to interesting hydrogen–bond (H–bond) behavior, polyurethanes have gained lots of attention for many decades including using experimental methods: FTIR Raman

31-34

, X-ray

35,36

23-28

, and simulation methods: molecular mechanics (MM) 39

dynamics simulations (MD) , quantum chemical calculations (QC)

40-46

, NMR

37,38

29,30

,

, molecular

.

The dissociation enthalpy of 2,6-TDI polymers, ∆H, was calculated by assuming 95~97% bonded NH, 80% bonded carbonyl, and values of 3-4 kcal/mol (12.55-16.74 kJ/mol) were obtained for carbonyl groups and 4-5 kcal/mol (16.74-20.92 kJ/mol) for N-H groups14 by curve resolving. For 2,4-TDI polymers, 95% bonded NH at 0 ℃ was considered to calculate the dissociation enthalpy, and values in range of 3-4 kcal/mol (12.55-16.74 kJ/mol) were obtained 14. Brunette et al.

28

calculated hydrogen–bonding distances R(N–H···O) by the linear relationship

between IR frequency shift ∆ν and R: ∆ν =0.548×103(3.21-R) derived by Pimentel et al. 47, and values of 2.96 Å and 2.90 Å were obtained corresponding to 2,4-TDI-BD and 2,6-TDI-BD dimers, respectively. 3 ACS Paragon Plus Environment


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In some special molecular designs, HDI was used to make up part of the soft segment

48

.

The HDI-based PUs exhibited high Young’s modulus and tensile strength because of formation of hydrogen bonds and crystallization of the hard segment component and strong microphase separation 49. Wang et al. 41 used B3LYP/6-31G(d',p') method studying the effects of fluorination on the intermolecular hydrogen bonds, and 60.4 kJ/mol was obtained for the hydrogen–bonding energy of HDI hard segment dimers, without BSSE and ZPE corrections. In our previous studies, the hydrogen–bonding interactions of 4,4′-diphenylmethane diisocyanate (MDI) based polyurethane 40 and isophorone diisocyanate (IPDI) based polyurethane 46

were investigated using density functional theory (DFT) method, and found that carbonyl

hydrogen bonding is much stronger than the ester –O– ones, and the IPDI-based HS can form much stronger hydrogen bonds comparing with MDI-based HS. Yilgor et al

42

studied the

hydrogen–bonding interactions of polyether based segmented polyurethanes and polyureas using ab initio molecular orbital theory MP2 and DFT method to investigate the influence of competitive hydrogen bonding on microphase morphologies. Sun

43

used ab initio Hartree-Fock

(HF) and MP2 calculations with 3-21G and 6-31G(d) basis sets to investigate the intra- and intermolecular hydrogen–bonding interactions for a group of carbamic acid based urethane model molecules, and found that the N-H···O=C and N-H···O (ether) bonds are comparably strong and the N-H···O (ester) bond is only ca. 50-60% as strong as the other two. Furer

44

performed MINDO/3 computations to study the IR spectra of toluene-2,4-bis (methyl) carbamate. Masunov et al 45 studied the one–dimensional hydrogen–bonding aggregates of urea and thiourea in two patterns, chains and ribbons, using ab initial and semiempirical molecular orbital theory. To choose proper computational level in the theoretical calculations of hydrogen bonding is an important theme widely discussed several decades, and B3LYP and MP2 are two most common theoretical approaches among all the DFT and ab initio methods 50-53. The MP2 method considers electron correlation, can provide comparable data with experimental results, however, its high computational costs restrict its applications mainly based on small systems 50. Nowadays, the DFT method has been used as an alternative to MP2 scheme in the hydrogen-bonding studies, which is more efficient, and can offer a reasonable compromise between the accuracy and the computational effort 51.


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Figure 1. Three diisocyanate-based hard–segment (HS) models in polyurethane (a, b represent parts with different chemical environments).

Correlation between hydrogen bonding and macromolecular properties definitely depends on the relative strength of various hydrogen bonds and the number of such bonds in the bulk system. To the best of the authors’ knowledge, there are few theoretical attempts on the comparative studies of hydrogen–bonding interactions of 2,4-TDI, 2,6-TDI, and HDI based hard segments in polyurethanes. So, in present study, we use the DFT theory to investigate their hydrogen–bonding interactions. Three hard segment models were presented by the products from the reaction of diisocyanate and methanol, as generally showed in Figure 1, and named 2,4-TDIMeOH, 2,6-TDI-MeOH and HDI-MeOH, respectively. The relative strength of each potential hydrogen bonding will be found out, which can guide the design of shape memory polyurethanes and help us understand the hydrogen–bonding mechanism in details.

2. COMPUTATIONAL METHODS The HF method neglects electron correlation, which results in an overestimation in bond lengths

54

, while the density functional theory (DFT) based methods, such as the Becke–three

Lee–Yang–Parr (B3LYP) 55 one, have been shown to provide reliable trends of bonding energies even though the small energy differences often observed in relative bonding energies can be overshadowed by the DFT quadrature errors

54

. In the DFT calculations different functionals

were used. The Becke exchange functional 56, containing the gradient correction and denoted by B, was combined with correlation functionals by Lee, Yang, and Parr (LYP) and Wang (PW91)

58

57

and by Perdew

which resulted in BLYP and BPW91 exchange–correlation functionals.



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The hybrid method includes a mixture of the HF component and the DFT exchange-correlation functional, suggested by Becke 55 and denoted by B3LYP and B3PW91. In this study, the equilibrium structures, Mulliken charges, hydrogen–bonding energies, and IR spectra were calculated by B3LYP method using 6-31G(d) basis set. The obtained energies of hydrogen–bonding complexes were corrected both for basis set superposition error (BSSE) by the Boys–Bernardi full counterpoise method

59

and for zero–point vibrational energy (ZPE) at

298.15 K. The harmonic frequency analyses have been carried out and all the optimized structures have no imaginary frequency, which suggests that the optimized structure exists in the minimum point. It is well known that the vibrational frequencies obtained by quantum chemical calculations are typically larger than their experimental counterparts. Therefore, to compare the calculated vibrational frequencies with the experimental counterparts the former have been scaled by 0.9603 as recommended by Ref.

60

for the method mentioned above. All calculations

were performed with the Gaussian 03 program 61.

3. RESULTS AND DISCUSSION The hydrogen–bonding complexes of three diisocyanate based hard–segement models, mainly based on the hydrogen bonding between proton acceptors (C═O, ester –O–) and proton donor (N–H), are shown in Figure 2. Harmonic frequency analyses with no imaginary frequency for all optimized structures indicate that the obtained structures are true minima. Corresponding structure parameters are listed in Tables 1~3. Tables 4~6 present the Mulliken charges of key atoms involved in hydrogen bonding. Hydrogen–bonding energies are listed in Table 7. Figures 3~5 show the relationships between hydrogen–bonding papameters and energies. Figure 6 presents the IR spectra, and Table 8 lists IR frequency shifts (∆ν) for different functional groups due to hydrogen bonding. Figure 7 displays the relationship between IR frequency shift and hydrogen–bonding energies.

