Spherocylinder Model Research Articles

A Numerical Description of Fast Relaxation in Micellar Solutions on the Basis of the Spherocylinder Model

A semianalytical method for calculating the time of fast relaxation in surfactant solutions with cylindrical micelles has recently been developed on the basis of the Becker−Doring kinetic equations. This method enables one to make the calculation procedure substantially shorter with no loss in the accuracy. A model micelle having the shape of a prolate ellipsoid was there used to determine the kinetic coefficients of monomer attachment to an aggregate because the problem of finding the diffusion flux of monomers to a micelle has an analytical solution for this model. In this work, the diffusion flux and fast relaxation time have been numerically calculated in terms of a more realistic model of a micelle having the shape of a spherocylinder. The results obtained have been compared with previously known ones.

A bonded sphero-cylinder model for the discrete element simulation of elasto-plastic fibers

Based on the Discrete Element Method (DEM), a bonded sphero-cylinder model is developed to simulate flexible fibers that can undergo plastic bending deformation. In the model, a fiber is formed by connecting a number of identical sphero-cylinders using virtual bonds, which can experience bending, axial extension/compression, and twisting deformations. The elastic deformation and vibration of a single fiber are simulated and validated against elastic beam theories. In addition, an elasto-plastic constitutive model is implemented to simulate the elasto-plastic bending deformation of a fiber. The DEM results compare well with Finite Element Method (FEM) simulations, verifying the proposed elasto-plastic fiber model. By using bonded sphero-cylinders as opposed to more traditional bonded spheres, large aspect ratio fibers with smooth surfaces can be simulated effectively with fewer elements. The new constitutive model allows for the simulation of elasto-plastic materials, such as metals, plastics, and biomass.

The effect of side chain length on hydrodynamic and conformational characteristics of polyimide-graft-polymethylmethacrylate copolymers in thermodynamically good solutions

Samples of graft-copolymers with polyimide backbones and poly(methyl methacrylate) side chains synthesized by ATRP of methylmethacrylate on polyimide macroinitiator are investigated by 1H NMR, GPC, static and dynamic light scattering, sedimentation, and viscosimetry in chloroform and ethyl acetate solutions. Hydrodynamic and conformational behavior of graft-copolymers is well-described by the wormlike spherocylinder and Porod wormlike chain models. Samples of graft-copolymers have high equilibrium rigidity, the Kuhn segment length grows from 20 to 95 nm with the lengthening of side chains. The equilibrium rigidity and hydrodynamic diameter of the investigated graft-copolymers depend on the molar mass M of side chains as M 0.7.

Hydrodynamic properties and conformation of poly(3-hexylthiophene) in dilute solutions

Conducting polymers demonstrate low solubility in organic solvents. Introducing aliphatic substituents into polymer chains improves their solubility, but may also lead to changes in conformational characteristics of macromolecules. In the present work, the studies of hydrodynamic properties and conformational characteristics of comb-shaped poly(3-hexylthiophene) with aliphatic side substituents were carried out in chloroform solutions. Conformational analysis of the studied macromolecules was performed for the first time using homologous series with a wide range of molecular weights of the polymers in dilute solutions. The hydrodynamic properties of these macromolecules were interpreted using the worm-like spherocylinder model and the straight spherocylinder model. The projection of the monomer unit in the direction of the main polymer chain λ = 0.37 nm was determined experimentally. The following parameters of poly(3-hexylthiophene) were characterized and quantified: equilibrium rigidity (Kuhn segment length) А = 6.7 nm and hydrodynamic diameter of a polymer chain d = 0.6 nm. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 875–883

Investigation of dynamics simulation of granular particles using spherocylinder model

A dynamics simulation method for granular materials composed of cylindrical particles is investigated both experimentally and theoretically. A cylindrical particle is modeled as a cylinder with two hemispherical ends of the same diameter; this shape is also known as a spherocylinder. The motion of individual spherocylinders coming into contact with each other is solved by the discrete element method. There are four and two patterns in the cases of interparticle contact and particle–plane contact, respectively. The contact force acting on the particle is decomposed into normal and tangential components. The normal force is given by the sum of the damping force and the elastic force. To examine the validity of the simulation method, we conducted experiments for a vibratory conveyance and for an inclined chute flow. The behavior of spherocylinders was revealed by image processing. Through a comparison of the experimental and calculated results, it was found that the flow patterns obtained by this method appear realistic.

