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 263-8522, Japan Figure S1. Molecular weight distribution of the nylon 4 sample used in this study. S1
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 3 4 5 HNC=O ω CH β 2 CH α 2 CH 2 HNC=O gas 1 t t t 173.9135 46.4051 28.2943 36.5915 176.8719 2 t g + g + 173.7832 40.8084 30.6545 36.0875 174.1922 3 t g g + 174.2290 47.9885 27.3902 40.0637 181.6506 4 g + t t 173.4437 44.8944 33.7171 39.9360 176.7148 5 g + t g + 176.9749 46.0270 28.7512 37.2951 175.3528 6 g + t g 173.6031 43.3592 29.7211 36.8787 176.8504 7 g + g + t 173.5425 46.8200 32.0104 40.4142 176.9259 8 g + g + t 173.1857 43.6120 33.7603 40.6507 176.5110 9 g + g + g + 174.3774 43.8089 26.5642 33.3929 177.8080 10 g + g + g + 173.5625 40.4052 31.6140 38.3171 178.8105 11 g + g + g 173.3026 44.6341 32.8329 42.4355 180.2281 12 g + g t 174.2839 41.7282 33.4873 38.4436 177.9228 13 g + g t 174.2940 41.7391 33.5010 38.4771 177.8924 14 g + g g + 176.3471 44.8825 32.4588 39.3313 180.9882 15 g + g g 177.2895 43.3590 35.4151 37.3163 178.3155 average, < δ i > 176.4187 44.1049 33.3393 38.1765 179.2844 2,2,2-trifluoroethanol 1 t t t 178.1920 46.7026 28.3846 36.9040 180.7097 2 t g + g + 178.2390 41.5699 29.4948 37.6419 179.3136 3 t g g + 177.8612 48.4756 27.4363 40.2773 184.2477 4 g + t t 177.6938 45.1159 34.0629 40.4974 180.4926 5 g + t g + 180.4616 45.8477 28.3613 38.9216 180.4441 6 g + t g 177.8124 44.1771 30.3456 37.2735 179.9678 7 g + g + t 178.0633 46.8262 32.6491 41.0908 181.0202 8 g + g + t 177.6604 43.7242 34.1485 40.9532 180.7593 9 g + g + g + 178.8039 44.4989 27.4848 33.8500 181.0278 10 g + g + g + 177.3925 41.5772 31.8804 38.4450 181.2281 11 g + g + g 177.5338 44.7751 33.2327 42.4900 184.0302 12 g + g t 178.3741 42.2622 33.4061 38.9209 181.3354 13 g + g t 178.3818 42.2723 33.4208 38.9520 181.3012 14 g + g g + 179.6048 45.4477 32.8887 40.6706 184.4654 15 g + g g 180.6242 43.3885 35.1449 39.0838 182.8335 average, < δ i > 179.3005 44.9210 32.1506 39.4077 182.8062 a At the B3LYP/6-311++G(3df,3pd) level. b Relative to δ (0 ppm) of tetramethylsilane (TMS). The chemical shift of TMS was also calculated at the B3LYP/6-311++G(3df,3pd) level. S2
