Computational Characterization of Nylon 4, a Biobased and Biodegradable Polyamide Superior to Nylon 6

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1 Supporting Information Computational Characterization of Nylon 4, a Biobased and Biodegradable Polyamide Superior to Nylon 6 Yuichiro Fukuda and Yuji Sasanuma Department of Applied Chemistry and Biotechnology, Graduate School and Faculty of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba , Japan Figure S1. Molecular weight distribution of the nylon 4 sample used in this study. S1

2 Table S1. 13 C NMR Chemical Shifts of Conformers of the Model Compound, ABAMA, Evaluated from MO Calculations a conformer δ i k b (ppm) bond chemical species k HNC=O ω CH β 2 CH α 2 CH 2 HNC=O gas 1 t t t t g + g t g g g + t t g + t g g + t g g + g + t g + g + t g + g + g g + g + g g + g + g g + g t g + g t g + g g g + g g average, < δ i > ,2,2-trifluoroethanol 1 t t t t g + g t g g g + t t g + t g g + t g g + g + t g + g + t g + g + g g + g + g g + g + g g + g t g + g t g + g g g + g g average, < δ i > a At the B3LYP/ G(3df,3pd) level. b Relative to δ (0 ppm) of tetramethylsilane (TMS). The chemical shift of TMS was also calculated at the B3LYP/ G(3df,3pd) level. S2

3 Table S2. Fractional Coordinates of the α Form of Nylon 4, Optimized by the B3LYP D Calculations under the Periodic Boundary Condition a atom x/a y/b z/c C C C C C C C C C C C C C C C C N N N N O O O O H H H H H H H H H H H H H H H H H H H H H H H H H H H H a The monoclinic cell of space group P2 1. The lattice constants are a = 9.50 Å, b = Å, c = 7.39 Å, and β = The unit cell includes eight monomeric units. S3

4 Table S3. Comparison of Experimental and Calculated Cartesian Coordinates of Atoms in the Unit Cell of the α Form of Nylon 4 experiment a calculation b x (Å) y (Å) z (Å) x (Å) y (Å) z (Å) c (Å) C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C N N N N N N N N O O O O O O O O a Fredericks, R. J.; Doyne, T. H.; Sprague, R. S. J. Polym. Sci., Part A , 4, The monoclinic cell of space group P2 1. The lattice constants are a = 9.29 Å, b = Å, c = 7.97 Å, and β = b This study. a = 9.50 Å, b = Å, c = 7.39 Å, and β = c = [ ( x) 2 + ( y) 2 + ( z) 2] 1/2, where x, y and z are the differences in the x, y, and z coordinates between experiment and calculation. The mean value of all s, < >, is Å. S4

5 Table S4. Observed and Calculated Structure Factors of the α Form of Nylon 4 Fredericks et al. a this study no h k l F obs F calc F obs F calc F calc b F sum calc F obs F sum calc b a By X-ray diffraction (Fredericks, R. J.; Doyne, T. H.; Sprague, R. S. J. Polym. Sci.: Part A , 4, ). The isotropic temperature factor (B) was set equal to 0.80 (Å 2 ). The R factor was calculated from R = F obs F calc / F obs to be b For the crystal structure optimized at the B3LYP-D/6-31G(d,p) level. B = 0.80 (Å 2 ) and R = F obs F sum calc / F obs = S5

6 Table S5. Crystal Energies, Single Chain Energies, Basis Set Superposition Errors, and Interaction Energies of Nylons 4 and 6 crystal form basis set E Crystal /Z a E SC{SC}+D a BSSE b E CP ( ) b nylon 4 α 6 31G(d,p) pob_tzvp nylon 6 α 6 31G(d,p) pob_tzvp γ 6 31G(d,p) pob_tzvp a In au per repeating unit b In kcal per mol of repeating unit. S6

7 Appendix A. Stiffness (C) and compliance (S) tensors of the α form of nylon 4 and the α and γ forms of nylon 6 The stiffness (C) and compliance (S) tensors are defined in the orthogonal x, y, and z system. The unit vectors (e a, e b, e c ) along the a, b, and c axes of monoclinic cells of nylons 4 and 6 are expressed in the (x, y, z) coordinates as e a = (1, 0, 0) (S1) and e b = (0, 1, 0) e c = (cos β, 0, sin β) where β is the lattice constant. Young s modulus E(l 1,l 2,l 3 ) in an arbitrary direction defined with the unit vector (l 1, l 2, l 3 ) in a monoclinic lattice can be calculated from 1 E(l 1,l 2,l 3 ) = l 4 1 s l 2 1 l2 2 s l 2 1 l2 3 s l 3 1 l 3 s 15 + l 4 2 s l 2 2 l2 3 s l 1 l 2 2 l 3 s 25 + l 4 3 s l 1 l 3 3 s 35 + l 2 2 l2 3 s l 1 l 2 2 l 3 s 46 + l 2 1 l2 3 s 55 + l 2 1 l2 2 s 66 where s ij is the (i, j) element of the compliance tensor. For example, Young s modulus E b parallel to the b axis (chain axis) can be derived from the above equation with l 1 = 0, l 2 = 1, and l 3 = 0. (a) Stiffness (C) and compliance (S) tensors of the α form of nylon 4: C = (GPa) S = (TPa 1 ) (S6) The above S tensor yields crystalline moduli in the a, b, and c directions as E a = GPa, E b = GPa, and E c = GPa. (b) Stiffness and compliance tensors of the α form of nylon 6: (S2) (S3) (S4) (S5) S = C = (GPa) (TPa 1 ) (S7) (S8) S7

8 The above S tensor yields crystalline moduli in the a, b, and c directions as E a = GPa, E b = GPa, and E c = GPa. (c) Stiffness and compliance tensors of the γ form of nylon 6: C = (GPa) S = (TPa 1 ) (S10) The above S tensor yields crystalline moduli in the a, b, and c directions as E a = GPa, E b = GPa, and E c = GPa. (S9) S8

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