3.1. Equilibrium Structures. Comparing the chemical structures of three HS models, the compounds can be divided into two categories, which are aromatic HSs (2,4-TDI-MeOH and 2,6-TDI-MeOH) and aliphatic HS (HDI-MeOH). The difference of 2,4-TDI-MeOH and 2,6-TDI-MeOH is the position of methyl


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group on benzene ring. In Figure 2, the first three structures are free molecules or single molecules without being hydrogen–bonded, the others are hydrogen–bonding complexes. Due to asymmetry of 2,4-TDI-MeOH, functional groups in parts ‘a’ and ‘b’ show different characteristics (see Figure 1), which may induce different hydrogen bonding from two parts. Three types of carbonyl hydrogen bonds can be formed in 2,4-TDI-MeOH dimers among parts ‘b’, or between parts ‘a’ and ‘b’, or among parts ‘a’ with only one hydrogen bond; while the ester –O– hydrogen bonding can be formed between parts ‘a’ and ‘b’ with two hydrogen bonds (see Figures 1, 2). For 2,6-TDI-MeOH, due to its symmetrical structure, only two hydrogen–bonding complexes were found, one is carbonyl hydrogen bonding with one hydrogen bond, the other is ester –O– hydrogen bonding with two hydrogen bonds (see Figure 2). For carbonyl hydrogen bonding of HDI-MeOH, two complexes with one hydrogen bond and two hydrogen bonds are obtained (see HDI-MeOH-Ⅰ, Ⅱ in Figure 2) by changing the relative positions of two HDI-MeOH molecules; while for the ester –O– one, two hydrogen bonds are found, see HDI-MeOH-Ⅲ in Figure 2.

2,4-TDI-MeOH

2,6-TDI-MeOH

HDI-MeOH

2,4-TDI-MeOH-Ⅰ



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2,4-TDI-MeOH-Ⅱ

2,4-TDI-MeOH-Ⅲ

2,4-TDI-MeOH-Ⅳ

2,6-TDI-MeOH-Ⅰ

2,6-TDI-MeOH-Ⅱ

HDI-MeOH-Ⅰ


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HDI-MeOH-Ⅱ

HDI-MeOH-Ⅲ

Figure 2. Optimized possible hydrogen–bonding structures of three HS models in polyurethane (O in red, N in blue, C in grey, hydrogen bond in dashed).

Tables 1~3 list DFT calculated structure parameters of intermolecular hydrogen–bonding complexes of three HS models in polyurethane. The distances of carbonyl hydrogen bonds are in range of 2.925~3.014 Å, and the shortest one is HDI-MeOH-Ⅱ1,2, while the longest one refers to 2,6-TDI-MeOH-Ⅰ. For ester –O– hydrogen bonds, the hydrogen–bonding distances are in range of 3.028~3.196 Å, where the longest and shortest bydrogen bonds are in complexes 2,4-TDIMeOH-Ⅵ and 2,6-TDI-MeOH-Ⅱ, respectively. Comparing two types of hydrogen bonding, the ester –O– ones are much longer. The angles of hydrogen bonds are in range of 156.3~171.9° for carbonyl hydrogen bonds, and 169.9~178.2° for ester –O– ones. The smallest angle of carbonyl hydogen bonding is for the two hydrogen bonds of HDI-MeOH-Ⅱ, while the largest angle is in the hydrogen bond of 2,6-TDI-MeOH-Ⅰ. The smallest angle of ester –O– hydrogen bonding is for hydrogen bond 2,6-TDI-MeOH-Ⅱ2, while the largest one is in hydrogen bond HDI-MeOHⅢ2. Dihedral angle θ(C–NC–O) represents the relative position of function groups and the whole molecules. For 2,4-TDI-MeOH, the carbonyl hydrogen–bonding lengths are in range of 2.989~3.001 Å, and the angles are in range of 163.2~169.6°, compared well with refs.

28,47

(see Table 1). The

lengths and angles for two ester –O– hydrogen bonds are the same, much longer and wider than that of the carbonyl ones. The hydrogen–bonding distances in part ‘a’ are much shorter than that in part ‘b’, while the bond elongations in part ‘a’ are much larger than that of part ‘b’. From the molecular structure of 2,4-TDI-MeOH, we know, the methyl group in benzene ring is much closer to part ‘b’, its steric hindrance may be the main reason for the different hydrogen–bonding parameters for two parts. Bond length has a close relation with bond strength, for similar chemical environment, the longer of the bond the weaker of the strength. 9 ACS Paragon Plus Environment


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Table 1. Selected Structure Parameters of Hydrogen Bonding for Optimized 2,4-TDI-MeOH Complexes, Bond Distances in Å, Bond Angles in °, Change Ratio in % Hydrogen bonding Parameters* Length/Angle Change ratio Refs. Free R(C═O)a 1.216 R(N–H)a 1.011 R(–O–)a 2.796 θ(C–NC–O)a 0.764 R(C═O)b 1.215 R(N–H)b 1.012 R(–O–)b 2.795 θ(C–NC–O)b -8.991 Ⅰ Carbonyl bonded 1.223 0.7 R(C═O) b Ⅰa 1.018 0.7 R(N–H) Ⅰ 2.997 R(N–H···O) 2.96 28, 2.99～3.04 47 Ⅰ 163.2 α(N–H···O) θ(C–NC–O)a(N–H) 1.049 37.3 θ(C–NC–O)b(C═O) -5.878 -34.6 Ⅱ 1.222 0.6 R(C═O) b Ⅱ 1.018 0.6 R(N–H) b Ⅱ 3.001 R(N–H···O) Ⅱ 164.3 α(N–H···O) θ(C–NC–O)b(N–H) -8.693 -3.3 θ(C–NC–O)b(C═O) -5.187 -42.3 Ⅲ 1.224 0.7 R(C═O) a Ⅲa 1.018 0.7 R(N–H) Ⅲ 2.989 R(N–H···O) Ⅲ 169.6 α(N–H···O) θ(C–NC–O)a(N–H) 0.793 3.8 θ(C–NC–O)a(C═O) 1.242 62.6 Ⅳ Ester –O– bonded 2.814 0.6 R(–O–) 1b Ⅳ1a 1.016 0.5 R(N–H) Ⅳ 3.196 R(N–H···O) 1 Ⅳ 177.4 α(N–H···O) 1 θ(C–NC–O)a(N–H) 0.370 -51.6 θ(C–NC–O)b(–O–) -7.961 -11.5 Ⅳ 2.814 0.6 R(–O–) 2b Ⅳ 1.016 0.5 R(N–H) 2a Ⅳ 3.196 R(N–H···O) 2 Ⅳ2 177.4 α(N–H···O) θ(C–NC–O)a(N–H) 0.371 -51.4 θ(C–NC–O)b(–O–) -7.959 -11.5 * Superscripts a, b are in accordance with Figure 1, Ⅰ~Ⅳ and 1~2 are in accordance with Figure 2, (N–H) and (C═O) represent the function groups offering N–H and C═O in the hydrigen bonding, respectively.

