Random-coil dimensions and dipole moments of propylene–vinyl chloride copolymers

Mean-square unperturbed dimensions 〈r²〉₀ and dipole moments 〈μ²〉 have been calculated for propylene–vinyl chloride copolymers by means of rotational isomeric state theory. The calculations indicate that for these chain molecules 〈mu;²〉 is much more sensitive to chemical sequence distribution than is 〈r²〉₀, a conclusion in agreement with results of previous studies of ethylene–propylene copolymers and styrene-substituted styrene copolymers. In the case of propylene–vinyl chloride chains, both 〈r²〉₀ and 〈μ²〉 are most strongly dependent on chemical sequence distribution in the case of copolymers which are significantly syndiotactic in stereochemical structure. At equimolar chemical composition, increase in average chemical sequence length generally increases 〈r²〉₀ but decreases 〈μ²〉. Under some conditions, values of these statistical properties go through a minimum with increase in the reactivity ratio product r₁r₂, thus complicating the use of experimental values of these properties in the characterization of chemical sequence distributions in these copolymers.     

Configurational properties of aromatic polyesters: Dipole moments of poly(diethylene terephthalate) chains

Dielectric constants have been determined for a fraction of poly(diethylene terephthalate) in benzene at several temperatures. The data indicate that the dipole moment ratio 〈μ²〉/Nm² is somewhat higher than that of poly(ethylene oxide), and its temperature coefficient is in the vicinity of zero. Both the dipole ratio and its temperature coefficient are in very good agreement with those predicted by the rotational isomeric state theory. Using this theory, the unperturbed dimensions of poly(diethylene terephthalate) were calculated and it was found that (〈r²〉/M)_∞ = 0.80 Ų (g mol wt)^?1, a value intermediate between those of poly(ethylene oxide) (0.57) and poly(ethylene terephthalate) (1.05).     

Dipole moments and structure of poly(epoxypropylcarbazole)

The mean-square molecular dipole moments 〈μ²〉 of carbazole, N-ethylcarbazole and of the sequence of poly(epoxypropylcarbazole) (PEPCa) oligomers of various molecular weights have been evaluated in solutions of these organic compounds in dioxan. For PEPCa the values of 〈μ²〉 have also been determined in the solid state. On the basis of the experimental results and of molecular mechanics calculations it has been shown that the orientation of the lateral group of PEPCa favors noninteracting racemic dyads. The temperature-dependence of the effective dipole moment of solid PEPCa follows the Onsager theory above 295 K.     

Random-coil configurations of the polyformals. VI. Dipole moments of the stereochemically variable polymer prepared from 4-methyl-1,3-dioxolane

Mean-square dipole moments 〈μ²〉₀ for the (atactic) poly(4-methyl-1,3-dioxolane) chain [CH₂OCH(CH₃)CH₂O? ] were determined from dielectric-constant measurements carried out on two fractions dissolved in benzene. Simple examination of the chain structure leads to the predictions that this polymer should have a significantly larger value of 〈μ²〉₀ than poly(1,3-dioxolane) itself, but that 〈μ²〉₀ should be nearly independent of stereochemical structure. The first expectation is confirmed by the experimental results obtained, and the second by calculated results based on rotational isomeric state theory.     

Dielectric properties of aromatic polyesters: Relaxation behavior of poly(diethylene glycol terephthalate)

The dielectric behavior of a low molecular weight fraction of poly(diethylene glycol terephthalate) has been studied over the frequency range 10² to 10⁵ Hz for temperatures between ?67 and +51°C. Two relaxations, α and β, which exhibit pseudoactivation energies of 52 and 8 kcal/mole, respectively, have been found. The α relaxation, associated with the glass transition of the polymer, is amenable to a Williams–Landel–Ferry (WLF) analysis. The dipole moment ration 〈μ²〉/Nm² (where 〈μ²〉 is the mean square dipole moment of a chain consisting of N bonds and m² is the average of the squares of the bond moments) has also been calculated using the dielectric data obtained for the polymer in the undiluted state. The calculations yield 〈μ²〉/Nm² = 0.710, a value in very good agreement with that obtained from measurements in solution.     

Dipole moment characterization of phenol–, o-cresol–, and p-cresol–formaldehyde resins

Dipole moments and their temperature dependence have been measured in p-dioxane for fractionated novolac phenol–, o-cresol–, and p-cresol–formaldehyde polymers. The phenol–formaldehyde fractions covered a molecular weight range of 200 to 6100, and the limiting dipole moment ratio 〈μ²〉/xm² is 1.48. The p-cresol–formaldehyde dipole-moment ratio at a DP of 4 is 2.47, whereas the phenol–formaldehyde dipole-moment ratio is 1.40. That for o-cresol–formaldehyde is intermediate in value. The dipole-moment temperature coefficients are positive for p-cresol chains and negative for the phenol–formaldehyde chains. These results indicate that the hydroxyl groups along the p-cresol–formaldehyde polymer are highly ordered, with the aromatic rings closer to the sterically hindered planar position than in the phenol–formaldehyde polymers.     

