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Knowledge of the conformational evolution of a polymer chain provides invaluable information for all polymer properties. However, the chain evolution is usually determined by monitoring single beads for short times only. In this paper, we numerically determine the configuration evolution over extended time periods by monitoring the eigenvalues of the gyration tensor and applying the scaling law methodology. Results of Brownian dynamics simulations of initially straight chains reveal that after the early free transverse diffusion, flexible polymers exhibit a transverse intermediate-time behavior of t3/4, while stiff polymers reveal two intermediate-time behaviors: an early t5/6 power law accompanied by a late t3/4 evolution. These results are associated with the inherent nonlinearity of the problem. The scaling law methodology we develop in this paper for monitoring the chain configuration should have wide applications in the study of polymer rheology.

Monte Carlo simulations of a simple cubic lattice model of star-branched polymers were made. The solvent conditions (temperature) were varied in a wide range and the total chain length was up to 800 beads. The analysis of a shape of branched macromolecules was performed by means of the gyration tensor principal moments and asphericity factor. The changes of shape parameters during the transition from a random coil to a collapsed globule have been determined. In high temperatures, the instantaneous shape of the branched chain is more symmetric than that for linear chains. The shape of one star arm is very similar to that of the entire polymer. In lower temperatures, the collapsed model chain forms an isotropic globule. The shape of inner and outer parts of the star polymers is discussed.

We report the results of a computer simulation of the evolution of structure in a two component fluid consisting of a liquid phase and a dispersed colloidal phase subjected to a uniaxial field. Our primary objective is to understand the mechanism and kinetics of coarsening and the emergence of crystallinity. Using an efficient, linear-N simulation method we report studies of systems of N=10 000 particles over the concentration range of 10–50 vol %. We present a variety of methods of characterizing the structures that emerge, including the anisotropy of the conductivity, capacitance and dipolar interaction energy, the two-dimensional pair correlation function, principal moments of the gyration tensor, velocity correlation functions, microcrystallinity and coordination number, and the optical attenuation length. We conclude that athermal coarsening is effectively driven by the presence of defect structures and that as the concentration increases, the structures progressively lose the well-known “chain” anis...

We study in the present paper the response of a flexible macromolecular chain to the application or removal of an electric field. The polymer is mainly modeled as a Gaussian chain, and the case of freely jointed chains is also treated. We consider the dynamics of the chains, after the inception and subsequent cessation of an electric field. In particular, we calculate two properties. One of them is the time‐dependent chain expansion, as measured by the components of the gyration tensor, that can be determined by transient electric‐field light scattering. The other property is the transient electric birefringence, related to the reorientation of the chain segments. In this way, the dynamics of two different properties can be compared. The transient properties are analyzed in terms of a series of relaxation times. We propose the use of a mean relaxation time as a convenient representation of the rate of the dynamic process, and show that it can be deduced from simulation or experiments with more accuracy than the longest relaxation time. Our computational procedure is based on Brownian dynamics simulation. For Gaussian chains without hydrodynamic interaction, the results are compared with the predictions from the Rouse theory. We evaluate the influence of the strength of the force or field. Simulations are also carried out including hydrodynamic interactions, so that the importance of this effect can be assessed. We propose some combination of relaxation times with other macromolecular properties that take universal numerical values.

Fibrous and crystal structures of a helical polymer, poly‐L‐lactic acid (PLLA), were analyzed by using x‐ray diffraction experiments. It was confirmed that the molecular residues were arranged on a nonintegral 10/3 helix as De Santis and Kovacs [Biopolymers 6, 299 (1968)] reported. The atomic positions in a monomeric unit, which were proposed by Hoogsteen, Postema, Pennings, ten Brinke, and Zugenmaier [Macromolecules 23, 634 (1990)], were validated. However, the previous reports on the positions of the two helical chains were found to be in error. The correct positions were determined. The second helical chain shifts from the base center by 0.45, 0.25, and 0.61 A along a, b, and c axes. Besides, the second chain rotates by 2.46° with respect to the first. Distribution function of the crystallites in various drawn fibers were determined as a function of spiral angle. Optical gyrations of PLLA and poly‐D‐lactic acid fibers were successfully measured by using high accuracy universal polarimeter, as functions of temperature and drawing ratio. By using x‐ray data of the change of the fibrous structure by drawing treatments, the gyration tensor components of PLLA could be calculated. It is of great interest that gyration tensor component g33 along the helical axis is extremely large, ∼(3.85±0.69)×10−2, which corresponds to a rotatory power of (9.2±1.7)×103°/mm, about two orders of magnitude larger than those of ordinary crystals. This is the first experimental evidence that helical polymers will produce enormous optical activity in the solid state. Helical polymers will be important for the elucidation of gyro‐optical properties of solids and promising for new optical applications utilizing their large optical activity.