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 0.060 0.469 0.012 C 0.042 0.268 0.024 C 0.048 0.127 0.019 C 0.053 0.167 0.009 C 0.063 0.309 0.472 C 0.042 0.010 0.472 C 0.047 0.096 0.496 C 0.055 0.111 0.500 C 0.458 0.005 0.028 C 0.453 0.101 0.004 C 0.437 0.196 0.028 C 0.445 0.106 0.000 C 0.458 0.273 0.476 C 0.452 0.378 0.481 C 0.440 0.474 0.488 C 0.447 0.328 0.491 N 0.019 0.073 0.011 N 0.015 0.205 0.496 N 0.485 0.299 0.004 N 0.481 0.423 0.489 O 0.186 0.171 0.002 O 0.190 0.107 0.484 O 0.310 0.397 0.016 O 0.314 0.325 0.498 H 0.151 0.315 0.327 H 0.106 0.015 0.431 H 0.128 0.011 0.324 H 0.132 0.100 0.349 H 0.106 0.102 0.403 H 0.124 0.204 0.495 H 0.368 0.377 0.332 H 0.128 0.272 0.172 H 0.131 0.372 0.168 H 0.112 0.380 0.077 H 0.121 0.314 0.424 H 0.351 0.469 0.342 H 0.382 0.470 0.408 H 0.125 0.074 0.006 H 0.379 0.191 0.076 H 0.349 0.190 0.173 H 0.394 0.106 0.097 H 0.368 0.105 0.151 H 0.372 0.007 0.176 H 0.394 0.010 0.069 H 0.376 0.301 0.005 H 0.118 0.034 0.092 H 0.149 0.035 0.158 H 0.372 0.276 0.328 H 0.394 0.263 0.428 H 0.388 0.384 0.423 H 0.106 0.259 0.072 H 0.375 0.421 0.494 a The monoclinic cell of space group P2 1. The lattice constants are a = 9.50 Å, b = 12.36 Å, c = 7.39 Å, and β = 111.6. The unit cell includes eight monomeric units. S3
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 0.386 6.120 0.051 0.535 6.561 0.106 0.469 C 0.386 0.000 0.051 0.535 0.380 0.106 0.412 C 0.386 3.623 0.051 0.330 3.315 0.180 0.339 C 0.386 2.497 0.051 0.330 2.865 0.180 0.394 C 0.348 1.248 0.051 0.396 1.565 0.152 0.336 C 0.348 4.872 0.051 0.396 4.616 0.152 0.279 C 0.348 2.362 0.051 0.527 2.066 0.033 0.356 C 0.348 3.758 0.051 0.527 4.114 0.033 0.407 C 1.267 3.672 3.677 1.012 3.819 3.581 0.310 C 1.267 2.448 3.677 1.012 2.361 3.581 0.286 C 1.267 0.049 3.677 1.211 0.123 3.572 0.140 C 1.267 6.071 3.677 1.211 6.058 3.572 0.120 C 1.258 1.200 3.575 1.094 1.189 3.412 0.232 C 1.258 4.920 3.575 1.094 4.992 3.412 0.242 C 1.258 1.310 3.575 1.002 1.373 3.390 0.322 C 1.258 4.810 3.575 1.002 4.807 3.390 0.316 C 4.250 0.000 0.051 4.431 0.066 0.025 0.194 C 4.250 6.120 0.051 4.431 6.115 0.025 0.182 C 4.259 1.248 0.051 4.313 1.246 0.185 0.242 C 4.259 4.872 0.051 4.313 4.935 0.185 0.250 C 4.250 2.497 0.051 4.231 2.418 0.016 0.088 C 4.250 3.623 0.051 4.231 3.762 0.016 0.145 C 4.250 1.236 0.051 4.221 1.316 0.207 0.178 C 4.250 4.884 0.051 4.221 4.864 0.207 0.160 C 2.598 3.672 3.677 2.890 3.372 3.417 0.493 C 2.598 2.448 3.677 2.890 2.809 3.417 0.532 C 2.561 4.920 3.677 2.823 4.672 3.445 0.429 C 2.561 1.200 3.677 2.823 1.508 3.445 0.467 C 2.598 6.071 3.677 2.685 6.504 3.491 0.479 C 2.598 0.049 3.677 2.685 0.324 3.491 0.425 C 2.598 3.684 3.677 2.693 4.057 3.630 0.388 C 2.598 2.436 3.677 2.693 2.123 3.630 0.330 N 0.324 1.236 0.044 0.143 0.896 0.084 0.387 N 0.324 4.884 0.044 0.143 5.284 0.084 0.441 N 1.329 2.436 3.670 1.371 2.535 3.343 0.344 N 1.329 3.684 3.670 1.371 3.645 3.343 0.332 N 4.321 3.758 0.044 4.590 3.702 