Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

The average instantaneous shape of an unperturbed polyethylene chain is studied with a Monte Carlo technique. Different short-range interactions in the polyethylene chain are considered. The shape is evaluated as the ratio 〈L〉:〈L〉:〈L〉, where L₁≤L₂≤L₃ are the orthogonal components in the system of principal axes of gyration. Differences are found for different interactions in short- and medium-length chains, while for long chains all ratios converge to a common limit, which is about 1:2.7:12.0 for polyethylene chains.     

Anisotropy in the dimensional and elastic parameters of confined macromolecules

Using lattice simulations the effect of confinement on the size, orientation and elastic properties of athermal chains was investigated. For chains confined in a slit or in a “cylinder” with square profile a minimum was observed in the dependence of the mean‐square end‐to‐end distance 〈R²〉 on the plate distance D. However, the components of the mean chain dimensions perpendicular and parallel to the walls, 〈R²_⟂〉 and 〈R²_∥〉, steadily diverge with reduction of the pore size. In a slit the distribution functions of the chain vector perpendicular and parallel to the plates, W〈R²_⟂ 〉 and W〈R²_∥〉, respectively, were computed. The marked difference between these distribution functions is interpreted as a sign of enhanced alignment of chains of the shape of elongated ellipsoids along the pore walls. A major part of the free energy of confinement ΔA_cf stems from this mechanism of pore‐induced macromolecular orientation. A striking anisotropy was observed in the elastic free energies A^el_⟂ and A^el_∥ of chains deformed in the direction perpendicular and parallel to the walls and in the corresponding force‐displacement functions. Finally, the relation between the elastic free energy A^el and the free energy of confinement ΔA_cf and between the forces f and f_solv derived thereof is analysed.     

Computer simulation of brownian motion of a polyelectrolyte molecule (charged bead-spring model)

A Langevin equation of motion for a charged bead-spring statistical chain is written in difference form and the relaxation and equilibrium behavior of the chain is studied by computer simulation. Results are presented for the behavior of end-to-end length h, principal axes of the polymer ellipsoid L₁, L₂, L₃, and chain contour length c in terms of their averages, root mean square values, root mean square fluctuations, orientations, and relaxation strengths and times. The simulation was made with various sets of parameters, bead number N, charge on the bead q, and radius of ion atmosphere around the bead k^?1. It is found that 〈h²〉^1/2 and 〈L₁²〉^1/2 increase more strongly with increasing q and decreasing κ than 〈L₂²〉^1/2, 〈L₃²〉^1/2, and 〈c₁²〉^1/2, indicating that the chain is expanded in three dimensions and at the same time is extended along the end-to-end direction. The relaxation time τ_rot of rotation of the end-to-end vector, which is proportional to N² at q = 0, increases with increasing q and tends to be proportional to N³ for an extended chain, while the relaxation time τ_conf of the magnitude of h is almost independent of q and is always proportional to N². It is concluded that the extended chain possesses a well-defined end-to-end axis and the chain rotates as a whole with a relaxation time τ_rot which is much longer than τ_conf. The complex viscosity of the chain is calculated from the Fourier transform of the time–correlation function of momentum flux and is found to have a frequency spectrum similar to that observed for aqueous solutions of poly(acrylic acid). The dominant mode appearing in the low-frequency range is evidenced to arise from the rotation of the extended chain.     

Novel one‐ and two‐dimensional ZnII coordination polymers based on a versatile 3,6‐bis(pyridin‐4‐yl)phenanthrene‐9,10‐dione ligand

