Measurement of the orientational elastic constants and the twist viscosity of nematic side chain polymers

Abstract

The temperature dependence of the three elastic constants k _ii (i = 1, 2, 3) and the twist viscosity γ₁ of two nematic side chain polyacrylates and one comparable low molecular weight compound have been measured by means of the Freedericksz effect. The change from the low to the high molecular liquid crystal causes a change of the ratio k ₃₃/k ₁₁ from greater to less than unity, but the order of magnitude of the elastic constants remains the same. In contrast, the twist viscosity of the polymeric liquid crystal is about 1000 times greater in magnitude than that of a comparable low molecular weight liquid crystal. The activation energy for the viscosity of the polymer differs by a factor 3–4 from that of the low molecular weight liquid crystal. The elastic constants as well as the twist viscosity show a quadratic dependence on the order parameter S over a wide temperature range.     

A Conformational Study on Silacyclohexane. Comparison of ab initio (HF,MP2), DFT,and Molecular Mechanics Calculations. Conformational Energy Surface of Silacyclohexane

The structures and relative energies for the basic conformations of silacyclohexane 1 have been calculated using HF, RI‐MP2, RI‐DFT and MM3 methods. All methods predict the chair form to be the dominant conformation and all of them predict structures which are in good agreement with experimental data. The conformational energy surface of 1 has been calculated using MM3. It is found that there are two symmetric lowest energy pathways for the chair‐to‐chair inversion. Each of them consists of two sofa‐like transition states, two twist forms with C₁ symmetry (twist‐C₁), two boat forms with Si in a gunnel position (C₁ symmetry), and one twist form with C₂ symmetry (twist‐C₂). All methods calculate the relative energy to increase in the order chair < twist‐C₂ < twist‐C₁ < boat. At the MP2 level of theory and using TZVP and TZVPP (Si atoms) basis sets the relative energies are calculated to be 3.76, 4.80, and 5.47 kcal mol^–1 for the twist‐C₂, twist‐C₁, and boat conformations, respectively. The energy barrier from the chair to the twisted conformations of 1 is found to be 6.6 and 5.7 kcal mol^–1 from MM3 and RI‐DFT calculations, respectively. The boat form with Si at the prow (C_s symmetry) does not correspond to a local minimum nor a saddle point on the MM3 energy surface, whereas a RI‐DFT optimization under C_s symmetry constraint resulted in a local minimum. In both cases its energy is above that of the chair‐to‐twist‐C₁ transition state, however, and it is clearly not a part of the chair‐to‐chair inversion.     

A dielectric study of molecular relaxation in oxidized and chlorinated polyethylenes