Constrained self-consistent-field wave functions with improved long-range behavior

The recent suggestion that the long-range behavior of energy-optimized Gaussian basis sets can be improved by augmenting them with a Gaussian chosen to satisfy a constraint involving a linearly averaged position moment is explored. Calculations indicate that the high-order moments 〈r^k〉, with k > 4, in He, Be, and Li^?, and 〈x^kz^L?k〉, with L > 4 and k ≤ L, in H₂ are improved by the constraint, but that lower-order moments and dipole polarizabilities are not. In H₂, the higher moments with a given L improve by different amounts for different k, and, hence, the multipole moments do not improve. The basis-set superposition error in He? He and Be? Be interaction energy calculations decreases if the internuclear distance is large enough. Thus, the constraint procedure improves the very long range behavior of the self-consistent-field wave functions. © 1992 John Wiley & Sons, Inc.     

Theoretical analysis of conformational energies,unperturbed dimensions,and dipole moments of poly(dichlorophosphazene)

A theoretical analysis of the conformational energies of poly(dichlorophosphazene) (PDCP) is presented. The results indicate that the bond pair P? N? P possesses a considerable conformational freedom, whereas the bond pair N? P? N is relatively rigid. This difference explains the low glass transition temperatures T_g and large end-to-end distances measured for polyphosphazenes. A statistical model containing four rotational isomers (ie., trans, gauche, cis, and negative gauche) is developed and used to calculate unperturbed dimensions and dipole moments of PDCP. The results, obtained at 25°C with n = 400 skeletal bonds (200 repeating units), were C_n = 〈r²〉₀/nl² = 13.5; C_T = 10³d(ln〈r²〉₀)/dT = ?3.0 K^?1; D_n = 〈μ²〉/nμ = 0.35; D_T = 10³d(ln〈μ²〉)/dT = ?3.4 K^?1. All the calculated magnitudes are extremely sensitive to the energy E_σ that controls the statistical weights of the conformations tg, tc, tg^?, gt, ct, and g^?t relative to tt for the bond pair P? N? P. A qualitative explanation for this sensitivity is discussed.     

Thermoelastic and dielectric studies of poly(3,3-dimethyl oxetane) chains

Poly(3,3-dimethyl oxetane) was synthesized by ring opening polymerization of 3,3-dimethyl oxetane. Elongation experiments were performed on unswollen elastomeric networks prepared from this polymer over the temperature range 30–90°C. The changes in the tensile stress while the networks crystallized were examined at various elongations. From thermoelastic data which were free from the effects of network crystallization, the temperature coefficient of the chain dimensions was found to be 1.1 × 10^?3 K^?1 in the vicinity of 60°C. The dipole moment ratio and its temperature coefficient were also measured; the average values of these parameters at 30°C were 0.20₆ and 2.5 × 10^?3 K^?1, respectively. All of these experimental-configuration-dependent properties were critically interpreted in terms of the rotational isomeric-state model. In comparing theory and experiment, conclusions were obtained which confirm earlier results according to which gauche states about C—C skeletal bonds in poly(3,3-dimethyl oxetane) are strongly favored over the alternative trans states.     

How does hybrid bridging core modification enhance the nonlinear optical properties in donor‐π‐acceptor configuration? A case study of dinitrophenol derivatives

This study spotlights the fundamental insights about the structure and static first hyperpolarizability (β) of a series of 2,4‐dinitrophenol derivatives (1–5), which are designed by novel bridging core modifications. The central bridging core modifications show noteworthy effects to modulate the optical and nonlinear optical properties in these derivatives. The derivative systems show significantly large amplitudes of first hyperpolarizability as compared to parent system 1 , which are 4, 46, 66, and 90% larger for systems 2, 3, 4 , and 5 , respectively, at Moller–Plesset (MP2)/6‐31G* level of theory. The static first hyperpolarizability and frequency dependent coupled‐perturbed Kohn–Sham first hyperpolarizability are calculated by means of MP2 and density functional theory methods and compared with respective experimental values wherever possible. Using two‐level model with full‐set of parameters dependence of transition energy (ΔΕ), transition dipole moment (μ⁰) as well as change in dipole moment from ground to excited state (Δμ), the origin of increase in β amplitudes is traced from the change in dipole moment from ground to excited state. The causes of change in dipole moments are further discovered through sum of Mulliken atomic charges and intermolecular charge transfer spotted in frontier molecular orbitals analysis. Additionally, analysis of conformational isomers and UV‐Visible spectra has been also performed for all designed derivatives. Thus, our present investigation provides novel and explanatory insights on the chemical nature and origin of intrinsic nonlinear optical (NLO) properties of 2,4‐dinitrophenol derivatives. © 2014 Wiley Periodicals, Inc.     