Table 2 showes the structure parameters of hydrogen bonding in 2,6-TDI-MeOH dimers. Hydrogen–bonding distances are in range of 3.014~3.149 Å, comparing well with refs. 28,47, and hydrogen–bonding angles are in range of 169.9~171.9°, close to 180°. The carbonyl hydrogen bond is much shorter than the ester –O– ones. Comparing two types of TDI-MeOH models, the


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carbonyl hydrogen bond in 2,6-TDI-MeOH is much longer than that in 2,4-TDI-MeOH, but the ester –O– hydrogen bonds in 2,6-TDI-MeOH are a little shorter. For the 2,6-TDI-MeOH, the methyl group on benzene ring is in the ortho position relative to both urethane functional groups, while that for 2,4-TDI-MeOH is in the ortho position and the forth position relative to two urethane groups, respectively, which indicates that the position of methyl group on benzene ring largely affects the properties of hydrogen bonding. The methyl group on benzene ring of 2,6TDI-MeOH is in the middle of two functional groups, which supplies a plane–trend distribution of the whole molecular chain, which can be seen from the dihedral angle θ(C–NC–O) close to 0, and results in high steric hindrance for the formation of hydrogen bonds. From Figure 2, we can also see, hydrogen bonds in 2,6-TDI-MeOH induce much larger twist in the involved functional groups compared with 2,4-TDI-MeOH. Table 2. Selected Structure Parameters of Hydrogen Bonding for Optimized Bond Distances in Å, Bond Angles in °, Change Ratio in % Hydrogen bonding Parameters* Length/Angle Change ratio Free R(C═O) 1.215 R(N–H) 1.009 R(–O–) 2.797 θ(C–NC–O)1 -1.451 θ(C–NC–O)2 1.431 Ⅰ Carbonyl bonded 1.223 0.7 R(C═O) Ⅰ 1.018 0.8 R(N–H) Ⅰ 3.014 R(N–H···O) Ⅰ 171.9 α(N–H···O) θ(C–NC–O)N–H -2.524 73.9 θ(C–NC–O)C═O -0.973 -32.9 Ⅱ1 Ester –O– bonded 2.814 0.6 R(–O–) Ⅱ 1.016 0.7 R(N–H) 1 Ⅱ 3.149 R(N–H···O) 1 Ⅱ 171.1 α(N–H···O) 1 θ(C–NC–O)N–H -4.578 215.5 θ(C–NC–O)–O– 1.985 38.7 Ⅱ2 2.815 0.6 R(–O–) Ⅱ2 1.016 0.7 R(N–H) Ⅱ 3.028 R(N–H···O) 2 Ⅱ 169.9 α(N–H···O) 2 θ(C–NC–O)N–H 1.985 38.7 θ(C–NC–O)–O– -4.578 215.5 * Superscripts Ⅰ~Ⅱ and 1~2 are in accordance with Figure 2, (N–H) and (C═O) offering N–H and C═O in the hydrigen bonding, respectively.


2,6-TDI-MeOH Complexes, Refs.

2.99～3.04 47, 2.90 28

represent the function groups


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The hydrogen–bonding parameters for HDI-MeOH are listed in Table 3. The hydrogen– bonding distances are in range of 2.925~3.077 Å, compared well with ref.

47

. The lengths for

complex with two carbonyl hydrogen bonds are much shorter than that of the others, maybe due to the cooperative effect of two hydrogen bonds forming at the same time (see Table 3).

Table 3. Selected Structure Parameters of Hydrogen Bonding for Optimized HDI-MeOH Complexes, Bond Distances in Å, Bond Angles in °, Change Ratio in % Hydrogen bonding Parameters* Length/Angle Change ratio Refs. Free R(C═O) 1.219 R(N–H) 1.010 R(–O–) 2.795 θ(C–NC–O)1 -9.663 θ(C–NC–O)2 9.637 Ⅰ Carbonyl bonded 1.226 0.6 R(C═O) 2.99～3.04 47 Ⅰ 1.017 0.7 R(N–H) Ⅰ 2.941 R(N–H···O) Ⅰ 162.3 α(N–H···O) θ(C–NC–O)N–H -2.504 -74.1 θ(C–NC–O)C═O -6.694 -30.7 Ⅱ 1.226 0.6 R(C═O) 1 Ⅱ1 1.016 0.6 R(N–H) Ⅱ 2.925 R(N–H···O) 1 Ⅱ 156.3 α(N–H···O) 1 θ(C–NC–O)N–H 9.500 -1.4 θ(C–NC–O)C═O 6.656 -30.9 Ⅱ 1.226 0.6 R(C═O) 2 Ⅱ 1.016 0.6 R(N–H) 2 Ⅱ 2.925 R(N–H···O) 2 Ⅱ 156.3 α(N–H···O) 2 θ(C–NC–O)N–H -9.497 -1.7 θ(C–NC–O)C═O -6.659 -31.1 Ⅲ 2.813 0.6 Ester –O– bonded R(–O–) 1 Ⅲ 1.016 0.6 R(N–H) 1 Ⅲ1 3.068 R(N–H···O) Ⅲ 177.6 α(N–H···O) 1 θ(C–NC–O)N–H 6.429 -33.3 θ(C–NC–O)–O– -5.453 -43.6 Ⅲ 2.814 0.6 R(–O–) 2 Ⅲ 1.016 0.6 R(N–H) 2 Ⅲ2 3.077 R(N–H···O) Ⅲ 178.2 α(N–H···O) 2 θ(C–NC–O)N–H -5.453 -43.6 θ(C–NC–O)–O– 6.429 -33.3 * Superscripts Ⅰ~Ⅲ and 1~2 are in accordance with Figure 2, (N–H) and (C═O) represent the function groups offering N–H and C═O in the hydrigen bonding, respectively.

The bond distances of ester –O– hydrogen bonds are much longer than that of the carbonyl ones. The hydrogen–bonding angles are in range of 156.3~178.2°, and the smallest one is in 12 ACS Paragon Plus Environment

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HDI-MeOH-Ⅱ with two carbonyl hydrogen bonds, while the largest one is corresponding to one ester –O– hydrogen bond HDI-MeOH-Ⅲ2. All the change ratios of dihedral angles for urethane functional groups θ(C–NC–O) are negative, and become much closer to 0 degree indicating that the formation of hydrogen bonding induces the whole molecule HDI-MeOH more planar. To show the bonding–length state of different HS models, average hydrogen–bonding lengths for different complexes are calculated. The order of carbonyl hydrogen bonds is: RHDIMeOH-Ⅱ

< RHDI-MeOH-Ⅰ < R2,4-TDI-MeOH-Ⅲ < R2,4-TDI-MeOH-Ⅰ < R2,4-TDI-MeOH-Ⅱ < R2,6-TDI-MeOH-Ⅰ, while

that of the ester –O– ones is: RHDI-MeOH-Ⅲ < R2,6-TDI-MeOH-Ⅱ < R2,4-TDI-MeOH-Ⅳ, respectively. We can find that the HS models with benzene ring have much longer hydrogen bonds, due to steric hindrance of benzene ring, while the aliphatic model form much shorter hydrogen bonds. Bonds N–H, C═O, –O– involved in hydrogen bonding are elongated with stretched ratios in range of 0.5~0.8%, 0.6~0.7%, and 0.6%, respectively. For carbonyl hydrogen bonding, average elongation of C═O is in the order: ∆RHDI-MeOH-Ⅰ = ∆RHDI-MeOH-Ⅱ = ∆R2,4-TDI-MeOH-Ⅱ < ∆R2,6-TDIMeOH-Ⅰ

= ∆R2,4-TDI-MeOH-Ⅰ = ∆R2,4-TDI-MeOH-Ⅲ, while that of N–H is in the order: ∆RHDI-MeOH-Ⅱ =

