Single-chain Model Research Articles

A new theoretical model about shear stress in magnetorheological fluids with small shear deformation

Based on the single-chain structure model of magnetorheological fluids, a formula for the calculation of shear stresses was established. The interaction force of two magnetic particles in an infinite single-chain was deduced using a new theoretical model which is founded on Ampere’ molecular current hypothesis, dipole theory and Ampere’ law. Furthermore, the resultant force on a particle was then deduced by taking into account of the action caused by all the other particles in the single-chain. A predictive formula for shear stresses was made corresponding to the case that MR fluids were sheared by a small angle and the calculating results fit well on the order with the yield stresses of the commercial MR fluids.

Molecular Dynamics Simulations on Crystallization of Polyethylene Copolymer with Precisely Controlled Branching

Molecular dynamics simulations of three kinds of linear low-density polyethylene (LLDPE) single-chain models with precisely controlled branching are performed. It is shown that the crystallinity of copolymers with branches shorter than C10H21 decreases with increasing branch length, whereas for copolymers having branches longer than C10H21, the crystallinity increases as the branch length increases. From the simulations of ethylene/vinyl chloride copolymer model, it is found that the crystallization process and driving force of LLDPE chain with polar comonomer are similar to those having a nonpolar comonomer, and the MD simulations of the models with branches of different flexibilities show that as branch flexibility decreases, the side-chain co-crystallization becomes more difficult, and the corresponding lamella is packed more loosely.

Rod Formation of Ionic Surfactants: Electrostatic and Conformational Energies

We present a thermodynamic model that describes the formation of micelles from ionic surfactants in aqueous solution at varying counterion concentrations. The micellar aggregates may be spheres, dumbbells, and rods. A former theory [Heindl, A.; Kohler, H.-H. Langmuir 1996, 12, 2464] is refined by the introduction of detailed models for the conformational energy of the surfactant chains and the electrostatic interaction of the ionic headgroups. The standard Gibbs energy of a surfactant ion is minimized under constraints imposed by the micelle shape. The conformational energy is calculated from an appropriately modified single-chain mean-field model proposed in another work [Ben-Shaul, A.; Gelbart, W. M. In Membranes, Microemulsions and Monolayers; 1994]. For the electrostatic interactions, we use a previously developed local balance model for a charged interface [Woelki, S.; Kohler, H.-H. Chem. Phys. 2000, 261, 411-419; 421−438]. This leads to a marked counterion specificity of the standard Gibbs energies ...

Luminescence properties and energy transfer in the mixed thin film of Alq3 and PVK

In this paper, the properties of fluorescence were studied of the thin films with different component ratios of polyvinyl carbazole(PVK)and Alq3. The energy transfer between PVK and Alq3 was studied through analysis of absorption spectra, excitated spectra, emission spectra of the thin films. When the content of Alq3 was high enough，the peak of Alq3 was quite evident in the abs orption spectra and excitated spectra, at the same time the emission spectra was the characteristic emission band of Alq3.When the content of PVK was high enough, the peak value of PVK is much greater than that of Alq3. At this time the extraordinary strong characteristic emission band of Alq3 and the feeble charac teristic emission band of PVK was observed. It is proved that the energy can transfer from PVK to Alq3 in a wide concentration range and it is most efficient at the concentration of 1∶7. A model Hamitonian based on single chain model including the dopant was put forward to simulate the experiment .This model can explain the experimental results very well.

Latent mixed Markov modelling of smoking transitions using Monte Carlo bootstrapping