Solution behavior of polyimide‐graft‐polystyrene copolymers in selective solvents

ABSTRACTA polyimide‐graft‐polystyrene (PI‐g‐PS) copolymer with a polyimide backbone and polystyrene side chains was synthesized by the “grafting from” method using styrene polymerization on a polyimide multicenter macroinitiator via ATRP mechanism. The side chain grafting density z = 0.86 of PI‐g‐PS is rather high for graft‐copolymers synthesized by the ATRP method. Molecular characteristics and solution behavior of PI‐g‐PS were studied in selective solvents using light scattering and viscometry methods. In all solvents, the backbone tends to avoid contact with a poor solvent. To describe the conformation and hydrodynamic properties of PI‐g‐PS macromolecules in thermodynamically good solvents for side chains and PI‐g‐PS, the wormlike spherocylinder model is used. Macromolecules of the studied graft‐copolymer are characterized by high equilibrium rigidities (Kuhn segment length >20 nm). In Θ‐conditions, PI‐g‐PS macromolecules may be modeled by a rigid prolate ellipsoid of revolution with a low asymmetry form and a collapsed backbone as the ellipsoid core. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 1539–1546

Reentrant structural phase transition in amphiphilic self-assembly

Amphiphilic molecules can self-assemble into a variety of aggregates and mesophases. Yet, predictions of phase transitions are not always met. In this communication, we demonstrate a novel structural phase transition of amphiphilic molecules, quillaja saponin/cholesterol, and discuss the relevance of precursors for forming hierarchical structures. In contrast to the standard sphero-cylinder model, we highlight a three-stage dynamic process of reentrant phase transition induced by cholesterol. It is expected that the obtained results would be helpful to rationalize the rich phase behavior exhibited by surfactant–cosurfactant systems, and to engineer complex nanoarchitectures with tunable size and shape and well-defined biological functions.

Fast off-lattice Monte Carlo simulations of soft-core spherocylinders: Isotropic-nematic transition and comparisons with virial expansion

We proposed a novel anisotropic soft-core potential for spherocylinders that takes into account the degree of overlap between two spherocylinders, thus superior to other soft-core spherocylinder models depending only on the minimum distance between two line segments representing spherocylinders, for example, that used by Vink and Schilling [Phys. Rev. E 71, 051716 (2005)]. Using Monte Carlo simulations in an isothermal-isobaric ensemble with replica exchange at different pressures and multiple histogram re-weighting technique, we studied the isotropic-nematic transition of both models, which recover the standard model of hard spherocylinders for liquid crystals as the repulsion strength ε → ∞, and compared simulation results with virial expansion predictions. We found that isotropic-nematic transition still occurs at high enough densities even for small ε, and that virial expansion predictions become more accurate with increasing aspect ratio of spherocylinders and should be exact in the limit of infinitely large aspect ratio.

