Transient orientation distribution

Transient effects in the kinetics of oriented nucleation are considered for melt processing in a wide range of deformation rates using a theory of non-linear chain statistics with transient effects. Inverse Langevin elastic free energy of a polymer chain in a Pade approximation, averaged with transient distribution of the chain end-to-end vectors, as well as Peterlin s approximation for the modulus of nonlinear elasticity are used. The effects of transient orientation distribution of the chain segments is also considered. 

The chain relaxation time controls transient distribution of the chain end-to-end vectors in the system and the transient orientation distribution of chain segments. Time-dependent deformation rate and the chain relaxation introduce time- and orientation-dependent potential of cluster formation and the nucleation rate. The transient orientation-dependent potential of nucleation controls the orientation distribution of the critical cluster energy and the critical cluster size. 

The most common experiments of this type involve reorientation of the sample in the magnetic field [20, 118-125]. Either a sudden reorientation of the initially magnetically aligned sample by a fixed angle about an axis perpendicular to the magnetic field, followed by observation of the development of the transient orientational distribution of the director, or continuous rotation of the sample can be used. Both types of experiments yield /i, the twist or rotational viscosity. In sudden reorientation experiments with 6q>k/4, spatially periodic patterns of the director reorientation form and the director realignment becomes inhomogeneous. In this case, NMR spectra can yield four of the five independent viscosity constants and the ratio of two of the three elastic constants of the nematic phase [121]. 

Fuhs et al.m investigated P p0 Aj in multilayers of Synechocystis PCC 6803 oriented on mylar sheets by transient W-band EPR. They could show an enhanced resolution of structural parameters of the RP in this model system. A problem is the uncertainty of the orientation distribution (width 30 10°). Limitations and possibilities of the method are discussed in this work. The technique is interesting for all systems for which no single crystals are available. 

Here, 7 is the magnitude of the strain rate tensor and C/ is a phenomenological coefficient which models the interactions between the fibers, usually referred to as the Folgar-Tucker interaction coefficient. The coefficient varies between 0, for a fiber without interaction with its neighbors, and 1, for a closely packed bed of fibers. For a fiber reinforced polyester resin mat with 20-50% volume fiber content, CV is usually between 0.03 and 0.06. When eqn. (8.153) is substituted into eqn. (8.152), the transient governing equation for fiber orientation distribution with fiber interaction built-in, becomes... 

Applications of optical methods to study dilute colloidal dispersions subject to flow were pioneered by Mason and coworkers. These authors used simple turbidity measurements to follow the orientation dynamics of ellipsoidal particles during transient shear flow experiments [175,176], In addition, the superposition of shear and electric fields were studied. The goal of this work was to verify the predictions of theories predicting the orientation distributions of prolate and oblate particles, such as that discussed in section 7.2.I.2. This simple technique clearly demonstrated the phenomena of particle rotations within Jeffery orbits, as well as the effects of Brownian motion and particle size distributions. The method employed a parallel plate flow cell with the light sent down the velocity gradient axis. 

Larson and Doi introduced a mesoscopic polydomain model based on LE theory. This model includes a domain orientation distribution function and incorporates director tumbling, distortional elasticity, and texture size. Larson-Doi model can qualitatively predict the steady flow behavior and transient behavior. However, discrepancies between the theoretical predictions and the experiments of model systems were observed, especially when the shear history includes rest periods. ° This model is restricted to low shear rates without perturbing the molecular orientation distribution function in each domain.f ... 

The transient absorption method utilized in the experiments reported here is the transient holographic grating technique(7,10). In the transient grating experiment, a pair of polarized excitation pulses is used to create the anisotropic distribution of excited state transition dipoles. The motions of the polymer backbone are monitored by a probe pulse which enters the sample at some chosen time interval after the excitation pulses and probes the orientational distribution of the transition dipoles at that time. By changing the time delay between the excitation and probe pulses, the orientation autocorrelation function of a transition dipole rigidly associated with a backbone bond can be determined. In the present context, the major advantage of the transient grating measurement in relation to typical fluorescence measurements is the fast time resolution (- 50 psec in these experiments). In transient absorption techniques the time resolution is limited by laser pulse widths and not by the speed of electronic detectors. Fast time resolution is necessary for the experiments reported here because of the sub-nanosecond time scales for local motions in very flexible polymers such as polyisoprene. 