0.254 0.405 N 4.321 2.362 0.044 4.590 2.478 0.254 0.417 N 2.629 4.810 3.670 3.076 5.227 3.512 0.631 N 2.629 1.310 3.670 3.076 0.953 3.512 0.593 O 1.397 2.362 0.196 1.761 2.112 0.097 0.453 O 1.397 3.758 0.196 1.761 4.068 0.097 0.489 O 0.077 1.310 3.430 0.233 1.329 3.558 0.336 O 0.077 4.810 3.430 0.233 4.852 3.558 0.338 O 3.069 4.884 0.196 2.986 4.909 0.039 0.179 O 3.069 1.236 0.196 2.986 1.272 0.039 0.181 O 1.417 3.684 3.822 1.458 4.011 3.500 0.461 O 1.417 2.436 3.822 1.458 2.169 3.500 0.420 a Fredericks, R. J.; Doyne, T. H.; Sprague, R. S. J. Polym. Sci., Part A-2 1966, 4, 899 911. The monoclinic cell of space group P2 1. The lattice constants are a = 9.29 Å, b = 12.24 Å, c = 7.97 Å, and β = 114.5 b This study. a = 9.50 Å, b = 12.36 Å, c = 7.39 Å, and β = 111.6. 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 0.341 Å. S4
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 1 2 0 0 171.9 151.6 20.3 134.00 134.00 37.90 2 0 0 2 411.3 402.4 8.9 243.80 381.40 29.90 2 0 2 137.60 3 2 0 2 172.0 127.8 44.2 74.86 138.58 33.42 4 0 2 63.72 4 4 0 0 55.2 40.4 14.8 35.28 35.28 19.92 5 2 0 4 67.6 119.4 51.8 70.64 70.64 3.04 6 0 0 4 178.1 166.9 11.2 122.50 186.11 8.01 4 0 4 63.61 7 4 0 2 98.2 63.7 34.5 35.53 59.80 38.40 6 0 2 24.27 8 2 0 4 116.7 100.2 16.5 44.14 100.10 16.60 6 0 4 45.41 6 0 0 10.55 9 4 0 6 67.6 117.8 50.2 40.37 57.89 9.71 2 0 6 17.52 10 6 0 6 128.9 142.8 13.9 39.75 135.37 6.47 6 0 2 0.67 4 0 4 21.58 0 0 6 73.37 11 2 1 1 61.5 85.5 24.0 39.78 41.96 19.54 1 1 1 2.18 12 1 2 1 43.0 70.9 27.9 1.84 50.64 7.64 0 2 1 48.80 13 2 2 1 67.7 9.9 57.8 30.86 36.30 31.40 1 2 1 0.99 2 2 0 4.44 14 2 2 1 30.8 38.9 8.1 17.91 39.30 8.50 3 2 1 21.39 15 3 2 3 92.1 107.1 15.0 21.66 117.53 25.43 0 2 3 50.65 4 2 1 19.80 2 2 2 2.44 3 2 1 20.68 4 2 2 2.29 16 3 2 5 104.4 33.0 71.4 17.07 32.15 72.25 2 2 5 4.82 5 2 5 4.89 6 2 2 5.37 17 1 3 0 12.3 46.5 34.2 14.26 14.26 1.96 18 2 3 1 24.5 63.3 38.8 11.70 35.18 10.68 1 3 1 4.76 2 3 0 18.72 19 2 3 1 36.7 65.9 29.2 7.76 34.96 1.74 3 3 1 12.93 1 3 2 14.27 20 3 3 3 61.3 89.1 27.8 0.97 70.18 8.88 4 3 1 14.76 2 3 2 16.25 3 3 1 11.42 4 3 2 26.78 21 2 4 1 49.1 25.1 24.0 0.31 19.81 29.29 3 4 1 19.50 22 2 5 1 115.8 144.6 28.8 52.94 134.95 19.15 1 5 1 82.01 23 2 5 1 149.6 129.5 20.1 52.69 122.40 27.20 3 5 1 69.71 24 3 5 3 193.0 213.0 20.0 35.98 130.26 62.74 0 5 3 8.29 4 5 1 28.31 3 5 1 57.68 25 5 5 1 130.3 87.8 42.5 48.86 73.05 57.25 4 5 1 24.19 26 6 5 1 183.4 252.9 69.5 32.39 204.93 21.53 6 5 3 34.49 4 5 5 17.06 1 5 5 38.83 3 5 3 37.66 5 5 1 44.50 27 1 5 5 231.6 180.4 51.2 38.83 87.22 144.38 4 5 3 21.63 6 5 5 26.76 28 2 6 1 30.6 22.4 8.2 17.43 56.71 6.11 3 6 1 39.28 a By X-ray diffraction (Fredericks, R. J.; Doyne, T. H.; Sprague, R. S. J. Polym. Sci.: Part A-2 1966, 4, 899-911). 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 0.273. 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 = 0.253. S5