Simulation of bulk phases formed by polyphilic liquid crystal dendrimers

A coarse-grained simulation model for a third generation liquid crystalline dendrimer (LCDr) is presented. It allows, for the rst time, for a successful molecular simulation study of a relation between the shape of a polyphilic macromolecular mesogen and the symmetry of a macroscopic phase. The model dendrimer consists of a soft central sphere and 32 grafted chains each terminated by a mesogen group. The mesogenic pair interactions are modelled by the recently proposed soft core spherocylinder model of Lintuvuori and Wilson [J. Chem. Phys, 128, 044906, (2008)]. Coarse-grained (CG) molecular dynamics (MD) simulations are performed on a melt of 100 molecules in the anisotropic-isobaric ensemble. The model LCDr shows conformational bistability, with both rod-like and disc-like conformations stable at lower temperatures. Each conformation can be induced by an external aligning eld of appropriate symmetry that acts on the mesogens (uniaxial for rod-like and planar for disc-like), leading to formation of a monodomain smectic A (SmA) or a columnar (Col) phase, respectively. Both phases are stable for approximately the same temperature range and both exhibit a sharp transition to an isotropic cubic-like phase upon heating. We observe a very strong coupling between the conformation of the LCDr and the symmetry of a bulk phase, as suggested previously by theory. The study reveals rich potential in terms of the application of this form of CG modelling to the study of molecular self-assembly of liquid crystalline macromolecules.

Columnar phases of discotics with orientation-dependent interactions

The liquid crystal phase diagram of fluids of rigid discotics with soft interactions has been investigated by means of Monte Carlo simulations. The particles are modeled by spherocylinders or Gay-Berne ellipsoids with thickness/diameter aspect ratios of L/D=0.2. The study includes a variety of pair interaction potentials, featuring different energetic dependencies on the orientation of the particles. Three distinct types of models are considered: (i) models with a homogeneous interaction around the molecular core, (ii) models favoring stacked pair configurations, and (iii) models favoring edge-to-edge configurations. The stability and internal structure of the isotropic, nematic, and the different hexatic columnar phases exhibited by these fluids are discussed. The results indicate that the spherocylinder and ellipsoidal models differ in fundamental trends of their phase behavior. The spherocylinder fluids display more extended ranges of stability and longer pair correlation lengths in the columnar phases than the ellipsoidal models. As a consequence, as opposed to ellipsoids, the nematic phase for spherocylinders with the title aspect ratio tends to be entropically suppressed, even under favorable energetics.

Wormlike Micelles of Polyoxyethylene Alkyl Ethers CiEj

It is demonstrated that wormlike micelles of nonionic surfactants polyoxyethylene alkyl ethers H(CH2)i(OCH2CH2)jOH (CiEj) have been successfully characterized by static (SLS) and dynamic light scattering (DLS) measurements and viscometry with the aid of the theories developed so far in the field of polymer solution studies, i.e., a molecular thermodynamic theory for light scattering, chain statistical and hydrodynamic theories for semi-flexible polymers. The results for the excess Rayleigh ratio, radius of gyration, hydrodynamic radius, and intrinsic viscosity have been shown to be well represented by the theories based on a wormlike spherocylinder model. Some salient features found for the micelles of CiEj with various i or j, their binary mixtures, and the micelles including n-alcohol and n-alkane are discussed.

An investigation of soft-core potentials for the simulation of mesogenic molecules and molecules composed of rigid and flexible segments

The phase behaviour of three soft core spherocylinder models is investigated with a view to producing an effective potential for use in coarse-grained simulations of liquid crystal phases and polymers composed of rigid and flexible segments. Provided potentials are not made too soft, two of the soft core models are found to work well in terms of successfully reproducing mesophases and in providing considerable improvements in computational speed over other commonly used coarse-grained models. In Monte Carlo simulations a soft-core spherocylinder model in which a cut and shifted Lennard–Jones potential is truncated with a linear tangential potential is found to be particularly effective; while for molecular dynamics a better model is provided by a DPD-like quadratic potential. Here, computational speed-ups of 20 – 30 × are seen in equilibration times in comparison to the well-known soft repulsive spherocylinder (SRS) model. The quadratic potential is used in an additional set of coarse-grained simulations of a liquid crystal with a flexible chain, which exhibits spontaneous formation of a nematic phase. The use of different types of interaction sites is also illustrated by the simulation of a spherocylinder with two “tails” formed from spheres. Here, varying the hardness of the sphere-spherocylinder interaction potential allows the formation of a smectic-A phase which exhibits microphase separation.

