Measurements of relaxation time of a polyethylene melt

A device for measuring the elasticity of polymer melts has been designed by one of us (B. Maxwell). The device was used to obtain the relaxation modulus in shear of a linear polyethylene melt. From these data a discrete relaxation spectrum was derived. The range of the obtained spectrum was confirmed to correspond to the terminal zone of the “entanglement plateau” of the spectrum. The limiting dynamic viscosity (as frequency approaches zero) was obtained by integrating the relaxation modulus with respect to time. The viscosity and its activation energy were found to agree closely with the flow viscosity and the flow activation energy, respectively, involved in capillary flow.     

Viscoelastic and relaxation properties of a polystyrene melt in axial extension

On axial extension of polymer melts at constant deformation rates, the development of high-elastic deformation is of predominant importance during the initial period. High-elastic deformation is accompanied by a rise in viscosity and in the modulus of high-elasticity and by retardation of the relaxation processes in the region of large relaxation times. At relatively low deformation rates, the rise in viscosity and high-elasticity modulus and the retardation of relaxation processes may give way to a decrease in viscosity and high-elasticity modulus and acceleration of relaxation processes, so that stationary flow regimes are attained. The transition from strain regimes with increasing viscosity and modulus of high elasticity to those with a decrease of these quantities corresponds to an increase in the rate of accumulation of irreversible deformation. Accordingly, a competing influence due to the orientation effect and to destruction of the network of intermolecular bonds becomes evident while stationary flow is being attained. The orientation effect must be responsible for the retardation of the relaxation processes, whereas rupture of the intermolecular network bonds results in structural relaxation accelerating relaxation processes. In contrast to shearing, during extension the orientation effect is of predominant importance. Hence in stationary flow regimes the viscosity may not only remain independent of the rate of strain, but even increase with it. In this case the contribution of the large relaxation times to the relaxation spectrum increases with increasing stress in stationary flow regimes. The fact that the longitudinal viscosity and the modulus of high elasticity are independent of the stress in stationary flow regimes does not guarantee linearity of the mechanical properties of the polymer in the prestationary stage of deformation when complex changes occur in its relaxation characteristics. At high deformation rates the viscosity and the modulus of high elasticity keep rising with increasing deformation until rupture occurs. Determination of the strength of polystyrene samples vitrified after extension showed that it is due not to the entire degree of extension, but only to the value of accumulated high-elastic deformation. The strength of the vitrified samples is to a first approximation independent of the rate at which the melt was extended.     

Slow magnetic relaxation in a cobalt magnetic chain

A homospin ladder-like chain, [Co(Hdhq)(OAc)](n) (1; H(2)dhq = 2,3-dihydroxyquinoxaline), shows a single-chain-magnet-like (SCM-like) behavior with the characteristics of frequency dependence of the out-of-phase component in alternating current (ac) magnetic susceptibilities and hysteresis loops.     

Second normal stress difference relaxation in a linear polymer melt following step-strain

Flow birefringence is used to study stress relaxation following step strain deformations of a well entangled polyisoprene melt. The optical method employs multiple light paths to fully sample the three-dimensional stress tensor, and hence provides measurements of all three independent shear material functions (shear stress and both first and second normal stress differences). Experiments are complicated by multiple orders in retardation. However, data show that the ratio of the second to the first normal stress difference is a strain thinning function, with magnitude intermediate between the predictions of the Doi-Edwards model with and without independent alignment. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2671–2675, 1998     

Vibronic effects in elastic scattering of electrons

A method for obtaining general equations for the scattered intensities from vibronic systems is given. The approximate formulas obtained are used to calculate the effects on the electron diffraction pattern for molecules with doubly degenerate electronic E terms interacting with e-type vibrations (Ee-type of problem). The results of the approximate calculations are compared to more precise results, based on numerical solution of the vibronic problem.     

Theory of the shape relaxation of a rouse chain

An analytical interpretation is made for the Monte Carlo results on the shape of an unrestricted random flight chain. Both the average shape and the time correlation function of the shape fluctuation are discussed. The Monte Carlo results are well reproduced by assuming that the shape of the chain is primarily determined by the first few normal modes.     

Light scattering from a binary mixture with internal relaxation

The hydrodynamic modes of a binary liquid mixture are investigated for two cases: (1) the bulk viscosity contains a frequency dependent part, and (2) an additional internal variable is introduced. The consequences for the light scat- tering spectrum are discussed and comparisons are made with previous investigations by other authors.     

Ultra-low energy elastic scattering in a system of three He atoms

Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold.     

Rotational relaxation in simple chain models

The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems' rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents beta are found to be 0.75+/-0.02 for the freely jointed case and 0.68+/-0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-end relaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed.     

Stretching of a semiflexible chain composed of elastic bonds

We study the extension of semiflexible (persistent) polymer chains composed of elastic bonds under the action of forces applied to their ends. For a given discrete model of a chain, the effective potential energy includes three components: the energy of bonds in the external dipole field, the energy of elastic deformation of bonds, and the energy of bending, which depends on the angles between neighboring bonds. The extension/contraction modulus of bonds is high but finite. To calculate the relative extension and its variance, the variational method for finding the maximum eigenvalue of the transfer operator in the space of orientations of bonds is used. For chains composed of more than ten bonds, the results appear to approach the data of simulation of chain extension by the collisional molecular dynamics method. Two proposed extensionforce dependences are compared with the computer experiment, and this comparison makes it possible to define the limits of their applicability.     

The single chain limit of structural relaxation in a polyolefin blend

The influence of composition on component dynamics and relevant static properties in a miscible polymer blend is investigated using molecular dynamics simulation. Emphasis is placed on dynamics in the single chain dilution limit, as this limit isolates the role of inherent component mobility in the polymer's dynamic behavior when placed in a blend. For our systems, a biased local concentration affecting dynamics must arise primarily from chain connectivity, which is quantified by the self-concentration, because concentration fluctuations are minimized due to restraints on chain lengths arising from simulation considerations. The polyolefins simulated [poly(ethylene-propylene) (PEP) and poly(ethylene-butene) (PEB)] have similar structures and glass transition temperatures, and all interactions are dispersive in nature. We find that the dependence of dynamics upon composition differs between the two materials. Specifically, PEB (slower component) is more influenced by the environment than PEP. This is linked to a smaller self-concentration for PEB than PEP. We examine the accuracy of the Lodge-McLeish model (which is based on chain connectivity acting over the Kuhn segment length) in predicting simulation results for effective concentration. The model predicts the simulation results with high accuracy when the model's single parameter, the self-concentration, is calculated from simulation data. However, when utilizing the theoretical prediction of the self-concentration the model is not quantitatively accurate. The ability of the model to link the simulated self-concentration with biased local compositions at the Kuhn segment length provides strong support for the claim that chain connectivity is the leading cause of distinct mobility in polymer blends. Additionally, the direct link between the willingness of a polymer to be influenced by the environment and the value of the self-concentration emphasizes the importance of the chain connectivity. Furthermore, these findings are evidence that the Kuhn segment length is the relevant length scale controlling segmental dynamics.     

The observation of a picosecond transient in the relaxation of an iron porphyrin

Iron(III)tetraphenylporphyrin chloride, excited at 353 nm, showed significant bleaching and new absorption at 445 and 55 550 nm, which relaxed in 50 ps. Ground-state recovery occurs in ?100 fs; the bottleneck is populated with 3% efficiency. The photoproduct spectrum resembles a porphyrin ππ^* triplet, and provides evidence for intersystem crossing in an iron heme.