A study was made of the dielectric relaxation in polyethylenes rendered dielectrically active through oxidation (0.5–1.7 carbonyls/1000 CH₂) and chlorination (14–22 Cl/1000 CH₂). Both linear and branched polymers were studied. All of the relaxations between the melt and ?196° were studied in the frequency range 10 Hz to 10kHz (100 kHz in the chlorinated samples). In the linear samples a wide range of crystallinities was studied (55% in quenched specimens to 95% in extended-chain specimens obtained by crystallization at 5 kbar). As is consistent with its being a crystalline process, the α peak was found to discontinously disappear on melting of the samples and reappear on recrystallizing on cooling. The disappearance of the smaller crystals before the larger ones appeared to be evident in the isothermal loss versus frequency curves. The relaxation strength of the α process increases with crystallinity. The measured relaxation strength is less than that expected on the basis of direct proportionality to the crystalline fraction with full contribution of all dipoles in the crystalline material. However, the intensity is not sufficiently low for the process to be interpreted in terms of reorientation of localized conformational defects in the crystal. The variation of intensity with crystallinity is best interpreted in terms of full participation of crystalline dipoles but with selective partitioning of both carbonyls and chlorines favoring the amorphous domains. A strong correlation of the α loss peak location (T_max at constant frequency or log f_max at constant T) with crystallinity for both carbonyl and chlorine containing polymers was found. This variation is interpreted in terms of chain rotations in the crystal where the activation free energy depends on crystal thickness. The dependence of log f_max and T_max on lamellar thickness as well as a comparison with the loss peaks of ketones dissolved in parafins indicates that the chain rotation is not rigid and is accompanied by twisting as the rotation propagates through the crystal. In agreement with previous studies the β process is found to be strong only in the branched polymers but can be detected in the chlorinated linear polymer. The β process was resolved from the α in the branched samples by curve fitting and its activation parameters determined. The γ relaxation peak in oxidized polymers including its high asymmetry (low-temperature tail) and increasing ε_max with increasing frequency and temperature when plotted isochronally can be interpreted in terms of a simple nearly symmetrical relaxation time spectrum that narrows with increasing temperature. No increase in relaxation strength with temperature was found. The chlorinated polymers behave similarly but appear to have some Boltzmann enhancement (450–750 cal/mole) of relaxation strength with temperature. The dependence of relaxation strength on crystallinity indicates that the process is an amorphous one. Further, no evidence of relaxation peak shape changes with crystallinity that could be interpreted in terms of a crystalline component in addition to the amorphous one was found. The comparison of the γ relaxation strength with that expected on the basis of full participation of amorphous dipoles indicates that only a small fraction (～10% in oxidized linear polymers) of them are involved in the relaxation. Thus it would seem that a glass–rubber transition interpretation is not indicated but rather a localized chain motion. It is suggested that the γ process, including its intensity, width, and activation parameters, can be interpreted in terms of an (unspecified) localized conformational (bond rotation) motion that is perturbed by differing local packing environments. The thermal expansion lessens the effects of variations in packing and leads to narrowing with increasing temperature. The conformational motion itself leads to increase in thermal expansion and hence a transition in the latter property. Some previously proposed localized amorphous phase conformational motions appear to be suitable candidates for the bond rotation motion. A weak relaxation peak found at temperatures below the γ and at 10 kHz may possibly be the dielectric analog of the δ cryogenic peak found previously mechanically at lower frequencies.     

Light scattering from a nematic monodomain in an electric field Twist elastic constant and viscosity coefficient of nematic polymer–solvent mixtures

Abstract

The light scattering technique was used to investigate the viscoelastic parameters characterizing director twist distortions in miscible nematic mixtures of 5CB (pentacyanobiphenyl) with two side chain liquid crystal polymers and a main chain liquid crystal polymer. By applying an AC electric field to homeotropically-aligned nematic monodomains of the mixtures, the field-dependent scattering intensities and director orientation fluctuation relaxation rates yield, respectively, the twist elastic constant K ₂₂ and viscosity coefficient γ₁. The results directly demonstrate that the addition of liquid crystal polymers causes substantial decreases of the relaxation rates for dynamic light scattering from the twist mode and these changes are due to small decreases in K ₂₂ coupled with large increases in γ₁. The decrements in K ₂₂ are comparable for both side chain and main chain liquid crystal polymers. The relative increase in the twist viscosity for the side chain liquid crystal polymers is much smaller than those of main chain polymers. A theoretical model is used to qualitatively interpret the difference between the viscous behaviour of the twist mode for both side chain and main chain liquid crystal polymers in a nematic solvent.     

Conformational Flexibility of the Methoxyphenyl Group Studied by Statistical Analysis of Crystal Structure Data