∆R2,4-TDI-MeOH-Ⅱ < ∆RHDI-MeOH-Ⅰ = ∆R2,4-TDI-MeOH-Ⅰ = ∆R2,4-TDI-MeOH-Ⅲ < ∆R2,6-TDI-MeOH-Ⅰ. For ester –O– hydrogen bonding, the average elongation of –O– for three HS models are the same, while that of N–H is: ∆R2,4-TDI-MeOH-Ⅳ < ∆RHDI-MeOH-Ⅲ < ∆R2,6-TDI-MeOH-Ⅱ. Both N–H and C═O in 2,6TDI-MeOH hydrogen–bonding complexes show much larger elongation ratios, induced by larger twist of functional groups in the forming of hydrogen bonds. The elongation ratios of both N–H and C═O in HDI-MeOH are relative small. The N–H groups involved in carbonyl hydrogen bonding are more elongated than that involved in ester –O–hydrogen bonding, which may correspond to stronger carbonyl hydrogen bonding. The distances of hydrogen bond obtained by the DFT calculations are in excellent agreement with the experimental values

28,47

. The angles of hydrogen bonding θ(N–H···O) are

close to 180°, in accordance with the measurable criteria for hydrogen bond 62. From the above anlysis we can conclude that, the HDI-MeOH has much shorter hydrogen bonds, and less bond elongation due to less steric hindrance compared with the HS models with benzene ring.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 32

3.2. Mulliken Charges. Tables 4~6 show the Mulliken charges on key atoms involved in hydrogen bonding calculated by DFT method, where ∆Q is the change of charges. The charge distributions of key atoms show that nitrogen atoms and oxygen atoms carry negative partial charges, while hydrogen atoms are with positive partial charges. For different chemical environments of parts ‘a’ and ‘b’, Mulliken charges show some differences on the same type of atoms. All the atoms involved in hydrogen bonding have some changes in charges (∆Q), and the variation tendency of atoms nitrogen and oxygen are more negative, while that of hydrogen atoms are more positive (see ∆Q column in Tables 4~6), due to the shift of electron density from hydrogen atom toward nitrogen and oxygen atoms. For carbonyl hydrogen bonding in model 2,4-TDI-MeOH, the ∆Q in part ‘a’ are much higher than that in part ‘b’ (see Table 4), which is related to shorter hydrogen bond in part ‘a’. Its chemical structure presents that the electron–donating group, methyl group, is much closer to part ‘b’ compared with part ‘a’, inducing decrease in electron–withdrawing of C═O group and increase in electron–donating of N–H group (see Table 4) of part ‘b’. From Table 4, we can find that charge changes for atoms in part ‘b’ induced by methyl group are more positive compared with that of part ‘a’. The closer of methyl group to part ‘b’ also results in much larger steric hindrance for the formation of hydrogen bonding. The charge changes for atoms involved in ester –O– hydrogen bonding are the same. Also, we can find that, charge changes in carbonyl hydrogen bonding are much larger than that in ester –O– hydrogen bonding, in accordance with the hydrogen–bonding distances and bond elongation ratios.

Table 4. Predicted Mulliken Charges for 2,4-TDI-MeOH Hydrogen–bonding Complexes on Key Atoms Ⅰ Ⅱ Ⅲ Ⅳ Atoms Free ∆Q* OC═O O–O– N H *

a b b a b a b

-0.504 -0.502 -0.490 -0.749 -0.727 0.340 0.342

Ⅲ

-0.520 -0.517

-0.517

-0.782

-0.787

-0.5071/ -0.5072 -0.7811/ -0.7812

0.402

0.3831/ 0.3832

-0.753 0.398 0.392

-0.016 Ⅰ Ⅱ -0.015 / -0.015 Ⅳ1 Ⅳ -0.017 / -0.017 2 Ⅰ Ⅲ Ⅳ Ⅳ -0.033 / -0.038 / -0.032 1/ -0.032 2 Ⅱ -0.026 Ⅰ Ⅲ Ⅳ Ⅳ 0.058 / 0.062 / 0.043 1/ 0.043 2 Ⅱ 0.050

Superscripts Ⅰ~Ⅳ and 1~2 are in accordance with Figure 2, respectively.


Page 15 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For model 2,6-TDI-MeOH, due to its symmetric structure, the same type of atoms show the same charges (see Table 5). The ∆Q for atoms involved in carbonyl hydrogen bonding are much larger than that invoved in ester –O– ones. The ∆Q on atoms N, O and H for two ester –O– hydrogen bonds, 2,6-TDI-MeOH-Ⅱ1 and 2,6-TDI-MeOH-Ⅱ2, are different, the latter are much larger, maybe arised by differenet torsion degrees of related functional groups (θ(C–NC–O)), which is in accordance with hydrogen–bonding distances and bond elongation ratios.

Table 5. Predicted Mulliken Charges for 2,6-TDI-MeOH Hydrogen–Bonding Complexes on Key Atoms Atoms Free ∆Q* Ⅰ Ⅱ Ⅰ OC═O -0.502 -0.533 -0.031 Ⅱ Ⅱ O–O– -0.491 -0.5071/ -0.5092 -0.016 1/ -0.018 2 1 2 Ⅰ Ⅱ1 Ⅱ N -0.754 -0.782 -0.767 / -0.773 -0.028 / -0.013 / -0.019 2 Ⅰ Ⅱ Ⅱ H 0.344 0.403 0.3801/ 0.3892 0.059 / 0.036 1/ 0.045 2 *

Superscripts Ⅰ~Ⅱ and 1~2 are in accordance with Figure 2, respectively.

For model HDI-MeOH (see Table 6), comparing two carbonyl hydrogen-bonding complexes, the ∆Q on atoms O and H for complex HDI-MeOH-Ⅰwith one hydrogen bond are a little higher, and much higher on N, which may be the reason for the larger elongation of N–H in HDI-MeOH-Ⅰ, and resulting in longer hydrogen bond. The charge changes for two ester –O– hydrogen bonds are close to each other with the largest difference 0.002, resulting in a little difference in corresponding hydrogen–bonding lengths. The ∆Q on atom H in carbonyl hydrogen bonding are much higher than that in the ester –O– one. Table 6. Predicted Mulliken Charges for HDI-MeOH Hydrogen–bonding Complexes on Key Atoms Atoms Free Ⅰ Ⅱ Ⅲ ∆Q* OC═O

-0.525

O–O–

-0.486

N

-0.614

-0.537

-0.657

-0.5351/ -0.5352

-0.6421/ -0.6422

Ⅰ

0.332

0.397

0.3841/ 0.3842

-0.018 1/ -0.019

-0.6501/ -0.6492

-0.043 / -0.028 1/ -0.028 2/ -0.036 1/

Ⅲ

Ⅰ

0.3771/0.3752

Ⅲ2

Ⅱ

Ⅱ

Ⅲ2

Ⅰ

Ⅱ

0.065 / 0.052 1/ 0.052 Ⅲ

Ⅲ2

0.045 1/ 0.043 *

Ⅱ2

-0.5041/ -0.5052

-0.035 H

Ⅱ

-0.012 / -0.010 1/ -0.010

Superscripts Ⅰ~Ⅲ and 1~2 are in accordance with Figure 2, respectively.