Configurational statistics of polyamide chains

The statistical mechanical treatment of polymeric chains in terms of the largest eigenvalue of the product of statistical weight matrices for the rotational interactions of skeletal bonds of the repeat unit becomes excessively complicated if the repeat unit spans more than three or four skeletal bonds. Moreover, such treatment is necessarily limited to chains in which the number of repeat units is indefinitely large. Newer methods are readily applicable to chains of any degree of polymerization comprising repeat units of any realizable length. If interdependence of neighboring bond rotations is confined to bond pairs within a given unit, rotations about a pair of bonds belonging to neighboring units being mutually independent, further simplifications may be introduced without sacrifice of rigor. Polyamides, in which rotation about bonds on opposite sides of the amide group are independent, are polymers of this type. Adherence of the amide group to the planar trans conformation favors a more extended configuration of the chain, but this effect is dominated by the smaller steric repulsions affecting rotations about bonds which are first, second, and third neighbors of the amide group. It is for this reason that the characteristic ratio 〈r²〉₀〉/nl² for poly(hexamethylene adipamide), ca. 6.0 according to experimental results of Saunders, is less than the value, 8.0, for polymethylene at 25°C. The characteristic ratios and molecular dipole moments are computed as functions of the degree of polymerization. The poly(εaminocaproamide) chain also is treated.     

Illuminating the origins of two-photon absorption properties in fluorescent protein chromophores

We provide here a structural impact on two-photon absorption cross-section (σ^TPA) for 22 distinct fluorescent protein (FP) chromophores. By employing time-dependent density functional theory, we gain insight into two-photon absorption (TPA) process by investigating relationship between σ^TPA and one-photon electronic transition dipole moment and permanent dipole moment change (Δμ) upon transition. Our results reveal that for the S₁ excited state, σ^TPA is proportional to (Δμ)² in agreement with two-state model of TPA process. On the contrary, the TPA spectroscopy of higher excited states (S _n, n > 1) is much more complex. We do not find a main driving force of large σ^TPA that would be common for investigated chromophores. Instead, it seems that channel interference between one-photon transition dipole moment vectors is responsible for enhancement or diminishment of σ^TPA. Our in vacuo results may serve as a benchmark to investigate a role of chromophore-protein interaction in shaping TPA spectra of FPs.     

Dipole moments,transition moments,oscillator strengths,radiative lifetimes,and overtone intensities for CH and CH+ as computed by quasi-degenerate many-body perturbation theory

The correlated, size-consistent, ab initio effective valence-shell dipole operator (μ^v) method is used to calculate dipole moments and transition dipole moments of the CH molecule and transition dipole moments of the CH⁺ ion as a function of internuclear distance. The dipole and transition dipole moments computed here compare well with those of other accurate ab initio methods. The transition dipole moments are then used to calculate oscillator strengths and radiative lifetimes for the A → X and B → A transitions of the CH⁺ ion and the A → X transition of the CH molecule. Comparisons are made with the best available theoretical and experimental lifetimes. Finally, the CH ground-state dipole moment function is used to evaluate overtone intensities and to examine simple models of the CH overtone intensities in polyatomic molecules.     

Copolymerization of oxetane with 3,3-dimethyloxetane-I. Reactivity parameters and microstructure of the copolymers

The copolymerization of 3,3-dimethyloxetane and oxetane has been studied in methylene chloride at 20°, with triethyloxonium tetrafluoroborate as initiator. The copolymerization reactivity parameters are r_DMOx = 0.95 and r_Ox = 1.19. By means of 300 MHz ¹H-NMR spectroscopy, the microstructure of the copolymers could be analyzed in terms of triad abundances. The observed values are in good agreement with the values calculated from the reactivity parameters thus showing the absence of penultimate effects and of re-distribution of the structural units in the copolymers. The results demonstrate that Ox is more reactive than DMOx to either of the two growing species in the copolymerization.     