Two new Zn^II coordination polymers, namely, catena‐poly[[dibromidozinc(II)]‐μ‐[3,6‐bis(pyridin‐4‐yl)phenanthrene‐9,10‐dione‐κ²N:N′]], [ZnBr₂(C₂₄H₁₄N₂O₂)]_n, (1), and poly[[bromido[μ₃‐10‐hydroxy‐3,6‐bis(pyridin‐4‐yl)phenanthren‐9‐olato‐κ³N:N′:O⁹]zinc(II)] hemihydrate], {[ZnBr(C₂₄H₁₅N₂O₂)]·0.5H₂O}_n, (2), have been synthesized through hydrothermal reaction of ZnBr₂ and a 60° angular phenanthrenedione‐based linker, i.e. 3,6‐bis(pyridin‐4‐yl)phenanthrene‐9,10‐dione, in different solvent systems. Single‐crystal analysis reveals that polymer (1) features one‐dimensional zigzag chains connected by weak C—H...π and π–π interactions to form a two‐dimensional network. The two‐dimensional networks are further stacked in an ABAB fashion along the a axis through C—H...O hydrogen bonds. Layers A and B comprise left‐ and right‐handed helical chains, respectively. Coordination polymer (2) displays a wave‐like two‐dimensional layered structure with helical chains. In this compound, there are two opposite helical –Zn–HL– chains [HL is 10‐hydroxy‐3,6‐bis(pyridin‐4‐yl)phenanthren‐9‐olate] in adjacent layers. The layers are packed in an ABAB sequence and are further connected through O—H...Br and O—H...O hydrogen‐bond interactions to form a three‐dimensional framework. In (1) and (2), the mutidentate L and HL ligands exhibits different coordination modes.     

Concentration dependence of the global and anisotropic dimensions of confined macromolecules

The chain dimensions 〈R²〉 of nondilute polymer solutions confined to a slit of the width D were studied using lattice simulations. It was found that the chain compression induced in good solvents by the concentration ϕ is enhanced in a slit relative to the bulk. The global dimensions of chains also change with ϕ in confined and unconfined theta solutions. At intermediate slit widths, a region was noted where coils are squeezed along all three axes. This region is manifested as a channel on the three‐dimensional surface 〈R²〉(D,ϕ) in both good and theta solvents. The coil anisotropy, given by the ratio of the parallel and perpendicular components of the chain dimensions 〈R_y²〉/〈R_x²〉, reaches high values at strong confinements, where coils form quasi‐two‐dimensional pancakes. The concentration‐induced reduction of the global chain dimensions in good solvents is almost fully transmitted to the parallel component 〈R_y²〉. The computed effects of concentration and confinement were compared with the predictions of mean‐field and scaling theories, and implications of the results to ultrathin films and layered nanocomposites were discussed. In addition, the distribution functions of the components of the end‐to‐end distance R perpendicular and parallel to the plates, W (R_x) and W (R_y), were calculated. The function W (R_x) combined with the concentration profile ϕ (x) along the pore provided details of the chain structure close to walls. A marked difference in the pace of the filling up of the depletion layer was noticed between chains in theta and good solvents. From the distribution functions W (R_x) and W (R_y), the highly anisotropic force‐elongation relations imply the deformation of chains in confined solutions and ultrathin bulk films.     

Monte carlo simulations of polydisperse polymers grafted on spherical surfaces

This article presents effects of polydispersity in polymers grafted on spherical surfaces on grafted polymer chain conformations, grafted layer thickness, and free‐end monomer distribution within the grafted layer. At brush‐like grafting densities, as polydispersity index (PDI) increases, the scaling exponent of radius of gyration of grafted chains approaches that of a single chain grafted on the same nanoparticle, because polydispersity alleviates monomer crowding within the brush. At high PDI, the chains shorter than the number average chain length, N_n, have more compressed conformations, and the chains longer than N_n overall stretch less than in the monodisperse case. As seen in polydisperse flat brushes at high grafting densities, the grafted layer thickness on spherical nanoparticle increases with PDI. Polydispersity eliminates the region near the surface devoid of free‐end monomers seen in monodisperse cases, and it reduces the width of free‐end monomer distribution and shifts the free‐end monomer distribution close to the surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Conformation study of poly(p‐dioxanone) fibers by polarized Raman spectroscopy,X‐ray diffraction,and conformation analysis