A method of calculating average moments, to an arbitrary order m, of the principal components of the gyration tensor of a Gaussian molecule imbedded in any k‐dimensional space is presented. These average moments are then used in generalized shape parameters Am of degree m≤k, which measure the asymmetry of the shapes of Gaussian molecules. Simple formulas for A2, A3, and the average moments up to third order are given. Explicit expressions for A2 and A3 for linear and circular chains, regular stars with infinitely long arms, double rings of a large number of beads, and combs with many side chains are obtained, and the shape characteristics of these molecules are discussed. It is found that Gaussian molecules are, on the average, prolate rather than oblate even in an infinite dimensional space, with the exception of regular stars with densely radiated long arms which exhibit perfect symmetry. The problem of analytic characterizations of shape asymmetry of Gaussian molecules or non‐self‐avoiding random walks...

We theoretically analyze diffusion trajectories of an anisotropic object moving on a two dimensional space in the absence of an external field. In determining diffusion parameters associated with the shape anisotropy, we devise a measure based on the gyration tensor and obtain its analytic expression exactly. Its efficiency and statistical convergence are examined in comparison with the fourth cumulant of particle displacement. We find that the estimation of diffusion constants based on the gyration measure is more efficient than the analysis adopting the fourth cumulant.

The structure and rheology of model polymer blends under planar elongational flow have been investigated through nonequilibrium molecular dynamics simulations. The polymeric blends consist of linear polymer chains (187 monomers per chain) and dendrimer polymers of generations g = 1 - 4. The number fraction, x, of the dendrimer species is varied (4%, 8%, and 12%) in the blend melt. We study the effect of extension rate, dendrimer generation, and dendrimer number fraction on pair distribution functions for different blend systems. We also calculate the extension-rate dependent radius of gyration and ratios of the eigenvalues of the gyration tensor to study the elongation-induced deformation of the molecules in the blend. Melt rheological properties including the first and second extensional viscosities are found to fall into the range between those of pure dendrimer and pure linear polymer melts, which are correlated with the mass fraction and generation of the dendrimers in the blend.

Surface-induced selective adsorption of homopolymers on a generic level is numerically analyzed for freely jointed chains (with a fixed bond length) whose monomers are attracted by the sites of regular periodic patterns. In particular, the behavior of the specific heat, the gyration tensor, and the bond order tensor are investigated as functions of the temperature. The properties of the transition are related to the interplay of the characteristic lengths. The adsorption proceeds in two steps for certain incommensurabilities of the bond length and the lattice constant. The corresponding adsorption mechanisms are elucidated by looking at the evolution of the inter bond angle distribution upon adsorption. Moreover, the origin of two steps in contrast to adsorption in one step is traced back to entropic restrictions caused by a strongly reduced phase space of the polymer for certain values of the incommensurability.

In a recent computational study, we found highly structured conformations for the polymer-attractive sphere model system. Those conformations are of highly ordered spherical shape or form two-dimensional planar, compact to extended, random coil structures. The observed conformations range from desorbed to partially or even completely adsorbed. In order to present their shape characteristics, here we calculate the gyration tensor and related shape descriptors.