The local definition of the Optimum ascent path on a multi-dimensional potential energy surface and its practical application for the location of saddle points

Density corrected distribution functions are used to calculate γ_o and γ₂ moments for the collision induced absorption spectra of a helium-argon system for a number of assumed dipole moment functions. These calculations indicate that corrections due to density effects can be of greater magnitude than the quantum corrections for these moments and can account for 10% of the moment at 200 amagats. The density corrections for γ_o show great variability with the choice of dipole parameters while the corrections for ν₂ were very consistent irrespective of the precise values of the dipole parameters. In addition, we correct some errors in our previous paper on the formal theory of these moments.     

The effective dipole moments of isobutyric acid in the liquid state and dilute solutions in methanol

The dipole moments of isobutyric acid (I) were determined in the liquid state (μ₁) and dilute solutions in methanol (μ₁) at 20–50°C. The permittivity of I in the liquid state was found to increase as the temperature grew, and the permittivity of solutions of I was lower than that of pure methanol; it decreased as the concentration of I and the temperature of solutions increased. The effective dipole moments of I were calculated using the Onsager polarization theory for the pure liquid and the Buckingham statistical polarization theory for solutions with various acid concentrations in methanol. The small μ₁ (～0.8 D) and higher μ₂ (～3.0 D) values compared with the dipole moment of I in the gas phase μ₀ (1.9 D) were analyzed as determined by the character of acid-acid, acid-solvent, and solvent-solvent intermolecular interactions, a key role in which was played by H-bonds. An analysis of the dipole moments of I in methanolic solutions led us to conclude that the μ₁ and μ₂ values corresponded to the dipole moments of associates and solvates comprising like and unlike molecules linked by intermolecular H-bonds. Their stoichiometry changed as the temperature increased.     

Inductive effect of substituents on the dipole moment of α-substituted vinyl methyl ether

Dipole moments of several α-substituted vinyl methyl ethers R(OMe)C:CH₂; R = Me, Et, i-Pr, t-Bu, cyclopropyl, vinyl, Ph) have been determined by the Halverstadt-Kumler method in benzene solution at 293 K. The square of the total dipole moment μ_r was found to be a linear function of the Taft's inductive constant σ_r^*: μ_r²/D²=(0.619±0.033)+(1.092±0.10) σ_r^*. The inductive contribution of the substituent R on the total dipole moment may be expressed by the equation μ_j/D = ?0.52 σ^* + 0.25. This is in good agreement with the corresponding equation for the dipole moments of alkyl-substituted ethenes: μ_i/D = ?0.58 σ^* + 0.28 (based on dipole moments obtained by PCILO calculations).     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.     

Lattice Monte Carlo investigations on copolymer systems, 3. Alternating and random copolymers

Alternating and random copolymers in dilute solution are investigated by means of Monte Carlo simulations on a cubic lattice. Each molecule consists of an equal number of A and B segments, either randomly distributed along the chain or forming an alternating sequence. The energy parameters chosen represent selective solvent conditions (the solvent is a good one for monomers of type A and a θ-solvent for B; between A and B repulsive interactions are operative). Comparison with di- and triblock copolymers of equal overall composition reveals that the behaviour of random or alternating copolymers (subject to the same selective solvent) is quite different. Their properties rather resemble those of homopolymers in a solvent of intermediate quality. The absolute chain dimensions (e.g. the mean square radius of gyration, 〈s²〉, and the mean square end-to-end distance, 〈h²〉) of random and alternating copolymers as well as their scaling exponents are significantly larger than those of block copolymers. The ratio between 〈h²〉 and 〈s²〉 as well as the shape of the polymer (expressed by the asphericity δ) are similar to those of athermal polymers indicating that there is no pronounced selectivity of the solvent. In contrast to block copolymers, these parameters exhibit no significant chain-length dependence. The number of the various types of polymer-polymer contacts (A-A, B-B and A-B) is almost independent of the type of contact at least for the solvent conditions investigated. This is in contrast to block copolymers where A-B contacts are widely suppressed and where the number of B-B contacts is approximately twice as high as that of A-A contacts.     

Rotary friction,dipole moments,conformation and rigidity of polybutylisocyanate molecules in solution

Experimental data on the dependence of the rotatory diffusion coefficients and dipole moments on molecular weight and the theory of hydrodynamic properties and of the size of wormlike chains were used for determining the main conformational characteristics of the polyisocyanate chain S is the number of molecular units in a segment, λ is the length of the projection of the monomer unit on the axis of the molecule, and μ_o is the dipole moment of the monomer unit. The values of S and λ agree with those found previously by hydrodynamic methods. It was shown that the flat cis-structure of the polyisocyanate chain corresponds to values of λ = 2 × 10^?8cm andμ_o = 1·8D. Analysis of experimental data indicates that dimensions of “geometrical” and “electrical” segments in the PBIC chain are identical.