Polymers torsional angle

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

Geometric Examination. The polymer chemist needs to examine the various characteristics of the molecule in the molecular workspace. Bond lengths, bond angles and torsional angles can be measured for the current structure and compared to accepted values. In addition, other geometric properties can be computed like overall dimension, moments of inertia, molecular volume and surface area. 

Maps of the values of the unit twist ( / ) and unit height (ft) as a function of the torsion angles 0i and 02, are reported for generic isotactic [s(M/N) symmetry] and syndiotactic [s(M/N)2 symmetry] vinyl polymers in Figures 2.5 and 2.6, respectively. It is apparent that only one set of symmetry-related curves corresponds to any given value of the unit twist / (different from 180°) for the isotactic polymer, while there are two such sets for the syndiotactic polymers.27... 

Figure 2.5 Maps of absolute value of unit twist t as function of backbone torsion angles 0, and 62 for (a) isotactic and (b) syndiotactic polymers.27 Curves corresponding to t = 180°, 160°, 140°, 120°, 100° are reported. (Reproduced with permission from Ref. 27. Copyright 1992 by the Society Chimica Italiana.)...

The conformation of the chains of isotactic polymers in the crystalline state is generally helical and corresponds to a succession of nearly trans and gauche torsion angles, the exact values depending on the bulkiness of the side groups. Molecular mechanics calculations have been extensively used for the prediction of the chain conformation of polymers in the crystal.29... 

Calculations of the conformational energy are performed according to the equivalence principle and, as a consequence, a succession of backbone torsion angles. .. 0i020i 20i 2- is generally assumed for isotactic polymers. 

Figure 2.10 Maps of conformational energy of various isotactic polymers as function of backbone torsion angles 0i and 02 (a) Isotactic polystyrene, (b) polypropylene, (c) poly(l-butene), and (d) poly(4-methyl-l-pentene). Succession of torsion angles. .. 0i020i02 [s(M/N) symmetry] has been assumed. Isoenergetic curves are reported every 10 (a,c,d) or 5 (b) kJ/mol of monomeric units with respect to absolute minimum of each map assumed as zero.

Data concerning the chain conformations of isotactic polymers are reported in Table 2.1. In all the observed cases the torsion angles do not deviate more than 20° from the staggered (60° and 180°) values and the number of monomeric units per turn MIN ranges between 3 and 4. Chains of 3-substituted polyolefins, like poly(3-methyl-l-butene), assume a 4/1 helical conformation (T G )4,45,46 while 4-substituted polyolefins, like poly(4-methyl-1-pentene), have less distorted helices with 7/2 symmetry (T G )3.5-39 When the substituent on the side group is far from the chain atoms, as in poly(5-methyl-1-hexene), the polymer crystallizes again with a threefold helical conformation (Table 2.1). Models of the chain conformations found for the polymorphic forms of various isotactic polymers are reported in Figure 2.11. 

Recently, a similar analysis of the conformational energy has been performed also for various new syndiotactic polymers.27,47 The conformational energy maps of syndiotactic polypropylene (sPP),48 polystyrene (sPS),49 poly butene (sPB),25 and poly(4-methyl-l-pentene) (sP4MP)26 are reported in Figure 2.12. A line repetition group s(M/N)2 for the polymer chain, and, hence, a succession of the torsion angles. .. 0i, 0i, 02, 02,..., has been... 

Figure 2.15 line repetition symmetry groups and corresponding sequences of torsion angles for cis and trails polydienes. Position of mirror planes (m), inversion centers (i), and binary axes (2) along polymer chain are also indicated. Torsion angle of single bond, CHA-CHA, is assumed to be trails (T) in both cis and lruns polydienes. 

When A A or B B, the symmetry is lower and the only possible line repetition groups are s(M/N) and tc for isotactic and syndiotactic polymers, respectively, in both cis and trans configurations. In these cases, two independent torsion angles in the main chain define the regular conformation (Oi and 02 in Figure 2.15). 

Figure 2.16 reports the conformational energy maps as a function of the torsion angles 0i and 02 of the two single bonds adjacent to the double bonds for 03 = T = 180° for cis-1,4-poly (1,3-butadicnc) (cisPBD),69 tranx-l,4-poly(l,3-butadiene) (transPBD),70 ds-l,4-poly (isoprene) (cisPI),68 trans-1,4-poly(isoprene) (transPI),71 ds-l,4-poly(2,3-dimethyl-l,3-butadiene) (cisPMBD),68 and lrans-, 4-poly(2,3-dimethy 1-1,3-butadicnc) (transPMBD).68 These polymers are representative examples of polydienes with A = A = H... 

For the isotactic polymer, highly extended chains with chain axis of 7.5-7.6 A can be obtained with a helix repeating after two structural units [s(2/l) line repetition group] when 01 02, and 03 are in the range 180° 8, with 8 being 25-30° and 8i + 82 + 83 0.125 The experimental values of the torsion angles found in the crystal structure of i-STCO123 are indeed 0i = —161.5°, 02 = 155.3°, and 03 = -171.4°. Similar values have been found by conformational... 

The torsion angles predicted by conformational analysis agree closely with those of crystalline cellobiose as measured by X-ray diffraction, the conformation of which is restricted by two chain-stabilising intramolecular hydrogen bonds between 0(3 )-H and 0(5) and also between 0(2 )-H and 0(6) (Figure 4.3). These are also found in cellulose and they assist in maintaining the highly extended conformation which allows it to function as a structural polymer. 

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