The molecular orientation distribution of poly(p‐dioxanone) (PPDX) uniaxially oriented commercial fibers was determined by polarized Raman spectroscopy and X‐ray diffraction. The order parameters 〈P₂₀₀〉 and 〈P₄₀₀〉 of the orientation distribution function were determined by polarized Raman spectroscopy. For the C?O stretching band, the values of 〈P₂₀₀〉 and 〈P₄₀₀〉 obtained are equal to ?0.40 ± 0.04 and 0.28 ± 0.04, respectively. These results clearly indicate that the carbonyl groups are highly oriented perpendicular to the fiber axis. X‐ray diffraction led to a fiber repeat value of 0.628 nm for these samples, and to 〈P₂₀₀〉 and 〈P₄₀₀〉 values of 0.93 and 0.82, respectively, for the c‐axis orientation, indicating a high orientation in the draw direction of the fibers. A Monte‐Carlo conformational search led to 20 low‐energy conformations, but only one of these was found compatible with both the fiber repeat and the angle between the C?O bond and the fiber axis. This conformation, a 2₁ helix with a tg^?ttg^? succession of torsion angles, is proposed as the existing conformation in the crystalline state. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 406–417, 2008     

Synthesis,crystal structure and studies on the interaction with albumin of a new silver(I) complex based on 2‐(4‐nitrobenzenesulfonamido)benzoic acid

In the present work, the two‐dimensional (2D) polymer poly[[μ₄‐2‐(4‐nitrobenzenesulfonamido)benzoato‐κ⁴O¹:O¹:O^1′:N⁶]silver(I)] (AgL), [Ag(C₁₃H₉N₂O₆S)]_n, was obtained from 2‐(4‐nitrobenzenesulfonamido)benzoic acid (HL), C₁₃H₁₀N₂O₆S. FT–IR, ¹H and ¹³C{¹H} NMR spectroscopic analyses were used to characterize both compounds. The crystal structures of HL and AgL were determined by single‐crystal X‐ray diffraction. In the structure of HL, O—H…O hydrogen bonds between neighbouring molecules result in the formation of dimers, while the silver(I) complex shows polymerization associated with the O atoms of three distinct deprotonated ligands (L^?). Thus, the structure of the Ag complex can be considered as a coordination polymer consisting of a one‐dimensional linear chain, constructed by carboxylate bridging groups, running parallel to the b axis. Neighbouring polymeric chains are further bridged by Ag—C monohapto contacts, resulting in a 2D framework. Fingerprint analysis of the Hirshfeld surfaces show that O…H/H…O hydrogen bonds are responsible for the most significant contacts in the crystal packing of HL and AgL, followed by the H…H and O…C/C…O interactions. The Ag…Ag, Ag…O/O…Ag and Ag…C/C…Ag interactions in the Hirshfeld surface represent 12.1% of the total interactions in the crystal packing. Studies of the interactions of the compounds with human serum albumin (HSA) indicated that both HL and AgL interact with HSA.     

Convergence of the partial wave expansion of the He ground state

The configuration interaction (CI) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each ? ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron–electron δ‐function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type ΔX_J = A_X[J + 1/2]^?p + B_X[J + 1/2]^?p?1 + …, gave an energy accurate to 10^?7 Hartree and a value of 〈δ〉 accurate to about 0.5%. Improved estimates of 〈E〉 and 〈δ〉, accurate to 10^?8 Hartree and 0.01%, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J → ∞ limit. Round‐off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and 〈δ〉 differences. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Isometric and Isotensional Force‐Length Profiles in Polymethylene Chains

Summary: The force‐length curves and related thermodynamic quantities of single polymethylene (PM) chains in the high‐force region were calculated by the statistical mechanics. Two statistical mechanics ensembles (isometric and isotensional) were used to represent the chain stretching under the conditions, respectively, of the fixed length L or of the fixed force F in single‐chain experiments by AFM and related techniques. The input deformation potentials of highly extended conformations of PM chains were obtained from the molecular‐mechanics calculations. Variations of the energy, entropy, and Helmholtz energy with the end‐to‐end length L of chains were computed under the condition of fixed length. The ensuing isometric profile of the mean force 〈F〉(L) is non‐monotonic, featuring a sawtooth‐like pattern of ascending peaks. In contrast, the mechanical equation under isotensional conditions, given by the variation of the mean length 〈L〉(F), shows a conventional monotonous shape with a distinct plateau region at low temperatures. The considerable difference in the shapes of 〈F〉(L) and 〈L〉(F) curves arises from the large fluctuations of mean values due to the small number of conformers present in molecules at high strains. The computed data should be relevant to the AFM stretching experiments on short polyethylenes or on other soft matter materials involving linear paraffinic chains. It is argued that the dual character of elastic response described by the conjugated force profiles is a universal feature of mechanochemistry of chain molecules whenever the chain length discontinuously increases at a transition.