In a large sample of observed methoxyphenyl groups, the twist angle τ about the MeO-C_Ph bond measuring internal rotation of the MeO group shows a continuous distribution with maxima at (0°) (coplanar conformation) and (～90°) (perpendicular conformation). The preferred conformation of methoxyphenyl depends on the nature of the ortho--substituents: In general, it is coplanar in the case of one or two ortho-hydrogens, and perpendicular in the case of two substituents. The internal rotation of the MeO group is accompained by systematic variations in bond angles and bond distances: 1 if MeO is twisted out of plane, the bond angle CH₃? O? C_Ph decreases from 117.7°, until it reaches a minimum of 114.9° at τ = ±90°. The O? C? C angle which is syn to CH₃ for τ = 0° decreases from 124.6° to a minimum of 115.4° at τ = ±180°. These angles changes keep the nonbonded distance CH₃ …? ortho substituent maximal during internal rotation of MeO and tend to minimize the corresponding strain energy. (2) In the perpendicular conformation, the O-atom is ～ 0. 06 Å displaced from the Ph plane, O and CH₃ and being on opposite sides of this plane. In addition, small but systematic increases of bond lengths MeO? C_Ph and CH₃? O are observed. These variations indicate a decrease in conjugation with increasing twist angle. Their interdependence during twisting and the magnitudes of the changes are close values obtained by ab initio calculations.     

An Unusual Fullerene–Carbene Adduct: Thermal Motion,Disorder, or Both?**

A single-crystal X-ray study of a fullerene-imidazole adduct at nine temperatures (80 K≤T≤480 K), accompanied by energy calculations, strongly suggested thermal motion of the C₆₀ moiety with respect to the imidazolium heterocycle. Analysis of the anisotropic displacement parameters, calculations of frequencies, and the refinement of disorder models for the crystal at four temperatures (230 K≤T≤380 K) lead to the conclusion that the rotator is moving at all temperatures. The rotation barrier is low, with one preferred crystallographic site and several other energy minima.     

Overcrowded twisted bi-4H-cyclopenta[def]-phenanthren-4-ylidene versus bi-9H-fluorenylidene,syn pyramidalization

A crystal structure determination for bi-4H-cyclopenta[def]-phenanthren-4-ylidene, 1, reveals a molecular conformation rather like that reported earlier for bifluorenylidene,2. However, unexpectedly, the twist angle about the ethylenic linkage is substantially smaller in1 (average values are 30.8 and 40.7°, respectively). Comparison of bonding geometry, combined with the results of molecular mechanics calculations for1, demonstrates that syn pyramidalization can play an important role in determining a stable conformation for overcrowded, twisted aromatic enes. The average out-of-plane bending angles for the ethylenic carbon atoms of1 and2 are 8.6 and 4.4°, respectively.     

Modeling the Fractionation Process in TREF Systems. III. Model Validation With Low Molecular Weight Homopolymers

Low molecular weight semicrystalline homopolymers are used as a model system for temperature rising elution fractionation (TREF) analysis. An already proposed thermodynamic model for TREF analysis is used to characterize TREF fractions from low molecular weight polyethylenes M?_n = 500 to 3000 and some of their mixtures. In this molecular weight range it is possible, under appropriate crystallization, conditions, to form extended-chain crystals, and therefore lamellar thicknesses become comparable to extended-chain lengths. Lamellar thicknesses calculated from TREF spectra permit calculations of the molecular weights of the fractions, up to a limit of about 142 CH₂, where partially folded-chain crystallites appear under these operating conditions. Also homopolymers blends are fractionated and the TREF spectra analyzed to test model predictions. It is shown that appearance of chain folding may set a resolution limit to the analysis of commercial copolymers by TREF. © 1996 John Wiley & Sons, Inc.     

The electronic structure and optical activity of conjugated dienes: 1,3-Butadiene and α- and β-phellandrene