Characteristics of Wormlike Pentaoxyethylene Decyl Ether C10E5 Micelles Containing n-Dodecanol

The wormlike micelles formed with the surfactant pentaoxyethylene decyl ether C10E5 containing n-dodecanol were characterized by static (SLS) and dynamic light scattering (DLS) experiments. The SLS results have been analyzed with the aid of the light scattering theory for micelle solutions, thereby yielding the molar mass Mw(c) as a function of concentration c along with the cross-sectional diameter d of the micelle. The observed Kc/DeltaR0 as a function of c and the hydrodynamic radius RH as functions of Mw have been well described by the theories for the wormlike spherocylinder model. It has also been demonstrated that the apparent hydrodynamic radius RH,app(c) as a function of c is well described by a fuzzy cylinder theory which takes into account the hydrodynamic and direct collision interactions among micelles. Our previous results for the hexaoxyethylene dodecyl ether C12E6 micelles containing n-dodecanol were reanalyzed in the same scheme. It has been found that the micellar length increases with increasing concentration c or with raising temperature T irrespective of the composition of the C10E5 + n-dodecanol and C12E6 + n-dodecanol systems. The length of the micelles at fixed c and T steeply increases with increasing weight fraction wd of n-dodecanol in both systems. The growth of the micelles accompanies the increase of the cross-sectional diameter d of the micelles and the results that the surfactant molecules are more densely assembled with increasing wd in order to keep n-dodecanol molecules inside the micelles.

Wormlike Micelles of Polyoxyethylene Alkyl Ether Mixtures C10E5 + C14E5 and C14E5 + C14E7: Hydrophobic and Hydrophilic Chain Length Dependence of the Micellar Characteristics

The wormlike micelles formed with the binary mixtures of surfactant polyoxyethylene alkyl ethers (CiEj), C10E5 + C14E5 (Mix1) and C14E5 + C14E7 (Mix2), were characterized by static (SLS) and dynamic light scattering (DLS) experiments. The SLS results have been analyzed with the aid of the light scattering theory for micelle solutions, thereby yielding the molar mass Mw(c) as a function of c along with the cross-sectional diameter d of the micelle. The observed Kc/DeltaR0 as a function of c, the mean-square radius of gyration (S2) and the hydrodynamic radius RH as functions of Mw have been well described by the theories for the wormlike spherocylinder model. It has been found that the micellar length increases with increasing concentration c or with raising temperature T irrespective of the composition of the surfactant mixtures. The length of the Mix1 and Mix2 micelles at fixed c and T steeply increases with increasing weight fraction wt of C14E5 in both of the surfactant mixtures, implying that the micelles greatly grow in length when the surfactant component with longer alkyl group or with shorter oxyethylene group increases in the mixture. The results are in line with the findings for the micelles of the single surfactant systems where the CiEj micelles grow in length to a greater extent for larger i and smaller j. Although the values of d and the spacing s between the adjacent surfactant molecules on the micellar surface do not significantly vary with composition of the surfactant mixture, the stiffness parameter lambda-1 remarkably decreases with wt in both Mix1 and Mix2 micelles, indicating that the stiffness of the micelle is controlled by the relative strength of the repulsive force due to the hydrophilic interactions between oxyethylene groups to the attractive one due to the hydrophobic interactions between alkyl groups among the surfactant molecules.

