Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level

An implementation of the gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational g tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing CC analytic second-derivative code is described, focusing on the required modifications concerning integral evaluation and treatment of the unperturbed and perturbed two-particle density matrices. An extensive set of test calculations for LiH and BH (up to the full configuration-interaction limit), for a series of simple hydrides (HF, H(2)O, NH(3), and CH(4)) as well as the more challenging molecules CO, N(2), and O(3) [employing the CC singles and doubles (CCSD) and the CCSD approximation augmented by a perturbative treatment of triple excitations] demonstrates the importance of electron correlation for high-accuracy predictions of magnetizabilities and rotational g tensors.     

Theoretical birefringence of ultraoriented polyethylene from model structure calculations

The birefringence of model structures of ultraoriented polyethylene has been calculated by using the point-dipole concept and the polarizability tensor of the methylene group derived recently by Pietralla. For well-oriented chains the birefringence is determined by the combination of a negative anisotropy of the polarizability tensor of the methylene group and a positive anisotropy of the Lorentz tensor, both with respect to the chain direction. As a consequence it decreases with increasing density. The results are in agreement with experimental values of Mead, Desper, and Porter. In the model the amorphous regions are regarded as a mixture of planar and helical segments arranged in nematiclike bundles which additionally may have a certain distribution of orientation. The birefringence is not much affected by defects which, on the other hand, strongly influence the ultimate mechanical properties.     

Relativistic four-component calculations of Buckingham birefringence using London atomic orbitals

We present the first relativistic study of the electric-field-gradient induced birefringence (Buckingham birefringence), with application to the series of molecules CX₂ (X?=?O, S, Se, Te). A recently developed atomic-orbital-driven scheme for the calculation of time-dependent molecular properties using one-, two- and four-component relativistic wave functions (Bast et?al. in Chem Phys 356:177, 2009) is extended to first-order frequency-dependent magnetic-field perturbations, using London atomic orbitals to ensure gauge-origin independent results and to improve basis-set convergence. Calculations are presented at the Hartree?CFock and Kohn?CSham levels of theory and results for CO₂ and CS₂ are compared with previous high-level coupled-cluster calculations. Except for the heaviest member of the series, relativistic effects are small??in particular for the temperature-independent contribution to the birefringence. By contrast, the effects of electron correlation are significant. However, the reliability of standard exchange-correlation functionals in describing Buckingham birefringence remains unclear based on the comparison with high-level coupled-cluster singles-and-doubles calculations.     

Correlated and gauge origin independent calculations of magnetic properties

Summary We have applied a gauge origin invariant method for calculations of nuclear magnetic shielding constants to the singly bonded molecules BF, F₂, BH₃, CH₄, NH₃, H₂O, and HF as well as to the¹H shielding constants of HCN and C₂H₂. The calculations were performed at the RPA and second order polarization propagator (SOPPA) level of theory. For most molecules the correlation contribution in SOPPA is less diamagnetic than in the comparable MP2 calculations. For F₂, SOPPA gives a large paramagnetic correlation correction whereas the MP2 method gives a very small correlation contribution. For all molecules agreement with experimental results is generally improved at the SOPPA level compared to RPA. We have also demonstrated that second order gauge origin invariant, common and local origin (SOLO) methods do not necessarily give the same shielding even in the limit of a converged basis set.     

Dynamic optical birefringence

The measurements of dynamic optical birefringence is described, together with instrumentation for this purpose. Complex birefringence, stress- and strain-optical coefficients are determined simultaneously with complex mechanical properties (E and tan δ_m). Results are shown for poly(vinyl chloride) comparing data obtained in this study with earlier measurements. Optical birefringence is shown to be a very sensitive probe for molecular motions and is therefore a useful structural elucidation tool.     

Magnetic birefringence of minerals

The earliest reports of magnetically induced optical birefringence included data for liquids, magnetic fluids and colloidal suspensions. Recent work has shown that with relatively straightforward apparatus, when carefully designed and aligned, measurable effects can be recorded even for suspensions of relatively weak diamagnetic materials, including mineral particles. By recording the magnitude of the birefringence induced in magnetic fields of up to two Tesla, a method for the analysis of the magnetic and optical characteristics of these diamagnetic colloids is evidenced. The principles, apparatus and methodology involved are described and novel data reported for the minerals attapulgite, bentonite, hectorite, kaolinite, montmorillonite and vermiculite. Preliminary experiments using pulsed fields on vermiculite sols show that, in favourable circumstances, estimates of particle size can be made by analysing signal response rates.     