Force‐length curves of short polymethylene chains at 300 K.     

The Influence of External Electric Field on Local Orientations and Phase Transitions in Polymer Liquid Crystals (PLCs)

The starting point is our previous study of influence of the internal molecular mean field of dipole‐dipole interactions on local orientation and phase transitions in polymer liquid crystal (PLC) systems of longitudinal chains.^{[1, 2]} Electric dipoles are created by LC mesogen moieties. The longitudinal PLC is a macromolecule of consecutively copolymerized LC and flexible polymer sequences. We now amplify the model by inclusion of dipole‐external electric field interactions. We find that the external fields can seriously modify the local orientational order of the system and affect phase transition parameters dependent on that order. In particular, the external fields induce the formation of disoriented nematic phases with negative values of the second order orientation parameter 〈P₂〉 for LC sequences in the longitudinal PLCs while the first order parameter 〈P₁〉 is positive. However, some rapid decreases in 〈P₁〉 are observed at points of positive‐to‐negative transitions of 〈P₂〉; thus the LC disorientation manifests itself. The limiting case of the monomer liquid crystal (MLC) systems is included also.     

Reversible addition–fragmentation chain‐transfer graft polymerization of styrene: Solid phases for organic and peptide synthesis

The γ‐initiated reversible addition–fragmentation chain‐transfer (RAFT)‐agent‐mediated free‐radical graft polymerization of styrene onto a polypropylene solid phase has been performed with cumyl phenyldithioacetate (CPDA). The initial CPDA concentrations range between 1 × 10^?2 and 2 × 10^?3 mol L^?1 with dose rates of 0.18, 0.08, 0.07, 0.05, and 0.03 kGy h^?1. The RAFT graft polymerization is compared with the conventional free‐radical graft polymerization of styrene onto polypropylene. Both processes show two distinct regimes of grafting: (1) the grafting layer regime, in which the surface is not yet totally covered with polymer chains, and (2) a regime in which a second polymer layer is formed. Here, we hypothesize that the surface is totally covered with polymer chains and that new polymer chains are started by polystyrene radicals from already grafted chains. The grafting ratio of the RAFT‐agent‐mediated process is controlled via the initial CPDA concentration. The molecular weight of the polystyrene from the solution (PS_free) shows a linear behavior with conversion and has a low polydispersity index. Furthermore, the loading of the grafted solid phase shows a linear relationship with the molecular weight of PS_free for both regimes. Regime 2 has a higher loading capacity per molecular weight than regime 1. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 4180–4192, 2002     

Elastic behavior of single polymer chains adsorbed on rough surfaces

In this paper, elastic behaviors of single polymer chains adsorbed on the rough surfaces with a substrate and some periodically tactic pillars are investigated by the pruned-enriched-Rosenbluth method (PERM). In our simulation, a single polymer chain is firstly adsorbed on the substrate and then pulled along the z-axis direction, which is vertical to the substrate. We investigate the chain size and shape of polymer chains, such as mean-square radii of gyration per bond 〈S²〉_xy/N, 〈S²〉_z/N and shape factor 〈δ^∗〉 in order to show how the size and shape of adsorbed polymer chains change during the desorption process. Due to the occurrences of separation of the chains from the substrate, farther adsorption on the upper surfaces of pillars and complete separation from the whole rough surfaces in the elastic process, the changes of 〈S²〉_xy/N, 〈S²〉_z/N and 〈δ^∗〉 during the process are complicated. On the other hand, some thermodynamic properties such as average energy per bond, average Helmholtz free energy per bond, elastic force f are investigated, and our aim is to study the elastic behaviors of polymer chains adsorbed on the rough surface during the elasticity process. Elastic force f has some plateaus during the desorption process for strong adsorption interaction. If there is no adsorption interaction, the chains can get away from the rough surfaces spontaneously. These investigations can provide some insights into the elastic behaviors of polymer chains adsorbed on the rough surface.     

