Orientation, molecular

The importance of molecular orientation has been discussed in Section 3.4.1. In particular, the linear relationship between the sonic modulus of the carbon fiber and that of the precursor was exemplified in Fig. 9. 

It appears plausible to identify the extrapolated value of the modulus at tenacity zero as the sonic modulus of unoriented fiber , (cf. Eq. 22). This magnitude. 

Most precursor copolymers have a specific viscosity in the range of 0.140-0.170, corresponding to a molecular weight range (weight average) of roughly (80-100) x 10.  

Characterisation of molecular orientation is important since many physical and mechanical properties of polymers depend upon the extent and uniformity of that orientation. Orientation can be measured by using a variety of techniques [260,261]. Vibrational spectroscopy is particularly attractive since it is widely applicable, it often allows characterisation of amorphous and crystalline phases separately, it simultaneously provides morphological data (section 4.9), and it can be used to map orientation with high spatial resolution. 

As the mechanical properties of the final product often depend on the orientation of the polymer chain, it is very important to characterize the orientation of the polymer chain both quickly and accurately in nondestructive fashion. When Edwards and Thomas [55] used the propagation velocity of an ultrasonic shear wave to detect anisotropic behavior in the mechanical properties of a solid, the results obtained indicated that this method was quite sensitive for semicrystalline polymers but much less effective for amorphous polymers. 

The time for the polymer to pass through the spirmeret charmel is rather short and is not sufficient for the molecular orientation to be fully developed. 

The polymer jet exiting from the spirmeret is subject to relaxation, which is indicated by the die swell phenomenon. As a resrrlt, the molectrlar orientation developed in the spinneret is largely relaxed. 

After the polymer is extmded from the spirmeret, the elongational flow of the spinning filament leads to molecular orientation in both amorphoirs and crystalline phases. For the melt spinning of polyester fibers, the polymer crystallizes slowly and the molecular orientation developed along the spinline is contributed mainly by the amorphous phase. However, for polyolefin and nylon fibers, the rapid crystallization process determines that the molecular orientation involves both the amorphous and crystalline phases. 

For tmiaxial molecular orientation, an orientation factor can be rrsed to describe the orientation of polymer chains relative to the filament axis. In general, the orientation factor (f) of a spinning filament is expressed by  

One of the most convenient methods to stndy the molecular orientation in a filament is the use of birefringence. The birelringence (An) of a filament is basically the refractive index difference between the axial and radial directions  

Mendoza et al. (2003) studied experimentally the influence of processing conditions on the spatial distribution of the molecular orientation in injection molded isotactic polypropylene (iPP) plates. They found that the anisotropy of injection molded semi-crystalline polymers is governed by the orientation of the crystalline phase, and the distribution of the orientation strongly depends on the shear rate. Doufas et al. (2000), followed by Zheng and Kennedy (2001), have applied a rigid dumbbell model to simulate crystalline orientation in injection molded semicrystalline polymers. The model reads, in the form used by Zheng and Kennedy (2001, 2004)  

Mendoza et al. (2003) used the Hermans orientation factor describe the measured results. The orientation factor is defined by 

Simulation results of Zheng and Kennedy (2001) compared with experiments of Mendoza et al. (2003) are shown in Fig. 4.4. The overall trend of the orientation distribution is captured. The shearing region exhibits the highest level of orientation, which is solidifled during Ailing. The orientation in the 1 mm-thick plate is 

It will be recalled that for the flexible rod model of Section 2.8, The constant p in the Gaussian function can thus be equated 

A further virtue of the Gaussian function is that it is frequentfy found to be a solution to problems involving random processes. The behavior of the flexible chain undergoing violent liquid like motions is one such random process. 

The Gaussian chain provides an exceQent description of conformations in unperturbed polymer liquids and in the glasses obtained cooling them. 