Ⅱ2

Ⅲ


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 32

In order to compare charge transfer states for different hydrogen–bonding models, average charge changes for each complexe have been calculated. For carbonyl hydrogen bonding, the order of average ∆Q on O is: ∆QHDI-MeOH-Ⅱ < ∆QHDI-MeOH-Ⅰ < ∆Q2,4-TDI-MeOH-Ⅰ = ∆Q2,4-TDI-MeOH-Ⅱ < ∆Q2,4-TDI-MeOH-Ⅲ < ∆Q2,6-TDI-MeOH-Ⅰ, while that on H is: ∆Q2,4-TDI-MeOH-Ⅱ < ∆QHDI-MeOH-Ⅱ < ∆Q2,4TDI-MeOH-Ⅰ

< ∆Q2,6-TDI-MeOH-Ⅰ < ∆Q2,4-TDI-MeOH-Ⅲ < ∆QHDI-MeOH-Ⅰ. For ester –O– hydrogen bonding,

the order of average ∆Q on O is: ∆Q2,6-TDI-MeOH-Ⅱ = ∆Q2,4-TDI-MeOH-Ⅳ < ∆QHDI-MeOH-Ⅲ, while that on H is: ∆Q2,6-TDI-MeOH-Ⅱ < ∆Q2,4-TDI-MeOH-Ⅳ < ∆QHDI-MeOH-Ⅲ. For the formation of hydrogen bonding, charges on atom N are also affected. For carbonyl hydrogen bonding, the order of its average ∆Q is: ∆Q2,4-TDI-MeOH-Ⅱ < ∆Q2,6-TDI-MeOH-Ⅰ =∆QHDI-MeOH-Ⅱ < ∆Q2,4-TDI-MeOH-Ⅰ < ∆Q2,4-TDIMeOH-Ⅲ

< ∆QHDI-MeOH-Ⅰ, while that for ester –O– hydrogen bonding is: ∆Q2,6-TDI-MeOH-Ⅱ < ∆Q2,4-

TDI-MeOH-Ⅳ

< ∆QHDI-MeOH-Ⅲ. For carbonyl hydrogen bonding, the charge transfers in two types of

TDI–MeOH are much higher between O and H, but lower between H and N, indicating the difference in electronegativity of C═O groups and electropositivity of N–H groups, resulting in different hydrogen–bonding lengths. For ester –O– hydrogen bonding, the charge transfer among O, H and N in HDI-MeOH is much larger, while that in 2,6-TDI-MeOH is the least. The charge transfer for hydrogen–bonding complexes of two types of HSs have some difference, induced by different positions of methyl group on benzene ring. There is no direct relation between the net charge (∆QO+∆QN+∆QH) for each hydrogen bond and corresponding structure

40

. Take 2,4-TDI-MeOH as an example, the net charges are

0.002, 0.009, 0.000, -0.006 for 2,4-TDI-MeOH-Ⅰ~Ⅳ, respectively. All are close to 0, indicating the charges mainly transferring among atoms N, H and O, and the adjacent atoms of hydrogen bonding may be involved in charge transfer, which determine the properties of hydrogen bond, and dominate the charge rearrangement in all complexes.

3.3. Hydrogen–Bonding Energies. In order to show the relationship between stability and hydrogen–bonding structures, number of hydrogen bonds (HB), relative bond energies ∆E, ∆E BSSE+ZPE (including the BSSE and ZPE corrections) and relative enthalpies ∆H of three hard–segment models are calculated by DFT method, which are listed in Table 7. To avoid errors induced by ZPE and BSSE,


Page 17 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


corresponding corrections are necessary. And the relationships between hydrogen–bonding parameters and hydrogen–bonding energies are described in Figures 3 and 4. Table 7. Hydrogen–bonding Energies ∆E (kJ mol−1), ∆EBSSE+ZPE* (kJ mol−1) and Enthalpies ∆H of Three Hard–segment Models Structure N (HB) ∆E BSSE ZPE ∆EBSSE+ZPE References ∆H -42.59 21.53 4.40 -16.66 -35.69 -19.25 28 a 2,4-TDI-MeOH-Ⅰ 1 -42.41 22.43 4.54 -15.44 -26.47 -12.55~-16.7414 a 2,4-TDI-MeOH-Ⅱ 1 -33.09 12.13 3.95 -17.01 -36.02 2,4-TDI-MeOH-Ⅲ 1 -33.54 23.86 4.23 -5.45 -26.93 2,4-TDI-MeOH-Ⅳ 2 1 -29.43 15.10 2.61 -11.72 -24.17 -29.3 24 a, 35.15 28 a 2,6-TDI-MeOH-Ⅰ -21.30 12.64 2.03 -6.63 -17.61 -12.55~-20.92 14 a 2,6-TDI-MeOH-Ⅱ 2 1 -33.00 14.34 3.60 -15.06 -26.68 HDI-MeOH-Ⅰ 2 -59.52 22.82 6.10 -30.60 -52.15 -60.4 41 b HDI-MeOH-Ⅱ 2 -29.51 10.69 3.77 -15.05 -23.32 -22.9 41 b HDI-MeOH-Ⅲ * Corrected by basis set superposition error (BSSE) and zero–point vibrational energy (ZPE); a References for enthalpies ∆H; b References for energies ∆E without BSSE and ZPE corrections.

For complexes 2,4-TDI-MeOH-Ⅰ~Ⅳ, the corrected bond energies (∆EBSSE+ZPE) of three carbonyl hydrogen–bonding complexes are close to each other with the largest difference 1.57 kJ mol-1 between 2,4-TDI-MeOH-Ⅱ and 2,4-TDI-MeOH-Ⅲ, while that of ester –O– hydrogen bonding are much lower. From Figure 2, we know, the ester –O– hydrogen bonding complex 2,4-TDI-MeOH-Ⅳ has two hydrogen bonds, indicating the weak of these hydrogen bonds. For carbonyl hydrogen bonding, complex 2,4-TDI-MeOH-Ⅲ is with the highest bond energy corresponding to parts ‘a’–‘a’ hydrogen bonding, while complex 2,4-TDI-MeOH-Ⅱ is with the lowest bond energy referring to parts ‘b’–‘b’ hydrogen bonding, induced by different steric hindrance of the methyl group on benzene ring. From Table 1, we know, 2,4-TDI-MeOH-Ⅲ has the shortest hydrogen bond, while the hydrogen bond in 2,4-TDI-MeOH-Ⅱ is the longest. And also, from Table 4, we can find that the charge transfer of atoms for 2,4-TDI-MeOH-Ⅲ is the largest, while that for 2,4-TDI-MeOH-Ⅱ is the least. So we can conclude that, in similar chemical environment, the shorter of the hydrogen bond, the more of the charge transfer, and the stronger of the hydrogen bond. The hydrogen-bonding enthalpies ∆H for the hydrogen-bonding complexes 2,4-TDI-MeOH-Ⅰ~Ⅳ from our calculations are much larger than that from the derivations of IR spectra in references

14,28

. Sung suggested that hydrogen bonding to the 4 17

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 32

position of the TDI ring is stronger than the 2 position, in good accordance with our calculations 14

.

For model 2,6-TDI-MeOH, the corrected energy of carbonyl hydrogen bonding is almost twice of that of ester –O– hydrogen bonding. Figure 2 shows that the ester –O– hydrogen bonding complex 2,6-TDI-MeOH-Ⅱ has two hydrogen bonds, also indicating the weak of these hydrogen bonds like complex 2,4-TDI-MeOH-Ⅳ . Compared with hydrogen–bonding enthalpies from experiments, the calculated values are compared well with that in refs. 14,24. For our calculations, the hydrogen-bonding enthalpies ∆H (HB) were calculated using: ∆H (HB) = ∆H(HB dimers) - 2∆H(free molecule), which is more directly than the experimental methods in refs.