Wormlike Micelles of Binary Polyoxyethylene Alkyl Ether Mixtures C10E6 + C14E6 and C14E8 + C14E6

The wormlike micelles formed with the binary mixtures of surfactant polyoxyethylene alkyl ethers (CiEj), C10E6 + C14E6 and C14E8 + C14E6, were characterized by static (SLS) and dynamic light scattering (DLS) experiments. The observed Kc/ΔR0 as a function of the surfactant concentration c have been successfully analyzed with the aid of the light scattering theory for micelle solutions, thereby yielding the molar mass Mw(c) of the micelle as a function of c along with the cross-sectional diameter d of the micelle. The mean-square radius of gyration <S2> and the hydrodynamic radius RH as functions of Mw have been well described by the theories for the wormlike spherocylinder model. The length of the micelles at fixed c and temperature T steeply increases with increasing weight fraction wt of C14E6 in both of the surfactant mixtures, implying that the micelles greatly grow in length when the surfactant component with longer alkyl group or with shorter oxyethylene group increases in the mixture. The results are in line with the findings for the micelles of the single surfactant systems where the CiEj micelles grow in length to a greater extent for larger i and smaller j. Although the values of d do not significantly vary with composition of the surfactant mixture, the stiffness parameter λ−1 remarkably decreases with wt in both of the mixtures, indicating that the stiffness of the micelle is controlled by the relative strength of the repulsive force due to the hydrophilic interactions between oxyethylen groups to the attractive one due to the hydrophobic interactions between alkyl groups among the surfactant molecules.

Wormlike Micelles of Pentaoxyethylene Tetradecyl Ether C14E5 and Hexaoxyethylene Hexadecyl Ether C16E6

Micelles of pentaoxyethylene tetradecyl C14E5 and hexaoxyethylene hexadecyl C16E6 ethers in dilute aqueous solutions were characterized by static (SLS) and dynamic light scattering (DLS) experiments at several temperatures T between the LCST and UCST phase boundaries. The SLS results were successfully analyzed with the aid of the thermodynamic theory formulated with wormlike spherocylinder model for SLS of micelle solutions, yielding the molar mass Mw of the micelles as a function of concentration c and the cross-sectional diameter d. The radius of gyration S21/2 of the micelles as a function of Mw was found to be well described by the corresponding theories for the wormlike chain model. Combining the present and previous results for various CiEj (polyoxyethylene alkyl ether) micelles, effects of the hydrophobic (alkyl) i and hydrophilic (oxyethylene) chain length j on the micellar characteristics have been clarified as: (i) The weight-average micellar length Lw becomes larger for larger i and smaller j. (ii) The d values do not significantly vary with the values of i and j. (iii) The stiffness parameter λ−1 decreases with increasing i at fixed j and increases with increasing j at fixed i.

Parsons−Lee and Monte Carlo Study of Soft Repulsive Nematogens

A general approach based on the Parsons-Lee theory for soft repulsive molecular fluids is employed to investigate the nematogenic behavior of prolate thermotropic liquid crystals over a broad temperature range. The theory is solved for the particular case of the Kihara soft repulsive spherocylinder model, which is mapped into an effective hard core interaction with a temperature-dependent molecular diameter, expected to resemble the average size and shape of the soft molecules at a given temperature. The reduction of the effective molecular diameter with temperature in the Kihara soft repulsive fluid implies implicitly an increase of the elongation of the molecule and induces the stabilization of the nematic phase at smaller effective packing fractions, contrary to what is found for other fluid models. The rationalization of this effect in terms of excluded volume steric arguments is corroborated by the good general agreement between the Parsons-Lee approach and Monte Carlo simulations for the equation of state of the fluid in the vicinity of the isotropic-nematic transition.

Effects of Hydrophobic Chain Length on the Characteristics of the Micelles of Octaoxyethylene Tetradecyl C14E8, Hexadecyl C16E8, and Octadecyl C18E8Ethers