It has been established that measures and reports of smoking behaviours are subject to substantial measurement errors. Thus, the manifest Markov model which does not consider measurement error in observed responses may not be adequate to mathematically model changes in adolescent smoking behaviour over time. For this purpose we fit several Mixed Markov Latent Class (MMLC) models using data sets from two longitudinal panel studies--the third Waterloo Smoking Prevention study and the UWO smoking study, which have varying numbers of measurements on adolescent smoking behaviour. However, the conventional statistics used for testing goodness of fit of these models do not follow the theoretical chi-square distribution when there is data sparsity. The two data sets analysed had varying degrees of sparsity. This problem can be solved by estimating the proper distribution of fit measures using Monte Carlo bootstrap simulation. In this study, we showed that incorporating response uncertainty in smoking behaviour significantly improved the fit of a single Markov chain model. However, the single chain latent Markov model did not adequately fit the two data sets indicating that the smoking process was heterogeneous with regard to latent Markov chains. It was found that a higher percentage of students (except for never smokers) changed their smoking behaviours over time at the manifest level compared to the latent or true level. The smoking process generally accelerated with time. The students had a tendency to underreport their smoking behaviours while response uncertainty was estimated to be considerably less for the Waterloo smoking study which adopted the 'bogus pipeline' method for reducing measurement error while the UWO study did not. For the two-chain latent mixed Markov models, incorporating a 'stayer' chain to an unrestricted Markov chain led to a significant improvement in model fit for the UWO study only. For both data sets, the assumption for the existence of an independence chain did not lead to significant improvement in model fit. The unrestricted two-chain latent mixed Markov model led to a significant improvement of model fit compared to a simple latent Markov model, but this model was overparameterized when the latent transition probabilities and/or response probabilities were assumed nonstationary. For the other models, the manifest/latent transition probabilities and response probabilities (for the four-wave Waterloo study only) were tested to be nonstationary for both data sets.

Roles of Branch Content and Branch Length in Copolyethylene Crystallization: Molecular Dynamics Simulations

Molecular dynamics simulations of two series of single copolymer chain models with precisely controlled methyl branching and with branches of different lengths are performed. For the models with precisely controlled methyl branching, the collapse process and the morphology of the lamellar structure are similar to those of the random copolymer. In particular, it is found that the branch content plays an important role in determining whether a single chain can form a lamellar structure or not. With the decrease of the branch contents, more perfect lamellar structure is formed, and the crystallinity of the copolymer increases. For the models with branches of different lengths, the simulations show that the branch point (CH unit) is always expelled from the crystalline phase as a defect, while the behavior of the branch chain in the crystallization depends on the chain length. When the chain has less than 10 carbon atoms, the branch is rejected to the folded surface of the lamellar structure as a defect, whereas when the branch length is longer, the branch is folded back and cocrystallizes with the main chain. In this case, the branch chain is packed in a manner as in polyethylene.

Crucial effects of intramolecular charge distribution on the neutral-ionic transition of tetrathiafulvalene–p-chloranil

We calculated the Madelung energies of both the ground state and excited states in tetrathiafulvalene - p-chloranil (TTF-CA) by taking into account intramolecular charge distribution. The distribution is found to be significant in the neutral-ionic (NI) transition. In the ionic phase, the Madelung energy depends more strongly on the intermolecular distance perpendicular to the $\pi$-stacking chains than on that along the chains. This indicates that simple single-chain models neglecting interchain electrostatic coupling are not adequate. The gain of the Madelung energy due to dimerization is concluded to be small compared with the other structural changes. We also calculated the formation energy of excited state domains, which appear in the initial process of the phase transition. A one-dimensional excited domain has the smallest energy among the possible domains with the same number of molecules, and the energy per molecule is considerably reduced in increasing the domain size. It is consistent with the experimental suggestion that a large number of excitations were generated by only one photon.

Bethe ansatz solvable multi-chain quantum systems

In this article we review recent developments in the one-dimensional Bethe ansatz solvable multi-chain quantum models. The algebraic version of the Bethe ansatz (the quantum inverse scattering method) permits us to construct new families of integrable Hamiltonians using simple generalizations of the well known constructions of the single-chain model. First we consider the easiest example (‘basic’ model) of this class of models: the antiferromagnetic two-chain spin- 1 model with the nearest-neighbour and next-nearest-neighbour spin-frustrating interactions (zigzag chain). We show how the algebra of the quantum inverse scattering method works for this model, and what are the important features of the Hamiltonian (which reveal the topological properties of two dimensions together with the one-dimensional properties). We consider the solution of the Bethe ansatz for the ground state (in particular, commensurate–incommensurate quantum phase transitions present due to competing spin-frustrating interactions are discussed) and construct the thermal Bethe ansatz (in the form of the ‘quantum transfer matrix’) for this model. Then possible generalizations of the basic model are considered: an inclusion of a magnetic anisotropy, higher-spin representations (including the important case of a quantum ferrimagnet), the multi-chain case, internal degrees of freedom of particles at each site, etc. We observe the similarities and differences between this class of models and related exactly solvable models: other groups of multi-chain lattice models, quantum field theory models and magnetic impurity (Kondo-like) models. Finally, the behaviour of non-integrable (less constrained) multi-chain quantum models is discussed.