The optical activity of conjugated dienes is investigated by means of ab initio SCF–CI calculations. The computed electronic spectrum of trans-1,3-butadiene is shown to be in good agreement with the results of more rigorous calculations of the valence transitions and in satisfactory agreement with experiment. The optical rotatory strengths of the lower electronic transitions of twisted 1,3-butadiene as a function of dihedral angle are presented and simulated CD spectra are produced. The N → V₁ (π₂ → π₃*) transition is predicted to have a positive rotational strength for all dihedral angles that correspond to a right-handed twist of the chromophore, in accord with the empirically deduced “diene rule” although for a twist angle of 60°, the rotatory strength is calculated to be almost zero. The role of the orientation of allylic bonds is investigated in the model system 1-butene in which the rotational strength of the π → π* transition as a function of rotation about the 2,3 bond is determined. The effect of allylic bond disposition in dienes on the optical activity of the long-wavelength π₂ → π₃* transition is simulated by use of the exciton coupling model of Harada and Nakanishi in which two 1-butene molecules with suitable geometries are coupled via interactions of the electric dipole transition moments of their π → π* transitions. The model systems 1,3-butadiene and 1-butene are used to rationalize the apparently anomalous optical activity of (?)-α-phellandrene and (?)-β-phellandrene, both of which should have a diene chromophore with a right-handed twist in their most stable conformers and so should be dextrorotatory. The experimental CD spectrum of α-phellandrene is determined at several temperatures down to ?180°C. The observed variation of the apparent rotational strength of the N → V₁ transition is in good agreement with that predicted by use of the exciton coupling model.     

Electron diffraction structure analysis of epitaxially crystallized n-paraffins

Electron diffraction data from a series of paraffins epitaxially crystallized on benzoic acid are used to determine their crystal structures. Even-chain paraffins from n-C₃₂H₆₆ to n-C₆₀H₁₂₂ are shown to crystallize isostructurally as the orthorhombic polymorph described for n-C₃₆H₇₄. Like the even-chain compounds, odd-chain paraffins do not crystallize in their lowest-energy form. A quantitative zonal crystal structure analysis for n-C₃₃H₇₄ suggests that the molecular packing is in the B-polymorphic form proposed earlier by other workers.     

Concomitant Polymorphism in an Organic Solid: Molecular and Crystal Structure and Intra- and Intermolecular Potential Contributions to tert-Butyl and Methyl Group Rotation

We investigate the relationship between structure (crystal and molecular) and tert-butyl and methyl group dynamics in 2-(tert-butyl)-9-(4-(tert-butyl)phenyl)anthracene. Powder and single-crystal X-ray diffraction, taken together, show that different polycrystalline samples recrystallized from different solvents have different amounts of at least four polymorphs (crystallites having different crystal structures), of which we have identified three by single crystal X-ray diffraction. The molecules in the asymmetric units of the different crystal structures differ by the dihedral angle the tert-butylphenyl group makes with the anthracene moiety. Ab initio electronic structure calculations on the isolated molecule show that very little intramolecular energy is required to change this angle over a range of about 60° which is probably the origin of the concomitant polymorphism (crystals of more than one polymorph in a polycrystalline sample). Solid state ¹H nuclear magnetic resonance (NMR) spin-lattice relaxation experiments support the powder and single-crystal X-ray results and provide average NMR activation energies (closely related to rotational barriers) for the rotation of the tert-butyl groups and their constituent methyl groups. These barriers have both an intramolecular and an intermolecular component. The latter is sensitive to the crystal structure. The intramolecular components of the rotational barriers of the two tert-butyl groups in the isolated molecule are investigated with ab initio electronic structure calculations.     

Conformational analysis and molecular dynamics simulation of cellobiose and larger cellooligomers

The conformational behavior of cellobiose (D -glc-ß(1→4)-D -glc), cellotetraose, and cellooctaose was studied by a combination of energy minimization and molecular dynamics simulations in vacuo at 400 K. These diand oligosaccharide models have considerable flexibility and exhibit a variety of different motions in glycosidic and exocyclic torsions. The glycosidic ?, ψ torsions moved frequently between two local minima on the cellobiose energy surface in the region of known crystal structures. Transitions of the hydroxymethyl side chain were observed between gt,gg, and tg conformations accompanied by changes in intramolecular hydrogen bonding patterns. A reasonable fit to the experimental optical rotation and nuclear magnetic resonance vicinal coupling data of cellobiose in solution required a distribution of its conformations. The oligomers, although generally extended, assumed a more coiled or twisted shape than is observed in the crystalline state of cellulose and exhibited considerable backbone motion due to local ring rotations about the glycosidic bonds. Long-lived transitions to structures having torsion angles 180° from the major minima (ring flips) introduced kinks and bends into the tetramer and octamer. While the glucose rings of the structures remained primarily in the ⁴C₁ conformation, twist and boat structures were also observed in the tetramer and octamer structures. Reducing the simulation temperature to 300 K eliminated some of the transitions seen at 400 K. © 1993 John Wiley & Sons, Inc.     

