Molecular elastic properties

Stannarius R 1998 Elastic properties of nematic liquid crystals 1998 Handbook of Liquid Crystals Vol 2A. Low Molecular Weight Liquid Crystals led D Demus, J Goodby, G W Gray, Fl-W Speiss and V Vill (New York Wiley-VCH)... 

To obtain high molecular weight polymers the tetramer is equilibrated with a trace of alkaline catalyst for several hours at 150-200°C. The product is a viscous gum with no elastic properties. The molecular weight is controlled by CcU eful addition of monofunctional material. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

The Debye temperature, can be calculated from the elastic properties of the solid. Required are the molecular weight, molar volume, compressibility, and Poisson s ratio.11 More commonly, do is obtained from a fit of experimental heat capacity results to the Debye equation as shown above. Representative values for 9o are as follows ... 

Southwick, J.G. and Manke, C.W. "Molecular Degradation, Injectivity, and Elastic Properties of Polymer Solutions," SPE paper 15652, 1986 SPE Annual Technical Conference and Exhibition, New Orleans, October 5 8. 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

Figure 5.48 Geometry discussed in Section 6.3 for tubule formation based on chiral elastic properties. Here, r is tubule radius, l is tubule length, n is molecular director, m is projection of n into local tangent plane (normalized to unit magnitude), <(> is angle in tangent plane between m and curvature direction (equator running around cylinder), and N is local normal vector. Adapted from Ref. 132 with permission of the author. Copyright 1996 by the American Physical Society.

Cyclic polymers form nearly 50 per cent of the product while the tetramer, octamethylcyclotera siloxane (I) constitutes the main cyclic compound. Now the polymerisation of the tetramer is done by heating at 150-200°C with a trace of sodium hydroxide and a very small amount of non-functional material so as to control the Molecular weight. The products obtained is a highly viscous gum having no elastic properties. 

Molecular Dynamics Simulation Study of Elastic Properties of HMX. 

TATB or 1,3,5-triamino-2,4,6-trinitrobenzene (C6H6N6Oe) is a yellow-brown crystalline solid that has excellent thermal stability and is known as a heat-resistant explosive. TATB has a decomposition point of 325°C. Its molecular arrangement provides lubricating and elastic properties. 

For crystals with molecule-like constituents, like the BO, " and BO4 " groups in some borates, semi-quantitative models of the molecular component as a gas-phase entity have been proposed (Oi et al. 1989). This is conceptually similar to the approximation made for species in solution, although in practice most studies of crystals consider additional frequencies that reflect inter-molecular vibrations. The spectroscopic data on these vibrations (which typically have lower frequencies than the intra-molecular vibrations) are often available, at least approximately, from infrared and Raman spectroscopy and elastic properties. This type of hybrid molecule-in-crystal model has been applied to many minerals in theoretical studies of carbon and oxygen isotope fractionation, the most noteworthy being studies of calcite (Bottinga 1968 Chacko et al. 1991) and sihcates (Kieffer 1982). Because specfroscopic dafa are always incomplete (especially for subsfances substifufed wifh rare isolopes), some amounl of vibralional modeling is necessary. 

Astbury, W. T. Street, A., X-ray Studies of the Structure of Hair, Wool and Related Fibres. I. General. Trans. R. Soc. London 1931, A230,75 Astbury, W. T. Woods, H. J., II. The Molecular Structure and Elastic Properties of Hair Keratin. ibid. 1934, A232, 333 Astbury, W. T. Sisson, W. A., III. The Configuration of the Keratin Molecule and its Orientation in the Biological Cell, Proc. R. Soc. London 1935, A150, 533. 

An example of the elastomeric component is a combination of multifrmctional and difunctional aliphatic urethane oligomers. Suitable oligomers have relatively high molecular weights and glass transition temperatures (Tg), which enables the adhesive to have elastic properties at room temperature. Its deformability under... 

The mechanical assembly and microprocessing unit permit analysis of a broad spectrum of molecular responses yielding data on viscous and elastic properties of the test material. A more generally available laboratory Instrument is the Haake Roto-visco viscometer which also features a cone-plate attachment. 

For long chains, the modulus at about 106-107 dynes/cm2 passes into a domain of much slower relaxation (the plateau region). The width of the plateau depends strongly on molecular weight, while the characteristic modulus of the plateau region G is independent of molecular weight. The presence of the plateau confers rubber-like elastic properties over an intermediate range of frequencies or times. 

The ratio of elastic constants Ku, calculated for the S-effect according to the equation (4) appeared to be (Kn (polymer XIV)/Kn (polymer XIII)) x 1 100 and (Ku (polymer XVI)/Kn (polymer XV)) x 1 36. Yet, as we have just indicated, taking into account molecular masses of the LC polymers and reducing k, values for various polymers to equal values of DP one may come to substantially different values for ratios of constants presented. It is necessary to note that up to date no quantitative data on the determination of elastic constants of LC polymers has been published (excluding the preliminary results on Leslie viscosity coefficients for LC comb-like polymer127)). Thus, one of the important tasks today is the investigation of elastic and visco-elastic properties of LC polymers and their quantitative description. 

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