Size, shape, and flexibility of micelles of octaoxyethylene tetradecyl C(14)E(8), hexadecyl C(16)E(8), and octadecyl C(18)E(8) ethers in dilute aqueous solutions were determined at finite surfactant concentrations c by static light scattering (SLS) and dynamic light scattering experiments at several temperatures T below the critical points. The SLS results were successfully analyzed with the aid of the thermodynamic theory formulated with wormlike spherocylinder model for SLS of micelle solutions. The analysis yielded the molar mass M(w) of the micelles as a function of c and the cross-sectional diameter d. The hydrodynamic radius R(H) and the radius of gyration S(2)(1/2) of the micelles as functions of M(w) were found to be also well-described by the corresponding theories for the wormlike spherocylinder or wormlike chain models. The results of the stiffness parameter lambda(-1) have revealed that the micelles are far from rigid rods but rather stiff compared with typical flexible polymers and they grow in size with increasing T to greater length for longer hydrophobic chains, i.e., alkyl groups of the surfactants. As the alkyl group becomes longer, the d value increased, while the spacings s between adjacent hexaoxyethylene chains on the micellar surface were found to remain substantially constant.

Effects of Hydrophilic Chain Length on the Characteristics of the Micelles of Pentaoxyethylene n-Decyl C10E5 and Hexaoxyethylene n-Decyl C10E6 Ethers

Wormlike micelles of nonionic surfactants pentaoxyethylene decyl ether C(10)E(5) and hexaoxyethylene decyl ether C(10)E(6) in dilute aqueous solutions were characterized by static (SLS) and dynamic light scattering (DLS) experiments at several temperatures T below the critical points. The SLS results were analyzed with the aid of the molecular thermodynamic theory for SLS from micelle solutions formulated with the wormlike spherocylinder model, thereby yielding the molar mass M(w) of the micelles as a function of c and the cross-sectional diameter d of 2.6 nm for both C(10)E(5) and C(10)E(6) micelles. It has been found that the micelles grow in size with increasing c and T, following the relation M(w) proportional, variant c(1/2) in conformity with the theoretical prediction for highly extended polymerlike micelles. The hydrodynamic radius R(H) of the micelles as a function of M(w) was found to be also well described by the corresponding theories for the wormlike spherocylinder model. The results of the stiffness parameter lambda(-1) show that both micelles are rather stiff compared with those formed with other polyoxyethylene alkyl ethers C(i)E(j) but far from rigid rods. The values of the spacing s between two adjacent hexaoxyethylene chains on the micellar surface were found to be substantially the same for both micelles.

Light-Scattering Characterization of the Wormlike Micelles of Hexaoxyethylene Dodecyl C12E6 and Hexaoxyethylene Tetradecyl C14E6 Ethers in Dilute Aqueous Solution

The size, shape, and flexibility of hexaoxyethylene dodecyl ether C12E6 micelles and hexaoxyethylene tetradecyl ether C14E6 micelles in dilute aqueous solutions were determined at finite surfactant concentrations, c, by static (SLS) and dynamic light scattering (DLS) experiments at several temperatures T below the critical points. The SLS results were successfully analyzed with the aid of the thermodynamic theory for SLS from micelle solutions formulated with the wormlike spherocylinder model. The analysis yielded the molar mass Mw of the micelle as a function of c and the cross-sectional diameter d of 2.3 nm for the C12E6 micelles and 2.4 nm for the C14E6 micelles. It has been found that micelles grow in size with increasing c and T, following the relation Mw ∝ c1/2. The hydrodynamic radius RH and the radius of gyration 〈S2〉1/2 of the micelles as functions of Mw were found also to be well described by the corresponding theories for the wormlike spherocylinder and wormlike chain models, respectively. The results of the stiffness parameter λ-1 have shown that both micelles are far from rigid rods but rather stiff compared with typical flexible polymers. It has been revealed that the C14E6 micelles grow in size to a much greater length than the C12E6 micelles, presumably because of the thermodynamic reason that attractive interactions among C14E6 molecules are much stronger than those among C12E6 molecules as embodied by the values of the free-energy parameter g2, reflecting the difference in the hydrophobic chain length. The values of d and the spacings s between two adjacent hexaoxyethylene chains on the micellar surface were found to be substantially the same for both of the micelles.