Crystallization of polyethylene at high pressure: A kinetic view

A model for the crystallization kinetics of polymers is outlined and is used to interpret observations of the crystallization of polyethylene at high pressures. This model introduces a distinction between σ_e the lamellar surface energy which controls the lamellar thickness, and σ_e′, the surface nucleus surface energy which controls the growth rate. Differential scanning calorimetry and electron microscopy data for several polyethylenes crystallized at pressures of up to 8 kb are presented. From the dependence of lamellar thickness on the crystallization undercooling at 5 kb, it is found that σ_e increases markedly with pressure leading to the formation of very thick crystals at high pressures. The magnitude of the increase in σ_e is in agreement with σ_e values calculated from the dependence of melting temperatures on pressure. The nucleus surface energy σ_e′ is not expected to vary significantly with pressure, and estimates of growth rates of 5 kb which indicate that the growth rate does not vary significantly with pressure at constant under-cooling confirm this. Fractionation effects and the differences in behavior between different polyethylenes are also discussed.     

Role of CA2+ ion in the abortifacient action of prostaglandins. II. Molecular orbital and conformation energy calculations of PGA1

This paper reports some theoretical studies of PGA₁ using conformational and molecular orbital techniques. The conformation energy (CE ) calculations, using empirical potential-energy functions, for intrinsic torsional rotations around C₁₂? C₁₃ (θ), C₇? C₈ (Ψ), and C₁₄? C₁₅ (?) show a number of energy minima. The relative value of the CE for these minima ranges from 4.09 to 8.01 kcal/mol. An additional rotation around C₄? C₅ (χ) giving “twist” to the carboxyl chains lowers the CE value by 2–3 kcal/mol and a conformation with CE value 2.39 kcal/mol less than crystallographic one is obtained. The interchain interaction energy showed changes with conformations. No significant change in the interchain interaction energy was observed due to “twist” in the carboxyl chain. The isopotential mapping study demonstrated the probable ionic binding site near the carboxyl and the ring (O₉) oxygens. Conformational and molecular orbital results are discussed in the light of the reduced abortifacient potency of PGA₁ with respect to PGF_2α and the possible role of Ca²⁺ ions in this action.     

Synthesis,vibrational, and conformational properties of novel polyazadioxime chain molecules

Novel large polyazadioxime molecules 4,5,8,9-tetraaza-3,6,7,10-tetramethyl -3,5,7,9-dodecatetraene-2, 11-dione-2, 11-dioxime (H₂doxN₄) and 4,5,8,9,12, 13-hexaaza-3,6,7,10,11,14-hexamethyl-3, 5,7,9,11,13-hexadecahexane-2,15-dione-2, 15-dioxime (H₂doxN₆) were synthesized. The molecular geometries of these molecules as well as smaller dioxime molecules, H₂dox and H₂doxN₂ were optimized by using modified intermediate neglect of differential overlap (MNDO) calculations. The optimized conformations for all the molecules under study are close to the all-E, all-s trans conformation of C_2h symmetry group. However, the energy barriers of internal rotation around the N-N single bonds were found to be low. Therefore some distortions of the polyazabackbone through internal rotation the N-N bonds have been evidenced. By infrared and Raman spectroscopies in the solid state as well as in solution. From the MNDO calculations and vibrational spectroscopy, the polyaza chain molecules under study appear as a poorly conjugated system and can be represented as a sequence of single and double bond alternation.     