Molecular dynamics studies of the effects of branching characteristics on the crystalline structure of polyethylene

Molecular dynamics simulations were carried out on single chain models of linear low-density polyethylene in vacuum to study the effects of branch length, branch content, and branch distribution on the polymer’s crystalline structure at 300 K. The trans/gauche (t/g) ratios of the backbones of the modeled molecules were calculated and utilized to characterize their degree of crystallinity. The results show that the t/g ratio decreases with increasing branch content regardless of branch length and branch distribution, indicating that branch content is the key molecular parameter that controls the degree of crystallinity. Although t/g ratios of the models with the same branch content vary, they are of secondary importance. However, our data suggests that branch distribution (regular or random) has a significant effect on the degree of crystallinity for models containing 10 hexyl branches/1,000 backbone carbons. The fractions of branches that resided in the equilibrium crystalline structures of the models were also calculated. On average, 9.8% and 2.5% of the branches were found in the crystallites of the molecules with ethyl and hexyl branches while C13 NMR experiments showed that the respective probabilities of branch inclusion for ethyl and hexyl branches are 10% and 6% [Hosoda et al., Polymer 1990, 31, 1999–2005]. However, the degree of branch inclusion seems to be insensitive to the branch content and branch distribution.

Experimental Investigation of Mooring Line Loading Using Large and Small-Scale Models

For catenary mooring lines, the relationship between excursion of the point of suspension and the length of suspended line is highly nonlinear. If the point of suspension is then set in motion, the velocity of the line resulting from a change in catenary profile induces additional nonlinear hydrodynamic loading components. The sensitivity of the mooring line to initial and oscillatory conditions results in a complicated tension history at the point of suspension, with line tensions possibly greatly exceeding those predicted by static analyses. This paper presents results from an experimental investigation into the response of a large (1:16) and small (1:70) scale single-chain catenary model mooring line when subject to a comprehensive, and equivalent, range of excitation parameters. Tests were performed at purpose-built test facilities. Small-scale model tests were carried out at University College London (UCL). Large-scale model mooring line tests were completed at the Ship Dynamics Laboratory, Canal de Experiencias Hidrodinamicas de El Pardo (CEHIPAR), Madrid, Spain. Funding for the model tests performed in Spain was provided through the European Union Access to Large Scale Facilities—Training and Mobilisation of Researchers Program.

NMR relaxation and NMR imaging of elastomers in the course of thermal aging

A complex aging regime occurs in the course of thermal aging of elastomers. Depending on the type and the content of the rubber filler materials, temperature, chemical environment (normally air), and time, a different aging process can be observed also by nuclear magnetic resonance (NMR) [1–6]. The methods used are the common spin-echo 1H-NMR, including variable echo times and parameter-selective NMR-1H-imaging (material properties imaging). The decay of the echo-magnetization is discussed on the basis of a single-chain model with a distribution of dipolar interactions. This model is based on the influence of a very fast, but anisotropic, local motion, as well as larger and slower motions, which are able to diminish the residual dipolar interaction. Carbon-black-filled natural rubber, as well as silica and carbon-black-filled E-SBR (emulsion-polymerized styrene butadiene rubber) and S-SBR (solution-polymerized SBR) are the systems under investigation, with the results showing some characteristic features of the course of aging observable by NMR.

