Rod Molecules Research Articles

Phase Transitions in the Systems of Identical Rigid Molecules in Perfect Alignment–Relations of the Smectic A and Columnar Orderings in Liquid Crystals and the Crystalline Ordering to the Molecular Shape

The method of symmetry breaking potential is applied to the system of identical rigid molecules with simple typical shapes (rod with square cross-section, square plate and cube), which are perfectly aligned, to examine the occurrences of such various types of spatial ordering as in smectic, columnar and crystalline phases in relation to the molecular shape. A smectic A phase occurs in the system of rigid rod molecules much more easily than the close packed crystal structure does in the system of rigid sphere molecules. Columnar and crystalline phases do also similarly in the system of molecules of square plate and cube, respectively. It is also shown that the nematic-smectic A transition in the case of rigid rod molecules in perfect alignment is the second order one, in contrast with those in the others of typical first order transitions. The effect of orientational fluctuation is discussed in short.

Statistical thermodynamics of isolated rigid rod-like molecules near a surface

The configurational behaviour and thermodynamic properties of a dilute gas of rigid rod-like molecules in the vicinity of a macroscopic planar adsorption surface are investigated using statistical mechanics. The interaction energy between the surface and a rod-like molecule is determined as a function of both its molecular centre of mass separation R and its orientation relative to the surface. In calculating this interaction energy, each rod segment and molecule comprising the surface is assumed to interact through a Lennard-Jones pair potential. The average molecular order parameter is then determined as a function of R. We find that an isolated rod-like molecule tends to align nearly parallel to the surface for small separations. However, as R increases the order parameter first passes through a maximum then decays to zero as R -5 for large R. The configurational behaviour of an isolated rod-like molecule located between two parallel adsorption surfaces is also considered briefly. The surface spreading...

Evidence for molecular interactions in drag reduction in turbulent pipe flows

AbstractExperiments which test the concentration and molecular weight dependence of turbulent pipe flow drag reduction for random coiling polymers in dilute solutions show correlations with concentration to the one‐half power and molecular weight to the 0.8 power for good solvents. This result is not consistent with a model of extension of single1 molecules, but could be related to the increase in bulk viscosity of interacting molecules after some extension. In this work, measurements for very low amounts of drag reduction for rigid rod molecules arc reported, and the effect of tube diameter on the amount of drag reduction is examined for fiexible rod molecules. No diameter effect is observed for the rigid rods, but an increase in drag reduction with increase in pipe diameter is found for the flexible polyeleetrolytes. In all cases, the volume occupied by spheres which circumscribe the molecules is greater than the actual volume when drag reduction is found. The results indicate that combined effects of individual molecule stretching and molecular interactions are present in drag reduction for random coiling or flexible rod molecules.

Effect of Orientational Fluctuation on Nematic-Smectic A Transition in the System of Hard Rod Molecules

By applying the method of symmetry breaking potential to Zwanzig's three direction model for liquid crystal, the nematic-smectic as well as isotropic-nematic transitions are investigated. Particular attention is paid to the effect of orientational fluctuation on the nematic-smectic A transition. It is shown that the nematic-smectic A transition is reduced to the one of first order owing to that kind of fluctuation for the case of short molecule.

Nematic-Smectic Transition in an Aligned Rod System

The nematic-smectic transition in the system of completely aligned hard cylindrical rods is investigated, by making use of the method of symmetry breaking potential. In the second virial approximation the transition is found to occur in the 3-dimensional system but not in the 1- and 2-dimensional systems, in contrast with the result obtained by Wadati and Isihara that the 2-dimensional system also exhibits such a transition. It is shown that the transition is very like the second order one. A shape effect is also studied. Furthermore, by introducing an isotropic attractive intermolecular force, the dependence of the transition on the strength of that force as well as the length and diameter of the rod molecule is investigated.

A general method for evaluation of diffusion constants, dilute-solution viscoelasticity, and the dielectric property of a rigid macromolecule with an arbitrary configuration. I.

AbstractAs the first part of the study on relaxational behavior of rigid macromolecules in solution, a general method for evaluating diffusion constants of a rigid macromolecule with an arbitrary configuration in a viscous solvent is presented. The evaluation is made by modeling the molecule with a rigid assembly of Stokes spheres. The diffusion constants are expressed by a 6 × 6 matrix which consists of translational, rotational, and cross constants, each being a 3 × 3 submatrix. Procedures of numerical calculation are presented for a given configuration of the molecule, together with some exemplifying results for the rigid rod, rigid sphere, and myosin molecule. The results for the rod and the sphere are compared with analytical results.