19 An amorphous polymer is extended above the glass transition and then quenched to the glassy state. The resulting conformations are no longer random there is irozen-in molecular orientation, which remains virhen stress is removed. 

The really important practical effect of molecular orientation is that an 

Thierry Lefevre, Christian Pellerin and Michel Pezolet 

The physical properties of materials, especially their mechanical properties, are intimately related to their structural organization at all length scales. It is 

Comprehensive Analytical Chemistry, Volume 53 ISSN 0166-526X, DOI 10.1016/S0166-526X(08)00408-X 

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The external reflection of infrared radiation can be used to characterize the thickness and orientation of adsorbates on metal surfaces. Buontempo and Rice [153-155] have recently extended this technique to molecules at dielectric surfaces, including Langmuir monolayers at the air-water interface. Analysis of the dichroic ratio, the ratio of reflectivity parallel to the plane of incidence (p-polarization) to that perpendicular to it (.r-polarization) allows evaluation of the molecular orientation in terms of a tilt angle and rotation around the backbone [153]. An example of the p-polarized reflection spectrum for stearyl alcohol is shown in Fig. IV-13. Unfortunately, quantitative analysis of the experimental measurements of the antisymmetric CH2 stretch for heneicosanol [153,155] stearly alcohol [154] and tetracosanoic [156] monolayers is made difflcult by the scatter in the IR peak heights. 

Photopolymerization reactions of monolayers have become of interest (note Chapter XV). Lando and co-workers have studied the UV polymerization of 16-heptadecenoic acid [311] and vinyl stearate [312] monolayers. Particularly interesting is the UV polymerization of long-chain diacetylenes. As illustrated in Fig. IV-30, a zipperlike process can occur if the molecular orientation in the film is just right (e.g., polymerization does not occur readily in the neat liquid) (see Refs. 313-315). 

The strong dependence of the PES on molecular orientation also leads to strong coupling between rotational states, and hence rotational excitation/de-excitation in the scattering. This has been observed experimentally for H2 scattering from Cu surfaces. Recent work has shown that for H2 the changes m rotational state occur almost exclusively when the molecular bond is extended, that is, longer than the gas-phase equilibrium value [ ]. 

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

The nonlinear response of an individual molecule depends on die orientation of the molecule with respect to the polarization of the applied and detected electric fields. The same situation prevails for an ensemble of molecules at an interface. It follows that we may gamer infonnation about molecular orientation at surfaces and interfaces by appropriate measurements of the polarization dependence of the nonlinear response, taken together with a model for the nonlinear response of the relevant molecule in a standard orientation. 

We now consider this issue in a more rigorous fashion. The inference of molecular orientation can be explamed most readily from the following relation between the surface nonlinear susceptibility tensor and the molecular nonlinear polarizability... 

Here the ijk coordinate system represents the laboratory reference frame the primed coordinate system i j k corresponds to coordinates in the molecular system. The quantities Tj, are the matrices describing the coordinate transfomiation between the molecular and laboratory systems. In this relationship, we have neglected local-field effects and expressed the in a fomi equivalent to simnning the molecular response over all the molecules in a unit surface area (with surface density N. (For simplicity, we have omitted any contribution to not attributable to the dipolar response of the molecules. In many cases, however, it is important to measure and account for the background nonlinear response not arising from the dipolar contributions from the molecules of interest.) In equation B 1.5.44, we allow for a distribution of molecular orientations and have denoted by () the corresponding ensemble average ... 

Here/(9,(p, i ) is the probability distribution of finding a molecule oriented at (0,cp, li) within an element dQ of solid angle with the molecular orientation defined in tenus of the usual Euler angles (figure B 1.5.10). 

FigureBl.5.10 Euler angles and reference frames for the discussion of molecular orientation laboratory frame (v, y, z) and molecular frame (x y, z).

Thus, a well-defined measure of molecular orientation is uiferred from the measurement of the macroscopic... 