On the nature of electronic excitations in poly(paraphenylenevinylene): A quantum-chemical investigation

Correlated quantum-chemical calculations are performed on phenylenevinylene oligomers containing up to eleven repeat units, to characterize the nature of the electronic excitations relevant for the photophysical properties of the corresponding polymer. The focus is first on the nonlinear optical response of model conjugated chains and the simulation of their frequency-dependent (third-harmonic generation, electroabsorption, and two-photon absorption) response. From the assignment of the calculated resonance features, the excited states dominating the third-order nonlinear polarizability are identified and their chain-length dependence is investigated. On that basis, we build an essential-state single-chain model (that includes the 1Bu, 2Ag, mAg, and nBu states) and apply it to the interpretation of recent experimental data reported for poly(paraphenylenevinylene) and derivatives. We then examine how the exciton binding energy, here defined as the difference between the energies of the charge-separated nBu and the strongly optically allowed 1Bu excited states, is affected by both intrachain and interchain polarization effects.

Non-linear magnetorheological behaviour of an inverse ferrofluid

The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made magnetorheometer. Both curves were found to scale linearly with the volume fraction and quadratically with the magnetic moment of the silica particles. Affine deformation cannot lead to the observed yield stresses. Instead, a bead–rod model is described that gives results closer to what is observed experimentally. A master curve for the viscosity was obtained by plotting the dimensionless viscosity versus the Mason number, Mn. The free single chain model of Martin and Anderson does not give a good description of the measured curves. This may be due to the simplifications with respect to the microstructure of and processes in the suspension.

The use of NMR relaxation and NMR imaging in studying the aging of rubber

Nuclear magnetic resonance was used to study the aging of rubber filler materials. The methods used are the common spin-echo 'H NMR including variable echo times and parameter-selective NMR 1 H-imaging (material properties imaging). The decay of the echo-magnetization is discussed on the basis of a single chain model with a distribution of dipolar interactions. This model is based on the influence of a very fast but anisotropic local motion as well larger and slower motions, which are able to diminish the residual dipolar interaction. Carbon black filled natural rubber as well as silica and carbon black filled E(mulsion)-and S(olution)-SBR and milled tire rubber are the systems under investigation showing some characteristic features of the aging course observable by NMR.

The use of NMR relaxation and NMR imaging in studying the aging of rubber

Nuclear magnetic resonance was used to study the aging of rubber filler materials. The methods used are the common spin-echo 1H NMR including variable echo times and parameter-selective NMR 1H-imaging (material properties imaging). The decay of the echo-magnetization is discussed on the basis of a single chain model with a distribution of dipolar interactions. This model is based on the influence of a very fast but anisotropic local motion as well larger and slower motions, which are able to diminish the residual dipolar interaction. Carbon black filled natural rubber as well as silica and carbon black filled E(mulsion)- and S(olution)-SBR and milled tire rubber are the systems under investigation showing some characteristic features of the aging course observable by NMR.

Blue Electroluminescence from Novel Silicon-Containing Poly(Cyanoterephthalylidene) Copolymers

A new class of silicon-containing poly(cyanoterephthalylidene) copolymers with a uniform π-conjugated segment was synthesized using the Knoevenagel reaction between the dialdehyde monomer and the appropriate diacetonitrile. The incorporation of organosilicon units with the flexible alkyl side group into the polymer rigid backbone would afford processable electroluminescent materials and interrupt the regular π-conjugated chains. The resulting polymers were highly soluble in common organic solvents. The Mn and Mw of the resulting polymers are in the range 3800−4200 and 5400−6000 with a polydispersity index range of 1.38−1.43, respectively. Their glass transition temperature was in the range of 82−87 °C. According to the molecular mechanical calculations for single chain models of SiBuPPV and SiBuCNPPV, trans conformations are more stable than cis conformations. The UV−visible absorbance of present polymers show strong absorption bands around 340−360 nm, since the π-conjugated system is regulated by organosilicon units. Their photoluminescence spectra appeared around 460−470 nm in the blue region. The threshold voltage of the SiHMCNPPV was about 7 V. Surprisingly, these polymers exhibit blue light-emitting diodes in the EL emissive band at 480 nm in the blue region, instead of red light-emitting diodes, when an operating voltage of higher than 7 V is applied. These copolymers show a relatively low operating voltage compared with a block copolymer having well-defined structures because the incorporation of electron-withdrawing cyano groups into the π-conjugated system increased the electron affinity of those polymers and decreased the LUMO energy level.