Crystallization during Polymerization of Lithium Dihydrogen Phosphate. II. Crystal growth by dimer addition

The crystal growth of LiPO₃ from the polymerizing LiH₂PO₄ melt is studied using optical nicroscopy, thermogravimetry, electron microscopy and model calculations. It is shown that the linear crystal growth rate is constant at a given temperature and has an activation energy of 110kJ/mole. The major molecule involved in the simultanous crystallization during polymerization, which leads to extended chain crystals, is the dimer.     

The S1 ← S0 0–0 transition energies of polychlorinated dibenzofurans (PCDFs) revisited: CIS(D) and MP2 calculations with correction for correlation energies

This paper reexamines the structures and energies of dibenzofuran and twenty PCDFs in S₁–S₃ states. It was demonstrated that, although the CIS method gives a false relative ordering of excited states, the false ordering can be remedied by the CIS(D) method. Moreover the CIS geometries of typical PCDF molecules reasonably agree with their SAC-CI geometries. It was found that molecules chlorinated at the 1- and 9-positions are twisted in the S₂ state but are planar in other states, except for 1,4,6,9-TeCDF and fully chlorinated dibenzofuran (OCDF). The twisted structure of 1,4,6,9-TeCDF occurs in the S₃ state, but the structure of OCDF is twisted in every state. We partitioned the molecule into the parent structure and four chlorine groups and measured the twist energy with reference to the ground state. Then, the S_i ← S₀ 0–0 transition energies (i = 1, 2) calculated using the CIS(D) and MP2 methods could be expressed as a multiple linear equation with components and twist energy. It was further confirmed that if the multiple linear equation is corrected for residual correlation energies of the parent structure, it can predict the S₁ ← S₀ 0–0 transition energies with high precision.     

3‐Hydro­xy­benz­aldehyde

The title compound, C₇H₆O₂, forms infinite chains where the mol­ecules are hydrogen bonded via the hydroxyl and aldehyde groups, with an O?O distance of 2.719 (3) Å. Interchain interactions are weak. The geometry of the ring differs from the ideal form due to the effect of the substituents. Abinitio (Hartree–Fock self‐consistent field–molecular orbital and density functional theory) calculations for the free mol­ecule reproduce well the observed small distortions of the ring. In the crystal, the geometry deviates from the ideal C_s symmetry of the free mol­ecule, as given by the ab initio calculations. The aldehyde and hydroxyl groups are twisted around the single bonds which join them to the ring as a result of the intermolecular hydrogen‐bond interactions. These are also responsible for an elongation of the hydroxy C—OH bond compared with that calculated for the free mol­ecule.     

Solid solutions of normal paraffins

The results of the X-ray diffraction and thermal X-ray diffraction studies of the paraffins C_nH_2n+2 are revised based on new principles asserting the existence of several types of rotator states of paraffins. Along with the known isomorphism factors, such as the parity (symmetry) of the starting components and the difference between the chain lengths of their molecules (Δn), there is a factor that is specific to paraffins: differences in the energy state of molecules entering solid solutions. St. Petersburg State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 5, pp. 929–938. September–October, 1996. Translated by L. Smolina     

The Electrocyclic Cyclopropyl-Allyl Rearrangement. Preliminary communication

MINDO-2 SCF calculations indicate that ring-opening of cyclopropyl radical (I) to allyl radical (II) is more favourable via a disrotatory reaction path, the calculated activation energy being ～30 kcal/mole. (For conrotatory opening the activation energy was found to be ～44 kcal/mole.) The two critical motions of the nuclei during the transformation are found to be strongly decoupled, i.e. rupture of the CH₂βCH₂ bond precedes rotation of the CH₂ groups. As predicted by qualitative theories both ring-opening modes are unfavourable since they involve a change in electronic ground-state symmetry between I and II. The preferred ring-opening mode is discussed qualitatively in terms of Evans' principle.