Heinz T F, Tom H W K and Shen Y R 1983 Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation Phys. Rev. A 28 1883-5... 

Zhuang X, Miranda P B, Kim D and Shen Y R 1999 Mapping molecular orientation and conformation at interfaces by surface nonlinear optics Phys. Rev. B 59 12 632-40... 

It is occasionally desirable to retain a small proportion of molecular orientation, in order to quantitate the dipolar interactions present, whilst minimizing their contribution to the linewidth. Partial orientation may be achieved by using a nematic solvent. In large, magnetically anisotropic molecules it may occur naturally at the highest magnetic fields. 

Figure Cl.5.3. Near-field fluorescence image 4.5 p.m square) of single oxazine 720 molecules dispersed on die surface of a PMMA film. Each peak (fwhm 100 nm) is due to a single molecule. The different intensities are due to different molecular orientations and spectra. Reprinted widi pennission from Xie 11221. Copyright 1996 American Chemical Society.

Figure Cl.5.15. Molecular orientational trajectories of five single molecules. Each step in tire trajectory is separated by 300 ms and is obtained from tire fit to tire dipole emission pattern such as is shown in figure Cl.5.14. The radial component is displayed as sin 0 and tire angular variable as (ji. The lighter dots around tire average orientation represent 1 standard deviation. Reprinted witli pennission from Bartko and Dickson 11481. Copyright 1999 American Chemical Society.

Crockett R G M, Campbell A J and Ahmed F R 1990 Structure and molecular-orientation of tetramethoxy-tetraoctoxy phthalocyaninato-polysiloxane Langmuir-Blodgett-films Po/yme/ 31 602-8... 

Clearly, a free energy of binding computed with (9), (10) and (13) refers to a highly restricted state of the dissociated ligand. In order to convert such a free energy to a free energy relative to a normal standard state with volume per molecule Vg and no restriction on the molecular orientation, the following term must be added... 

Molecular simulation techniques can be used to predict how a compound will interact with a particular active site of a biological molecule. This is still not trivial because the molecular orientation must be considered along with whether the active site shifts geometry as it approaches. 

The susceptibility tensors give the correct relationship for the macroscopic material. For individual molecules, the polarizability a, hyperpolarizability P, and second hyperpolarizability y, can be defined they are also tensor quantities. The susceptibility tensors are weighted averages of the molecular values, where the weight accounts for molecular orientation. The obvious correspondence is correct, meaning that is a linear combination of a values, is a linear combination of P values, and so on. 

This approach works quite well for species at metal surfaces. It has been used extensively in recent years to ascertain information about organic thin films on metal surfaces. Of particular interest in many of these studies, and indeed the real forte of this technique, has been the deterrnination of molecular orientation on surfaces from such studies. Few other techniques are quite so useful for unambiguously ascertaining molecular orientation. 

Mechanical Properties. Polyester fibers are formed by melt spinning generally followed by hot drawing and heat setting to the final fiber form. The molecular orientation and crystalline fine stmcture developed depend on key process parameters in all fiber formation steps and are critical to the end use appHcation of the fibers. 

Flow processes iaside the spinneret are governed by shear viscosity and shear rate. PET is a non-Newtonian elastic fluid. Spinning filament tension and molecular orientation depend on polymer temperature and viscosity, spinneret capillary diameter and length, spin speed, rate of filament cooling, inertia, and air drag (69,70). These variables combine to attenuate the fiber and orient and sometimes crystallize the molecular chains (71). 

EOY speeds are the most recent development in PET spinning (78). Properties are similar to HOY and appear to be limited by the differential cooling rate from filament surface to filament core. This leads to radial distribution of viscosity, stress, and, consequentiy, molecular orientation (75). Eiber tensde strength is limited. Nevertheless, speeds up to 7000 m /min are commercial and forecasts are for speeds up to 9000 m /min by the year 2000 (79). Speeds to 9000 m/min have been studied (68,80,81). 

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