Electric birefringence and streaming-electric birefringence of synthesized imogolite: the anisotropy of electric polarizability

Imogolite synthesized from sodium orthosilicate and aluminum trichloride was fractionated into four fractions by centrifuging at 12,000 x g (1h). The supernatant, which did not deposit by three times centrifugations, was used for all measurements. The signal of birefringence under a reversing electric pulse showed that the permanent dipole moment is negligibly small at low fields. The electric birefringence under a rectangular electric pulse is positive. The saturated value is proportional to the concentration of imogolite in the range of 0-0.1mg/ml and decreases rapidly with an increase of added salt concentration for NaCl and AgNO(3). It slightly depends on the pH of solution and is biggest in pure water. Then we have determined the anisotropy of electric polarizability (Deltaalpha) for imogolite in pure water at 0.05 mg/ml. Deltaalpha we obtained from the method decreases rapidly at low fields and slowly at high fields as shown in references [M. Matsumoto, Colloids Surf. A 148 (1999) 75, M. Matsumoto, Biophys. Chem. 58 (1996) 173]. It is approximately shown by the following expression, Deltaalpha=Deltaalpha(infinity)+(Deltaalpha(0)-Deltaalpha(infinity))/(1+KE), (Deltaalpha(0):Deltaalpha at E=0, Deltaalpha(infinity):Deltaalpha at E=infinity). Using this relation we can draw the curve of electric birefringence as a function of electric field and compare it with experimental values. The results, when Deltaalpha(0)=1.17x10(-28)Fm(2), Deltaalpha(infinity)=0.005x10(-28)Fm(2) and K=0.00031 m/V, are in good agreement with each other. In order to explain the reason why the anisotropy of electric polarizability rapidly decreases with an increase of electric field we propose that the difference of electrophoretic mobility between parts of colloidal particle causes the orientation of a rod like particle. The theoretical electric birefringence as a function of electric field we obtained is considerably in good agreement with the experimental values.     

Viscoelasticity and birefringence of polyisobutylene

The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), were measured for polyisobutylene (PIB) over a wide temperature range near and above its glass transition temperature. The master curves could be constructed well for each function with the method of reduced variables. The shift factor, a_T, for E*(ω) is the same as that for O*(ω). The ratio of the imaginary parts of O*(ω) and E*(ω), O″(ω)/E″(ω), takes an extremum, which has never been observed for other polymers. The relation between O*(ω) and E*(ω) cannot be described by a modified stress-optical rule (MSOR) which has been found valid for various polymers. The basic concept of the MSOR. i.e., the chain orientation and the orientation of flat monomer units in the stretch direction, is not sufficient to describe the behavior of PIB and another origin of stress, presumably due to the fluctuation of local stress, should be included. This term does not contribute to the birefringence. The main maximum of tan δ is ascribed to the relaxation of the chain orientation in contrast with many other polymers, such as polyisoprene and polycarbonate, for which the maximum of tan δ is ascribed to the rotational relaxation of monomer units. © 1995 John Wiley & Sons, Inc.     

Viscoelasticity and birefringence of polyisoprene

The complex Young's modulus, E^*(ω), and the complex strain-optical coefficient, O^*(ω), which is the ratio of the birefringence to the strain, were measured for polyisoprene (PIP) over a frequency range of 1 ～ 130 Hz and a temperature range of 22 ～ ?100°C. The imaginary part of O^*, O″, was positive at low frequencies and negative at high frequencies. The real part, O′, was always positive and showed a maximum. The complicated behavior of O^* could be understood by the assumption that E^* = E_R^* + E_G^* and O^* = C_RE_R^* + C_GE_G^*, where E_R^* and E_G^* were complex quantities and C_R and C_G were constants. The C_R value, equal to the ordinary stress-optical coefficient measured in the rubbery plateau zone, was 2.0 × 10^?9 Pa^?1. The C_G value, defined as the ratio O″/E″ in the glassy zone, was ?1.1 × 10^?11 Pa^?1. The E_G^*, which was the major component of E^* in the glassy zone, showed almost the same frequency dependence as that of polystyrene and polycarbonate. The E_R^*, which was dominant in the rubbery zone, was described well by the bead-spring theory. The temperature dependence of the E_G^* was stronger than that of the E_R^*. This difference caused the breakdown of the thermorheological simplicity for E^* and O^* around the glass-to-rubber transition zone. © 1995 John Wiley & Sons, Inc.     