Figure 2. Transient grating decays for 9,lO-bis(methylene)-anthracene labeled polyisoprene in dilute hexane solution. Tg and Tx are the diffraction efficiencies of the grating for the probe beam polarized parallel and perpendicular to the excitation beams (see Equations 1 and 2). The two curves are initially different because the excitation beams create an anisotropic orientational distribution of excited state transition dipoles. As backbone motions occur, the transition dipoles randomize and the two curves coalesce. Both curves eventually decay due to the excited state lifetime. The structure of the anthracene-labeled polyisoprene is also displayed, with the position of the transition dipole Indicated by a double arrow. (Reproduced from Ref. 7. Copyright 1986 American Chemical Society.)...

When any two atoms approach each other closely, they create a weak, nonspecific attractive force called a van der Waals interaction. These nonspecific interactions result from the momentary random fluctuations in the distribution of the electrons of any atom, which give rise to a transient unequal distribution of electrons. If two noncovalendy bonded atoms are close enough together, electrons of one atom will perturb the electrons of the other. This perturbation generates a transient dipole in the second atom, and the two dipoles will attract each other weakly (Figure 2-8). Similarly, a polar covalent bond in one molecule will attract an oppositely oriented dipole in another. 

In this paper we present a constitutive relation for predicting the rheology of short glass fibers suspended in a polymeric matrix. The performance of the model is assessed through its ability to predict the steady-state and transient shear rheology as well as qualitatively predict the fiber orientation distribution of a short glass fiber (0.5 mm, L/D < 30) filled polypropylene. In this approach the total extra stress is equal to the sum of the contributions from the fibers (a special form of the Doi theory), the polymer and the rod-polymer interaction (multi-mode viscoelastic constitutive relation). 

Transient turbidity is an optical technique for measuring the size of magnetic particles [63,64], It does this by aligning particles in an electric field, removing the field, and following their return to random orientation induced by Brownian motion. Their relaxation is measured by turbidity and this can be related to particle size distribution if assumptions are made... 

Relaxation behavior is deduced from measurements of various transient phenomena. Current interpretations of these phenomena dictate the definition of two processes by which the orientations of the nuclear magnetic moments reach the equilibrium distribution. These processes are described by characteristic times, designated Ti and T2. The first, Ti, is called the thermal or longitudinal relaxation time. 

In transient shear flows starting from an isotropic distribution of fiber orientations, considerably higher viscosities will be initially observed, until the fibers become oriented. In Bibbo s experiments, t]r for isotropically oriented fibers is around 3.5 for v = 75. These viscosities can also be predicted reasonably well by semidilute theory and by simulations (Mackaplow and Shaqfeh 1996). Figure 6-25 shows the shear stress as a function of strain for a polyamide 6 melt with 30% by weight glass fibers of various aspect ratios, where the fibers were initially oriented in the flow-gradient direction. Notice the occurrence of a stress overshoot (presumably due to polymer viscoelasticity), followed by a decrease in viscosity, as the fibers are reoriented into the flow direction. 

Equilibrium. From a thermodynamic point of view, interfacial tension is an equilibrium parameter. When enlarging an interface at a high velocity, equilibrium distribution and orientation of the molecules in the interface cannot be directly attained, and in order to measure y, the rate of change in interfacial area should be slow and reversible. Nevertheless, when enlarging a liquid surface at conditions that do not allow the establishment of equilibrium, a force can be measured, hence a surface or interfacial tension can be derived, which differs from the equilibrium value. It may be a transient value, but it is also possible that a constant surface tension is measured it then concerns a steady state. In other words, from a mechanical point of view, interfacial tension need not be an equilibrium value. 

Recently, we have investigated in detail the steady state and transients of the photoinduced polar order and its related anisotropy in both trans and cis molecular distributions [70]. The effect of all the physical parameters involved in the PEP phenomena has been considered. These include molecular anisometry, pump intensity, pump polarization, strength of the poling field, molecular mobility, and retention of memory of the molecular orientation. Here, we discuss the photostationary state of the PEP process by means of analytical expressions. 

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