14,24,28

. For the value of ∆H from experiment, its accuracy may be affected by

the IR spectra test, while the overlapping of peaks remains a problem, especially for the C═O groups. That can be found in the values from refs. 14,24,28 with big discrepancy. In ref.

14

, Sung pointed that the steric hindrance from the methyl group interferes with the

formation of urethane NH to carbonyl hydrogen bonds in the most stable configuration in 2,6TDI samples and the 2,4-TDI samples may form greater stability of hydrogen bonds with the urethane at the 4 position on the TDI ring. That is in good accordance with our calculation results, which is the hydrogen bonds in 2,4-TDI-MeOH-Ⅰ and Ⅲ should be with much higher strength. For the references 14,24,28, the hydrogen-bonding enthalpies ∆H for 2,6-TDI samples are all higher than that for the 2,4-TDI samples, may be due to the crystallization of 2,6-TDI samples, which induces much higher transition temperature, and affects the calculation of ∆H. For hydrogen–bonding complexes of HDI-MeOH, the corrected bond energy of HDI-MeOH-Ⅱ is higher than twice of that for HDI-MeOH-Ⅰ and HDI-MeOH-Ⅲ, indicating that double carbonyl hydrogen bonds are much stronger than twice of single carbonyl hydrogen bond, which also shows the weak of ester –O– hydrogen bonding. Also from Table 3, we know the hydrogen– bonding lengths of HDI-MeOH-Ⅱ are a little shorter than that of HDI-MeOH-Ⅰ. And from Table 6, we know the charge transfer between O and H for HDI-MeOH-Ⅰ is a little higher than that of HDI-MeOH-Ⅱ, while the charge transfer between N and H for HDI-MeOH-Ⅰ is much higher. The charge transfer between N and H may decrease the strength of hydrogen bond, and that between O and H strengthens the hydrogen bond. Also we can conclude that, the the shorter 18 ACS Paragon Plus Environment

Page 19 of 32

of the hydrogen bond, the stronger of the hydrogen bond, and the balance of charge transfer among H, O and N, determines the properties of hydrogen bond. Comparing with ref.

41

, the

uncorrected values of our calculations are much closer to that in ref. 41 using B3LYP/6-31G(d',p') method without any corrections. Figure 2 shows that complexes 2,4-TDI-MeOH-Ⅰ~Ⅲ, 2,6-TDI-MeOH-Ⅰ, HDI-MeOH-Ⅰ form one hydrogen bond, while complexes 2,4-TDI-MeOH-Ⅳ, 2,6-TDI-MeOH-Ⅱ, HDIMeOH-Ⅱ and HDI-MeOH-Ⅲ have two hydrogen bonds, respectively. To compare the hydrogen–bonding strength, the average hydrogen–bonding energy for each hard segment was calculated, and its order is: ∆E2,4-TDI-MeOH-Ⅳ < ∆E2,6-TDI-MeOH-Ⅱ < ∆EHDI-MeOH-Ⅲ < ∆E2,6-TDI-MeOH-Ⅰ < ∆EHDI-MeOH-Ⅰ < ∆EHDI-MeOH-Ⅱ < ∆E2,4-TDI-MeOH-Ⅱ < ∆E2,4-TDI-MeOH-Ⅰ < ∆E2,4-TDI-MeOH-Ⅲ. It indicates that hydrogen bonding in 2,4-TDI-MeOH model is much stronger, while HDI-MeOH forms medium–strength hydrogen bonds, that means the position of methyl group on benzene ring affects the properties of hydrogen bonds largely, even resulting in much weaker hydrogen bonds for 2,6-TDI-MeOH compared with aliphatic model HDI-MeOH. At the same time, carbonyl hydrogen bonds are much stronger than the ester –O– ones 40. To find out the relationships between hydrogen–bonding parameters and hydrogen–bonding energies, Figures 3, and 4 are deduced from Tables 1~7. Figure 3 shows that the hydrogen– bonding energies decrease with increasing hydrogen–bonding lengths, except that in three carbonyl hydrogen–bonding complexes 2,4-TDI-MeOH Ⅰ~Ⅲ (stronger but with longer bonding lengths). 18

2,4-TDI-MeOH-Ⅰ～Ⅲ

16 14

Energies (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


12 10 8 6 4 2 2.90

2.95

3.00

3.05

3.10

3.15

3.20

Bond lengths (Angstrom)

Figure 3. Relationship between hydrogen–bonding lengths and hydrogen–bonding energies.



Relationship between charge changes on atoms and hydrogen–bonding energies are shown in Figure 4. It is difficult to find a common law for the relationship between charge changes on each atom and hydrogen–bonding energies, there are always a half of complexes showing some differences. For carbonyl hydrogen bonding (see Figures 4a~c), 2,6-TDI-MeOH- Ⅰ shows obvious especially different from the others, lower hydrogen–bonding energies but higher charge changes. For ester –O– hydrogen bonding (see Figures 4d~f), higher charge changes on atom O correspond to larger bonding energies (see Figure 4e). While for Figures 4d and 4f, we can draw similar conclusion with complex 2,4-TDI-MeOH-Ⅵ as an exception. Figures 4a and 4c shows similar trend, while Figures 4d and 4f also have the same trend. All are refering to the relationship between charge changes on atoms H, N and hydrogen–bonding energies, that means the charge changes on atoms H and N have close links. a

b 17

17

H (C=O)

15

HDI-MeOH-Ⅱ

HDI-MeOH-Ⅰ

14

13

12

11 0.048

C=O

16

Energies (kJ/mol)

Energies (kJ/mol)

16

15

13

12

2,6-TDI-MeOH-Ⅰ 0.050

0.052

0.054

0.056

2,4-TDI-MeOH-Ⅱ HDI-MeOH-Ⅰ

14

0.058

0.060

0.062

0.064

11 0.005

0.066

2,6-TDI-MeOH-Ⅰ 0.010

Charge Changes

d 17

0.015

0.020

0.025

0.030

0.035

Charge Changes

c

8

N (C=O)

H (-O-) 7

16

15

HDI-MeOH-Ⅱ

Energies (kJ/mol)

Energies (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 32

HDI-MeOH-Ⅰ 14

13

12

2,6-TDI-MeOH-Ⅰ

6

5

4

3

2,4-TDI-MeOH-Ⅳ 2 0.0400 0.0405 0.0410 0.0415 0.0420 0.0425 0.0430 0.0435 0.0440 0.0445

11 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 0.042 0.044

Charge Changes

Charge Changes


Page 21 of 32

e

8

f

8

-O-

N (-O-)

7

7

6

6

Energies (kJ/mol)

Energies (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5

4

3

2 0.0168

5

4

2,4-TDI-MeOH-Ⅳ 3

2

0.0172

0.0176

0.0180

0.0184

0.015

Charge Changes

0.020

0.025

0.030

0.035

Charge Changes

Figure 4. Relationship between charge changes on atoms and hydrogen–bonding energies.

For hydrogen–bonding complexes, the BSSE corrections are in the range 36.2%~71.1% of the uncorrected ∆E. At the same time, the proportions of ZPE to the uncorrected ∆E are in the range 8.6%~12.8%. The BSSE corrections are much larger than that of the ZPE corrections, and both corrections are necessary for the calculations of hydrogen–bonding energies. The calculated hydrogen–bonding enthalpies are comparable with references

14,24,28,41

, which confirms the

validity of our calculations.