The influence of variant PE‐b‐PEO segments on physical properties of LLDPE graft copolymers

A method was adopted to fix a series of polymers of PE‐b‐PEO with different PEO/PE segments on the chains of LLDPE. Maleic anhydride (MA) reacting with hydroxyl group of PE‐b‐PEO (mPE‐b‐PEO) was used as the intermediate. The structures of intermediates and graft copolymers were approved by ¹H NMR and FTIR. XPS analysis revealed a great amount of oxygen on the surface of grafted copolymers although the end group of PEO was fixed on the LLDPE chains through MA. Thermal properties of the graft copolymers as determined by differential scanning calorimetry (DSC) showed that PE segments in the grafted monomers could promote the heterogeneous nucleation of the polymer, increase T_c, and crystal growth rate. While the amorphous PEO segments which attached to the crystalline PE segments in LLDPE, impaired their ability to fit the crystal lattice, and depressed the crystallization of LLDPE backbones. In this study, it was also verified through the dynamic rheological data that increasing M_n of grafted monomers significantly increased the complex viscosity and enhanced the shear‐thinning behavior. Long‐branched chains formed by grafted monomers enhanced the complex moduli (G′ and G″) value and retarded relaxation rate. However, there were little influence on the rheological properties when increasing the amounts of PEO segments (or decreasing PE segments) of grafted monomers with similar molecular weight. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 506–515, 2008     

A one‐dimensional coordination polymer formed from the reaction of 1,1‐diphenyl‐3,3′‐[(1R,2R)‐cyclohexane‐1,2‐diylbis(azanediyl)]dibut‐2‐en‐1‐one with MnCl2·4H2O

In the title coordination polymer, catena‐poly[[dichloridomanganese(II)]‐μ‐1,1‐diphenyl‐3,3′‐[(1R,2R)‐cyclohexane‐1,2‐diylbis(azaniumylylidene)]dibut‐1‐en‐1‐olate‐κ²O:O′], [MnCl₂(C₂₆H₃₀N₂)]_n, synthesized by the reaction of the chiral Schiff base ligand 1,1‐diphenyl‐3,3′‐[(1R,2R)‐cyclohexane‐1,2‐diylbis(azanediyl)]dibut‐2‐en‐1‐one (L) with MnCl₂·4H₂O, the asymmetric unit contains one crystallographically unique Mn^II ion, one unique spacer ligand, L, and two chloride ions. Each Mn^II ion is four‐coordinated in a distorted tetrahedral coordination environment by two O atoms from two L ligands and by two chloride ligands. The Mn^II ions are bridged by L ligands to form a one‐dimensional chain structure along the a axis. The chloride ligands are monodentate (terminal). The ligand is in the zwitterionic enol form and displays intramolecular ionic N⁺—H...O⁻ hydrogen bonding and π–π interactions between pairs of phenyl rings which strengthen the chains.     

Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.     

Structural analysis of aggregates formed by a thermoresponsive homopolymer in dilute aqueous solutions

The aqueous solution of a thermoresponsive polymer, poly[2‐(2‐ethoxy) ethoxyethyl vinyl ether] poly(EOEOVE), contains a tiny amount of large polymer aggregates at low polymer concentrations far below the lower critical solution temperature (～40 °C). The molar mass M_w,slow, radius of gyration 〈S²〉, and hydrodynamic radius R_H,slow of the aggregating component of poly(EOEOVE) were obtained by simultaneous static and dynamic light scattering as functions of the polymer concentration and temperature, while the weight fraction w_slow of the component was estimated by size‐exclusion chromatography. The M_w,slow dependencies of 〈S²〉 and R_H,slow, as well as the ratio 〈S²〉/R_H,slow, indicated that the poly(EOEOVE) aggregate takes a sparsely branched polymer‐like conformation. We have analyzed the structure of the aggregate, using the branched polymer model of random type. The M_w,slow dependence of 〈S²〉 obtained was favorably compared with this model with reasonable structural parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1179–1187, 2006     