Persistent current in a two-chain Hubbard model with impurities

The interplay between impurities and interactions is studied in the gapless phase in a two-chain Hubbard model in order to see how the screening of impurity potentials due to repulsive interactions in a single-chain model will be changed by increasing the number of channels. Renormalization-group calculations show that charge stiffness, and hence persistent current, of the two-chain model are less enhanced by interactions than in the single-chain case.

A single-chain analysis of doped quasi-one-dimensional spin-1 compounds: paramagnetic versus doping

We present a numerical study of single-chain models of doped spin-1 compounds. We use low-energy effective one-dimensional models for both the cases of paramagnetic and spin-1/2 doping. In the case of paramagnetic doping, the effective model is equivalent to the bond disordered spin-1/2 chain model recently analysed by means of the real space renormalization group by Hyman and Yang. By means of exact diagonalizations in the XX limit, we confirm the stability of the Haldane phase for weak disorder. Above a critical amount of disorder, the effective model flows to the so-called random singlet fixed point. In the case of spin-1/2 doping, we argue that the Haldane phase should be destabilized even for weak disorder. This picture is not in contradiction with existing experimental data. We also discuss the possible occurrence of (unobserved) antiferromagnetically ordered phases.

Enhanced magnetic fluctuations in doped spin-Peierls systems: A single-chain-model analysis

We analyze by means of the real-space renormalization group (RG) as well as by exact diagonalizations the properties of a single-chain model of a doped spin-Peierls system, where a major role is played by the localized moments created by the impurities. By the RG flow, we are able to follow the behavior of the disordered system for all temperatures below the spin-Peierls transition temperature. In particular, we find an enhancement of magnetic correlations due to disorder, coexisting with an underlying dimerization, in an intermediate temperature range below the spin-Peierls critical temperature and above the coherence temperature of a regular array built by those localized moments. The possible relevance of these results to the doped inorganic spin-Peierls compound ${\mathrm{CuGeO}}_{3}$ is discussed.

Cystine knot of the gonadotropin alpha subunit is critical for intracellular behavior but not for in vitro biological activity.

The common alpha subunit of glycoprotein hormones contains five disulfide bonds. Based on the published crystal structure, the assignments are 7-31, 59-87, 10-60, 28-82, and 32-84; the last three comprise the cystine knot, a structure also seen in a variety of growth factors. Previously, we demonstrated that the efficiency of secretion and the ability to form heterodimers by alpha subunits bearing single cysteine residue mutants in the cystine knot were significantly reduced. These results suggested that the cystine knot is critical for the intracellular integrity of the subunit. To assess if the presence of the free thiol affected the secretion kinetics, we constructed paired cysteine mutants of each disulfide bond of the alpha subunit. The secretion rate for these monomers was comparable with wild type except for the alpha-10-60 mutant, which was 40% lower. The recovery of the alpha7-31 and alpha59-87 mutants was greater than 95%, whereas for the cystine knot mutants, it was 20-40%. Co-expression of the wild-type chorionic gonadotropin beta subunit with double cysteine mutants did not enhance the recovery of alpha mutants in the media. Moreover, compared with wild-type, the efficiency of heterodimer formation of the alpha10-60 or alpha32-84 mutants was less than 5%. Because subunit assembly is required for biological activity, studies on the role of these disulfide bonds in signal transduction were not possible. To bypass the assembly step, we exploited the single chain model, where the alpha and beta subunits are genetically fused. The recovery of secreted tethered gonadotropins bearing mutations in the cystine knot was increased significantly. Although dimer-specific monoclonal antibodies discriminated the conformation of single chain alpha10-60 and alpha32-84 mutants from the native heterodimer, these mutants were nevertheless biologically active. Thus, individual bonds of cystine knot are important for secretion and heterodimer formation but not for in vitro bioactivity. Moreover, the data suggest that the native heterodimer configuration is not a prerequisite for receptor binding or signal transduction.