Flow birefringence and polydispersity

Flow birefringence data for dilute solutions of various linear and branched polymers of different degrees of polydispersity are discussed. The polymers considered are polystyrene, polypropylene, and polyethylene. By making use of a well-known stress-optical relation, reduced elastic normal stresses, which can also be interpreted as coil expansions, are plotted against reduced shear stresses. As elastic normal stresses are rather sensitive to the shape of the molecular weight distribution at high molecular weight, a characteristic, p, related to the skewness of the distribution, is obtained. Experimental values of p are compared with theoretical ones based on special types of distribution functions. Attention is paid to the method of extrapolating experimental results to zero shear stress and concentration.     

Electric birefringence of dispersions of platelets

This paper describes the electro-optic response of a suspension of disk-like colloids. We have considered aqueous suspensions of Gibbsite platelets and measured the electrically induced birefringence in the broad frequency range 10(2)-10(8) Hz. When simply dispersed in an electrolyte solution, these particles orient with their major axis parallel to the electric field at all frequencies. The spectral dependence of their Kerr coefficient features three regimes: an electrokinetic α-relaxation within the kHz range, a conductive Maxwell-Wagner-O'Konski (MWO) relaxation having characteristic frequency in the 1-10 MHz range, and a nonzero high frequency asymptote. We quantitatively analyze the MWO spectral component and the high-frequency asymptote on the basis of a model developed for oblate particles. This analysis enables us to obtain the relevant particle properties: surface conductivity, zeta potential, and intrinsic Gibbsite birefringence. When the particles are dispersed in a mixture that also contains smaller spherical particles that have a charge of the same sign, their electric birefringence becomes negative at low frequency. This anomalous orientation of the platelets is analogous to that observed in mixtures of prolate and spherical particles, and demonstrates the anomalous birefringence as a universal property of suspensions of nonspherical particles when surrounded by smaller charged particles.     

The dynamic birefringence of high polymers

The simultaneous measurement of the birefringence and strain of a sample subjected to sinusoidal strain is proposed as a means for elucidating the molecular mechanism of the response to high polymers to mechanical deformation. A linear phenomenologicical theory is proposed in which strain-optical coefficient distribution functions are assigned to the elastic and viscous members of a distribution of Maxwell elements. An apparatus has been constructed to determine the dynamic strain-optical coefficient at frequencies between 0 and 600 cycles/sec. By means of mechanical excitation of vibration at low frequencies and electromagnetic at high frequencies. The dynamic birefringences of polyethylene has been studied at room temperature over this frequency range.     

Dynamic birefringence studies of high-density polyethylene

A rheo-optical investigation has been carried out on a sample of high-density polyethylene (HDPE) in an attempt to examine the nature of the α-relaxation mechanism. Dynamic mechanical and bi-refringence behavior was measured over the frequency range of 0.008-4.3 Hz and temperature range ?40 to 100°C. The dynamic mechanical and birefringence data were reduced to a reference temperature of 50°C by a combination of horizontal and vertical superposition. The significance of the vertical shift factor has been discussed extensively in previous papers and is not dealt with here. An Arrhenius plot was made of the log of the horizontal shift factor versus reciprocal temperature for the mechanical and optical data. The mechanical data exhibited three distinct regions, the slopes of which led to activation energies of 70, 90, and 150 kJ mol^?1. The temperature at which these dispersions occurred suggested the observation of the β, α₁, and α₂ relaxation processes. The optical data contained two distinct regions from which activation energies of 55 and 95 kJ mol^?1 were obtained. The high-temperature α₂ process was not observed in the Arrhenius plot; however, a maximum in K′ and a change in sign of K″ probably reflects a contribution from the α₂ relaxation mechanism.     

Magnetic birefringence of cobalt ferrite ferrofluids

Properties of chemically synthesized ferrofluids based on nanoparticles of CoFe₂O₄ are investigated. Their rigid dipole behaviour is established through magnetic birefringence experiments. The dynamical response of such particles to crossed magnetic fields is analysed. In large applied fields, it leads to characteristic relaxation times independent of the mean particle size of the sample, allowing viscosity determination in anisotropic systems.     

Flow birefringence of temporary polymer networks

The statistical theory of temporary polymer networks is an effort of describing the macroscopic behavior of such networks based on molecular behavior analysis. The calculation of the stress tensor of a network and the satisfactory comparison with experimental viscosity results was shown before [Rheol. Acta 28 (1989) 193]. Here we present the foresights of the theory as regards flow birefringence. The polarizability tensor is calculated first and then the birefringence of a four-functional temporary polymer network is estimated for a stationary simple shear flow. The dependence of the calculated quantities on shear rate is in line with existing experimental evidence.     

Negative birefringence ferroelectric liquid crystals

The synthesis and evaluation of a negative birefringence material which possesses a wide smectic C phase is reported.