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) 286.515441220375 286.477256419110 6.06 17.90 pob_tzvp 286.586795157450 286.549368642830 5.24 18.25 nylon 6 α 6 31G(d,p) 365.098263404000 365.052643041425 7.38 21.25 pob_tzvp 365.186300060362 365.139582003650 7.67 21.65 γ 6 31G(d,p) 365.097956318000 365.053971418045 7.10 20.50 pob_tzvp 365.186199205100 365.140016606050 8.20 20.78 a In au per repeating unit b In kcal per mol of repeating unit. S6
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 11 + 2l 2 1 l2 2 s 12 + 2l 2 1 l2 3 s 13 + 2l 3 1 l 3 s 15 + l 4 2 s 22 + 2l 2 2 l2 3 s 23 + 2l 1 l 2 2 l 3 s 25 + l 4 3 s 33 + 2l 1 l 3 3 s 35 + l 2 2 l2 3 s 44 + 2l 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 = 61.186 6.531 6.222 0.000 3.810 0.000 335.146 4.647 0.000 0.477 0.000 25.998 0.000 1.575 0.000 2.091 0.000 0.477 3.027 0.000 3.701 (GPa) 18.6498 0.3179 6.0219 0.0000 26.6581 0.0000 2.9967 0.4199 0.0000 0.6541 0.0000 41.7523 0.0000 29.2434 0.0000 S = 492.7935 0.0000 63.5296 (TPa 1 ) (S6) 379.2492 0.0000 278.3835 The above S tensor yields crystalline moduli in the a, b, and c directions as E a = 53.62 GPa, E b = 333.7 GPa, and E c = 16.76 GPa. (b) Stiffness and compliance tensors of the α form of nylon 6: (S2) (S3) (S4) (S5) S = C = 50.711 1.224 6.989 0.000 3.215 0.000 318.845 7.972 0.000 0.531 0.000 23.811 0.000 2.247 0.000 3.567 0.000 0.386 3.824 0.000 1.661 22.4729 0.0962 8.9029 0.0000 24.1105 0.0000 3.1633 1.1154 0.0000 0.2972 0.0000 48.3550 0.0000 35.7377 0.0000 287.5556 0.0000 66.7480 302.7279 0.0000 617.5534 (GPa) (TPa 1 ) (S7) (S8) S7
The above S tensor yields crystalline moduli in the a, b, and c directions as E a = 44.50 GPa, E b = 316.1 GPa, and E c = 19.41 GPa. (c) Stiffness and compliance tensors of the γ form of nylon 6: C = 29.444 11.011 10.803 0.000 3.403 0.000 160.175 18.294 0.000 9.504 0.000 30.412 0.000 8.392 0.000 5.322 0.000 0.298 9.722 0.000 9.011 (GPa) 39.4549 1.7483 11.3946 0.0000 5.6850 0.0000 8.3710 8.9811 0.0000 16.5484 0.0000 57.3050 0.0000 54.2589 0.0000 S = 188.2514 0.0000 6.2176 (TPa 1 ) (S10) 167.8669 0.0000 111.1795 The above S tensor yields crystalline moduli in the a, b, and c directions as E a = 25.35 GPa, E b = 119.5 GPa, and E c = 38.11 GPa. (S9) S8