The three‐dimensional coordination polymer poly[[aqua[μ4‐2,2′‐(diazene‐1,2‐diyl)dibenzoato]lead(II)] 1,2‐bis(pyridin‐4‐yl)ethylene hemisolvate]

A novel three‐dimensional coordination polymer, {[Pb(C₁₄H₈N₂O₄)(H₂O)]·0.5C₁₂H₁₀N₂}_n, has been synthesized by hydrothermal reaction of Pb(OAc)₂·3H₂O (OAc is acetate), 2,2′‐(diazene‐1,2‐diyl)dibenzoic acid (H₂L) and 1,2‐bis(pyridin‐4‐yl)ethylene (bpe). The asymmetric unit contains a crystallographically independent Pb^II cation, one L²⁻ ligand, an aqua ligand and half a bpe molecule. Each Pb^II centre is seven‐coordinated by six O atoms of bridging–chelating carboxylate groups from L²⁻ ligands and by one O atom from a coordinated water molecule. The Pb^II cations are bridged by L²⁻ ligands, forming [PbO₂]_n chains along the a axis. These chains are further connected by L²⁻ ligands along the b and c axes to give a three‐dimensional framework with a 4¹²6³ topology. The channel voids are occupied by bpe molecules.     

A novel two‐dimensional framework based on unprecedented cadmium(II) chains

The bent ligand 4‐[(1H‐1,2,4‐triazol‐1‐yl)methyl]benzoic acid (HL) has been used to create the novel two‐dimensional coordination polymer poly[μ₂‐aqua‐μ₂‐chlorido‐{μ₂‐4‐[(1H‐1,2,4‐triazol‐1‐yl)methyl]benzoato}cadmium(II)], [Cd(C₁₀H₈N₃O₂)Cl(H₂O)]_n, under hydrothermal reaction of HL with cadmium chloride. The crystallographically unique Cd atom is seven‐coordinated in an approximately pentagonal–bipyramidal environment of two carboxylate O atoms, two water O atoms, two Cl atoms and one triazole N atom. A notable feature is the presence of zigzag ...Cd...Cd... inorganic chains, in which neighboring Cd^II ions are doubly bridged by pairs of μ₂‐Cl atoms and μ₂‐H₂O ligands in an alternating fashion. To the authors' knowledge, this is the first example containing this bridging mode in a cadmium(II) framework. The chains are connected to one another through the bridging L⁻ ligand into a two‐dimensional undulating network. All of the two‐dimensional nets stack exactly together in an …AA… stacking sequence along the crystallographic b axis. Neighboring layers are further linked into a three‐dimensional framework via interlayer hydrogen‐bonding interactions.     

Conformational characteristics of poly(ethylene phthalate)s

The conformational characteristics, as embodied in the unperturbed mean‐square end‐to‐end distances (〈r²〉_o) and the characteristic ratios of the dimensions [C_n = 〈r²〉_o/(n〈l²〉] are calculated for the para, meta, and ortho isomers of poly(ethylene phthalate)s: poly(ethylene terephthalate) (PET), poly(ethylene isophthalate) (PEI), and poly(ethylene phthalate) (PEP), respectively. Although each of these isomeric and partially aromatic polyesters has identical permissible conformations available to their ethylene glycol fragments, their connections through the ester bonds to the phenyl rings are quite distinct. In addition, for the ortho isomer (PEP), the close spatial proximity of the ester groups bonded to the same phenyl ring results in an interdependence of their orientations with respect to each other and the phenyl ring to which they are attached, unlike the independent orientations of ester groups in the para and meta isomers (PET and PEI). Conformational energy calculations, dependent on the orientation of the ester groups in PEP, are used to characterize their rotational interdependence to modify the rotational isomeric state (RIS) conformational models for PET and PEI and thereby obtain an RIS model appropriate for PEP. This leads to calculated relative dimensions (〈r²〉_o) of 1.0:0.70:0.37 PET:PEI:PEP and characteristic ratios [C_n = 〈r²〉_o/(n〈l²〉)] of 4.13:4.67:2.49 PET:PEI:PEP. These results are discussed in an effort to obtain some understanding of the inherent static (or equilibrium) and dynamic flexibilities of the isomeric poly(ethylene phthalate)s. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1254–1260, 2002