We have studied the birefringence decay of linear models of macromolecules for two different types of flexibility, the broken-rod chain and the wormlike chain, using a computer simulation of a transient electric birefringence experiment. We have paid particular attention to the influence of the intensity of the orienting field, including two orienting mechanisms, the induced dipole, and the permanent dipole. We have compared wormlike and broken-rod models of the same radius of gyration, finding that they present a different decay curve under the influence of the same intensity of the field. We have seen that these differences are due to the faster relaxation times (smaller in the wormlike chain model) and amplitudes, because, regardless of the type of flexibility, the overall size of a molecule (measured by the radius of gyration) essentially determines the longest relaxation time. We have also analyzed how the relaxation process is affected by the degree of flexibility, the orientation mechanisms, and the intensity of the field. Studying a different aspect, we have paid attention to the deformation of a molecule in a transient electric birefringence experiment as a source of information. In this work we have developed equations to characterize this deformation in terms of one of the components of the gyration tensor, if a dynamic light scattering experiment under the influence of an electric field could be performed. To develop this work we have simulated the Brownian dynamics of the different models, relaxing after the removal of an orienting external electric field of arbitrary strength. A comparison with other methods such a the rigid body treatment or the correlation analysis of Brownian trajectories has also been included. We have seen that differences between the two Brownian dynamics methods are small and that the rigid-body treatment is only an acceptable approximation to obtain the longest relaxation time.

The possibility to investigate optical activity of uniaxial media by measuring the difference between the intensities of reflected electromagnetic waves (emw) of different circular polarization (reflection optical activity—ROA) is discussed. The components of the gyration tensor and the polarization of the normal emw in uniaxial media are found. The reflection of emw is studied in two cases: (a) optical axis normal to the boundary; (b) optical axis normal to the plane of incidence. Three modifications of differential spectroscopy are proposed: (1) left and right circularly polarized waves—usual reflection; (2) total reflection–circular polarization (TROA); (3) total reflection of linearly polarized waves with different azimuths of vibration. The specific features of the proposed methods (ROA and TROA) are discussed as well as the possibility of studying the optical activity induced by nondegenerate and degenerate excitations (vibrations).

Two‐quanta anharmonic spectra, namely overtones and combination bands with degenerate vibrations, in uniaxial gyrotropic crystals from point group of symmetry C3, D3, C4, D4, are investigated, with due account taken of the time inversion. The symmetry of two‐phonon states is studied. A general model of the anharmonicity and the influence of the crystal chiral structure on intermolecular exchange of the circularly polarized degenerate vibrations is elaborated. The contribution of overtones and of the combination bands to dielectric permittivity tensor, and to the gyration tensor is studied too. The paper also deals with the IR and vibrational circular dichroism (VCD) spectra near the frequencies of the unbound and of the bound two‐phonon states as well as the general features of two‐phonon circularly polarized states appearing in the linear and in nonlinear optical processes in gyrotropic crystals.

A new and general method has been developed by which the optical activity of crystals can be measured along different directions from the optic axes. The principle of the method is to measure accurately the intensity of emergent light from parallel and crossed polarizers between which the specimen is properly oriented. The experimental apparatus is relatively simple and needs no elaborate machinery. By this method, gyration and birefringence can be obtained simultaneously as a function of wavelength. As a test of the applicability of the method, a component of the gyration tensor g11 and birefringence ne−n0 of quartz have been observed as a function of wavelength, e.g., g11=5.69×10−5, and ne−n0=9.15×10−3 at a wavelength of 550 nm. This method was also applied to the study of the optical activity of KH2PO4. It was found that the nonenantiomorphous D2d phase (paraelectric) of KH2PO4 is optically active, g11=2.28×10−4 at a wavelength of 506 nm.

A theory is developed for the IR absorption and vibrational circular dichroism (VCD) spectra of helical polymers in the frequency range of the frequency sum for two vibrational excitons. Bound and unbound two‐exciton states are shown to exist, using the model for first nearest neighbors interactions (applicable to the amide II vibration). The dielectric permittivity tensor and the gyration tensor are found in the following cases: (a) oriented helices; (b) isotropic solutions of helical polymers. The frequency dependence of the various VCD terms is studied in the vicinity of the bound two‐exciton states and in the band of unbound two‐exciton states.