Configurational packing statistics of polymers near a surface. I. The generalization of the rigid rod case to include both orientation dependence and spatial variation

The following problem is solved: What is the total number of ways to pack rigid rod molecules together given that the number density f (Ω,r) at each point r and each orientation Ω are specified. This constitutes a generalization of previous work which allowed for only Ω dependence. The problem is first solved for a cubic lattice and then generalized to a continuous variation of both position and orientation. The problem of minimizing the associated free energy is solved. The results are applicable to determination of the adsorption properties of rigid rod molecules near a surface as well as liquid crystal behavior.

Solution Properties of Synthetic Polypeptides. XIV. Synthesis and Characterization of Broken-rod Polypeptides

Attempts were made to obtain model compounds for once-broken rod molecules by two different methods. In one of them, N-carboxy anhydride of γ-benzylglutamate (BG–NCA) was polymerized in dimethylformamide (DMF) containing trimethylenediamine (TMDA) as an initiator. In the other, BLG–NCA was polymerized in DMF with the preformed polymer of BDG–NCA as an initiator. It is expected that the molecule obtained by the first method yields a polymer chain which contains the TMDA residue somewhere in its central portion, whereas the second method gives a block copolymer of the DL type. The initiator residue in the former and the boundary between the L and D chains in the latter are intolerant of helix formation even in helicogenic solvents, and they should act as flexible joints of two helical rods. As an additional attempt, BLG–NCA was polymerized in DMF containing the polymer preformed by TMDA-initiated polymerization of BDG–NCA, in the hope of synthesizing a block copolymer of the LDL type. This polymer is expected to assume the form of a thrice-broken rod when dissolved in a helicogenic solvent. The postulated structures of the polypeptides thus obtained were confirmed by measurements of polymerization rate and optical rotation. It was difficult to prepare high-molecular-weight samples of the desired broken-rod structure by the procedures employed.

Light Scattering of Stiff Chain Polymers

The angular distribution of scattered light (or the particle scattering factor) of the stiff chain polymers is calculated by assuming an appropriate Fourier transform of the distribution function of this polymer chain. For very small and very large scattering angles the result is respectively reduced to the forms of the Debye's scattering factor for random coil chain and to that for rigid rod molecule. By assuming that the polymer chain expansion by intramolecular forces is uniform, but the contour length is kept as constant the excluded volume effect on the angular distribution is calculated. The result shows that the transition point of scattering curve which gives a boundary between random coil- and rigid rod-scatterings is inversely proportional to the square of molecular expansion coefficient. This is in qualitative agreement with the recent experimental results by Wada and other. An approximate distribution function which gives the correct second and fourth moments of the chain end to end distance i...

Gel chromatography of once‐broken rod molecules

Gel chromatography of once‐broken rod molecules

Calculations of Contrast from Model Biological Systems

The quantitative interpretation of the contrast of electron micrographs of amorphous or partially crystalline materials depends on the use of an adequate basis of diffraction- and imaging theory. The treatment due to Zeitler and Bahr, which assumes contrast to arise from a pure absorption effect, appears to be a good approximation for calculating the contrast of thin amorphous films with thickness and composition uniform over regions 100Å or more in diameter, but when the scattering properties of the specimen vary over distances of about 10Å or less then phase-contrast predominates.In order to evaluate the relative importance of these contrast mechanisms for objects now being considered for quantitative study, we have made detailed calculations for model systems designed to represent negatively stained cylindrical rod molecules of protein or similar material. The rods have diameters of 10 to 100Å and the negative staining (one NaW03 molecule in 100Å) is assumed to change the refractive Index and absorption function of the surrounding material.

Theory of magnetic suspensions in liquid crystals

The present paper discusses some properties of small, elongated particles suspended in a nematic or cholesteric phase, with low concentrations (typical volume fraction occupied by the particle f ≊ 10-3). We find that in most cases the particle axis should be locked and parallel to the local nematic axis n(r). If such colloidal suspensions could be made successfully with magnetic grains, it should be possible to prepare « ferronematics » or « ferrocholesterics », where locally all particles are magnetized in one direction (colinear to n), and also « compensated » materials with no spontaneous magnetization. These three types of samples should all show remarkable distorsions and phase changes in low external fields H. Similar effects are expected under electric fields with colloidal suspensions of polar rod molecules such as helical polypeptides.