3.4. IR Spectra. Hydrogen bonding in polyurethanes has been extensively studied using IR spectroscopy 23-28, and is evidenced by a frequency shift to values lower than those observed when these groups are free (i.e., not hydrogen bonded). The frequency difference between the free group and that of the hydrogen–bonded one (∆ν) is a measure of the average strength of the interactions. In this study, the IR spectra of different diisocyanate based hard–segment models were obtained through frequency calculations of the optimized structures (see Figure 5). The frequency shifts are listed in Table 8. For free hard-segment molecules, there are mainly three IR regions involved in hydrogen bonding (see Figures 5a~c): N–H stretching vibrations at 3476 cm−1 for 2,4-TDI-MeOH (3460 cm−1 in 27, 3450 cm−1 in 28), 3505 cm−1 for 2,6-TDI-MeOH (3460 cm−1 in

27

, 3450 cm−1 in

28

), 3485 cm−1 for HDI-MeOH (3435 cm−1 in

18

, 3349 cm−1 in

C═O stretching vibrations at 1757 cm−1 for 2,4-TDI-MeOH (1740 cm−1 in

27

20,63

, 1735 cm−1 in

),

28

)

and 2,6-TDI-MeOH (1740 cm−1 in 27, 1735 cm−1 in 28), 1747 cm−1 for HDI-MeOH (1741 cm−1 in 19

, 1734 cm−1 in 18), –O– stretching vibrations at 1056 cm−1 for 2,4-TDI-MeOH (1080 cm−1 in 28),

1017 cm−1 for 2,6-TDI-MeOH (1080 cm−1 in

28

), 1046 cm−1 and 1017 cm−1 for HDI-MeOH,



respectively. All the calculated IR absorptions for three types of free functional groups are compared well with the experimental data, and the differences are in range of 6~63 cm–1. The analysis of the IR absorption of the functional groups are complicated due to the presence of several types of hydrogen bonds. a

500

1000

1500

2000

2500

3000

3500

2,4-TDI-MeOH-Ⅳ

600 1046

3409

300 0

2,4-TDI-MeOH-Ⅲ

600

3371

1719

300

Intensities (KM/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 32

0 800

2,4-TDI-MeOH-Ⅱ 1728

400

3380

0

2,4-TDI-MeOH-Ⅰ

1000

1719

500 0 600

3371

2,4-TDI-MeOH 1757

300 1056

3476

0 500

1000

1500

2000

2500

3000

-1

Wavenumbers (cm )


3500

Page 23 of 32

b

500 1000

1000

1500

2000

2500

3000

3500

2,6-TDI-MeOH-Ⅱ 3399

500 1017


0 1500

2,6-TDI-MeOH-Ⅰ

1000

1719

500

3371

0

2,6-TDI-MeOH 500

1757

3505

0 500

1000

1500

2000

2500

3000

3500

3000

3500

-1

Wavenumbers (cm )

500

c 900

1000

1500

2000

2500

HDI-MeOH-Ⅲ 3409

600 300

1017

0 900


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


HDI-MeOH-Ⅱ 1719

600

3399

300 0 900

HDI-MeOH-Ⅰ 1719

600

3389

300 0

HDI-MeOH

600 300

1747

1046

3485

0 500

1000

1500

2000

2500

3000

3500

-1

Wavenumbers (cm )

Figure 5. IR spectra for the hydrogen bonding complexes of three diisocyanate based hard–segment models obtained by DFT calculations.



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Figure 5a shows the IR spectra for hydrogen–bonding complexes of 2,4-TDI-MeOH-Ⅰ～ Ⅳ. Looking at the spectra, we can find that several strong absorption peaks locate at around 3371 cm−1, 3380 cm−1 (3320 cm−1 in 27, 3310 cm−1 in 28), and 3409 cm−1 arising from the N–H groups hydrogen bonded to carbonyl groups and ester –O– group, respectively. Free N–H stretching vibration appears as a weak shoulder. The frequency shifts are in range of 96~105 cm−1 for carbonyl hydrogen bonding (140 cm−1 in

28

, see Table 8) and 68 cm−1 for ester –O–

hydrogen bonding, respectively. It indicates that carbonyl hydrogen bonds are much stronger than the ester –O– one. The calculated IR absorption peaks of N–H hydrogen bonded with C═O are a little higher than that from experimental test 27,28 with the largest difference 70 cm–1, while the calculated IR frequency shifts are much closer to the experimental value with the difference 35 cm–1. Due to the overlap of IR absorptions in experiment, the absorption peaks for N–H hydrogen bonded with –O– are not found for reference. For complexes 2,4-TDI-MeOH-Ⅰ～Ⅲ, in the absorption region of C═O, three new absorptions appear at lower frequencies 1719 cm−1 for 2,4-TDI-MeOH-Ⅰ and 2,4-TDI-MeOH-Ⅲ, and 1728 cm−1 for 2,4-TDI-MeOH-Ⅱ (1720 cm−1 in

27

, 1708 cm−1 in

28

), due to forming hydrogen bonds with N–H, respectively. The

calculated IR absorption peaks of C═O are compared well with the experimental value, and the largest difference is 20 cm–1. Frequency shifts for both N–H and C═O in 2,4-TDI-MeOH-Ⅰ and 2,4-TDI-MeOH-Ⅲ are the same, which may be due to that both O–H groups are from part ‘a’, and the effect of the source of C═O groups is little. The frequency shifts for 2,4-TDI-MeOH-Ⅱ is smaller than that of 2,4-TDI-MeOH-Ⅰ and 2,4-TDI-MeOH-Ⅲ, in accordance with the orders of hydrogen–bond distances, atom charge changes and hydrogen–bonding energies, indicating the weak of hydrogen bonding in 2,4-TDI-MeOH-Ⅱ arised by the steric hindrance of methyl group on benzene ring. In the ester –O– absorption region, a weak absorption peak at 1046 cm−1 is found, with a frequency shift 10 cm−1 due to the formation of hydrogen bond with N–H. Figure 5b shows IR spectra for hydrogen–bonding complexes 2,6-TDI-MeOH-Ⅰ&Ⅱ. In the N–H absorption region, we can find that two strong absorption peaks locate at around 3371 cm−1 and 3399 cm−1 for two hydrogen–bonding complexes (3300 cm−1 in 27,28, 3290 cm−1 in 25), arising from hydrogen bonded to carbonyl group and ester –O– group, respectively. The free N– H stretching vibration appears as a weak shoulder. The frequency shifts are 134 cm−1 (150 cm−1 in

28

) and 106 cm−1 for two types of hydrogen bonding, respectively (see Table 8). It indicates 24 ACS Paragon Plus Environment

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that carbonyl hydrogen bond is a stronger than the ester –O– one, in accordance with their hydrogen–bonding energies. The calculated IR absorption peaks of N–H hydrogen bonded with C═O are much higher than that from IR test 25,27,28 with the largest difference 109 cm–1 25, while the IR frequency shifts from two methods are comparable with the difference 16 cm–1. For complex 2,6-TDI-MeOH-Ⅰ, a new absorption appears at lower frequency 1719 cm−1 (1700 cm−1 in 27, 1706 cm−1 in 28) in the absorption region of C═O, due to hydrogen bonded to N–H. The IR absorption peaks of C═O from two methods are compared well with the largest difference 19 cm–1

27

. For complex 2,6-TDI-MeOH-Ⅱ, no new absorption peak lower than 1017 cm−1 is

found in the ester –O– absorption region, indicating the weak of the corresponding hydrogen bond. Figure 5c shows IR spectra for hydrogen–bonding complexes HDI-MeOH-Ⅰ～Ⅲ. From the spectra, we can find that two new absorption peaks locate at around 3389 cm−1, 3399 cm−1 (3329 cm−1 in

20

, 3417 cm−1 in

18

, 3323 cm−1 in

19

, 3328 cm−1 in

63

) arising from N–H groups

hydrogen bonded to carbonyl groups, while one new absorption peak at 3409 cm−1 is found in spectra of HDI-MeOH-Ⅲ due to forming ester –O– hydrogen bonding, respectively. Free N–H stretching vibration appears as a weak shoulder. The frequency shifts of N–H are in range of 86~96 cm−1 for carbonyl hydrogen bonding (18 cm−1 in 18, 20 cm−1 in 20) and 76 cm−1 for ester – O– hydrogen bonding (see Table 8), respectively. It also indicates that carbonyl hydrogen bonds are much stronger than the ester –O– ones. The frequency shifts have some inconsistencies with hydrogen bonding energies. From the energy analysis, we know, double carbonyl hydrogen bonding is a little stronger than twice of the single one, where the frequency shift for the former is smaller. The calculated IR absorption peaks of N–H hydrogen bonded with C═O are in the range of 3323~3417 cm–1 by experiment 18-20,63, while the IR frequency shifts by calculations are much larger than that from experiment with the biggest difference 78 cm–1. It is seems that the hydrogen–bonding interactions of HDI-MeOH characterized by FTIR are much weaker than that of two types of TDI hard segments. In the absorption region of C═O, two new absorption peaks appear at lower frequencies, 1719 cm−1 for both HDI-MeOH-Ⅰ and HDI-MeOH-Ⅱ (1724 cm−1 in 18, 1718 cm−1 in 19, 1706 cm−1 in 63), due to the forming of hydrogen bonding with N–H. The IR absorption peaks of C═O by two methods are compared well with the largest difference 13 cm–1. In absorption region of –O–, no new absorption peak aroud 1046 cm−1 or 1017 cm−1 is found, indicating the weak of ester –O– hydrogen bond. 25 ACS Paragon Plus Environment


Table 8. IR Frequency Shifts (∆ν) for Different Functional Groups due to Hydrogen Bonding* Structure N–H C═O –O– Refs. for ∆ν 105a 38b – N–H: 140 in 28 2,4-TDI-MeOH-Ⅰ 96b 29b – 2,4-TDI-MeOH-Ⅱ a a 105 38 – 2,4-TDI-MeOH-Ⅲ 64a – 10b 2,4-TDI-MeOH-Ⅳ 134 38 – N–H: 150 in 28 2,6-TDI-MeOH-Ⅰ 106 – – 2,6-TDI-MeOH-Ⅱ 96 28 – N–H: (18 cm−1 in18, 20 cm−1 in 20) HDI-MeOH-Ⅰ 86 28 – HDI-MeOH-Ⅱ 76 – – HDI-MeOH-Ⅲ * Superscripts a, b represent atoms from parts ‘a’ and ‘b’, respectively.

For Table 8, two TDI-MeOH models have much higher frequency shifts than the HDIMeOH ones, indicating the aromatic hard segments has much higher activities than the aliphatic ones in hydrogen–bonding interactions, in good accordance with experimental evidence

18,20,28

.

Figure 6 shows the relationship between IR frequency shift and hydrogen–bonding energies. It seems that the larger of the frequency shift the higher of the hydrogen bonding energies, except HDI-MeOH- Ⅰ & 2,6-TDI-MeOH- Ⅰ in Figure 6a, and 2,6-TDI-MeOH- Ⅱ in Figure 6b. Although it is generally true that the frequency shifts induced by the hydrogen bonding are related to the strength of the bonding, it does not warrant that hydrogen–bonding strengths can be precisely estimated from the frequency shifts 43.

a

17

b

N-H

16

17

C=O

15 14

2,6-TDI-MeOH-Ⅰ

13

16

HDI-MeOH-Ⅰ

12

Energies (kJ/mol)

Energies (kJ/mol)

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11 10 9 8 7 6

15

14

13

2,6-TDI-MeOH-Ⅱ

5

2,6-TDI-MeOH-Ⅰ

12

4 3 2 60

11

70

80

90

100

110

120

130

140

28

-1

Frequency Shifts (cm )

30

32

34

36 -1

Frequency Shifts (cm )

Figure 6. Relationship between IR frequency shifts and hydrogen–bonding energies.


38

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From above analysis, we can find that all the regions of functional groups involved in hydrogen bonding show some frequency shifts, which confirms the formation of hydrogen bonding showed in Figure 2, and compares well with references. The DFT calculations can offer more specific details to distinguish different types of hydrogen bonding from IR spectra. For two TDI-MeOH hard–segment models, the position of methyl group on the benzene ring affects the forming of hydrogen bonding due to its steric hindrance and induced electronpositivity, and results in different frequency shifts. The frequency shifts of ester –O– group are not obvious, maybe due to the weak of this type of hydrogen bonding. The frequency absoprption obtained by DFT calculations are well compared with experimental data, which confirms the validity of our calculations.

4. CONCLUSIONS In present study, the hydrogen–bonding interactions of three widely used diisocyanate based hard–segment models in polyurethane, 2,4-TDI-MeOH, 2,6-TDI-MeOH, and HDI-MeOH, were systematically investigated by DFT calculations. The hard–segment models 2,4-TDI-MeOH and 2,6-TDI-MeOH, both with benzene ring, have much longer hydrogen bonds due to the steric hindrance of benzene ring. Different position of methyl group on benzene ring also induces different hydrogen–bonding forms for two TDIMeOH models. The balance of charge transfer among H, O and N determines the properties of hydrogen bond, and dominates the charge rearrangement in all hydrogen–bonding complexes. The hydrogen bonding formed in 2,4-TDI-MeOH is the strongest among the hard-segment dimers, and HDI-MeOH forms medium–strength hydrogen bonds. The carbonyl hydrogen bonds are much stronger than the ester –O– ones. The appearance of new bands in lower frenquency side of free N–H, C═O and –O– absorption is evidence for the formation of hydrogen bond, which can be well forecasted by the DFT methods with more specific details, but precise estimation of hydrogen–bonding strength cannot be obtained from the frequency shifts. From this comparative study, the inherent law for hydrogen bonding can be found, with similar chemical environment, the shorter of the hydrogen bond, the more of the charge transfer, the larger of the frequency shift, and the stronger of the hydrogen bond. This present study can supply guidance for the selection of hard segment in polyurethane synthesis involving hydrogen bonding and in-depth understanding of the hydrogen–bonding 27 ACS Paragon Plus Environment


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mechanism in polyurethane hard segments. The distribution of different types of hydrogen bonding and their effect on the phase separation in shape memory polyurethanes will be investigated in our future work.

ACKNOWLEDGEMENTS The authors wish to express their gratitude for the support of a Ph.D. studentship from the Hong Kong Polytechnic University, the Hong Kong Research Grants Council projects (RGCGRF/5161/11E, RGC-GRF/5162/12E, RGC-GRF/d00914), National Natural Science Foundation of China (51373147), and Shenzhen biological, new energy, new material industry development special funds of China (JC201104210132A).

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Hydrogen-Bonding Interactions in Hard Segments of Shape Memory

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