Detailed Molecular Model

In addition to quantitative estimates of material properties, molecular modeling can offer valuable qualitative insights into the dynamical properties of materials, without resorting to direct simulation (e g., molecular dynamics), where the rigorous treatment of all the dynamics at the atomic scale would be prohibitively time-consuming. To illustrate this point, the second part of this chapter describes recent studies of the a, relaxation in the crystalline a-phase of PVDF. Molecular modeling provides a way to characterize the mechanism of 

The state of polarization, and hence the electrical properties, responds to changes in temperature in several ways. Within the Bom-Oppenheimer approximation, the motion of electrons and atoms can be decoupled, and the atomic motions in the crystalline solid treated as thermally activated vibrations. These atomic vibrations give rise to the thermal expansion of the lattice itself, which can be measnred independently. The electronic motions are assumed to be rapidly equilibrated in the state defined by the temperature and electric field. At lower temperatures, the quantization of vibrational states can be significant, as manifested in such properties as thermal expansion and heat capacity. In polymer crystals quantum mechanical effects can be important even at room temperature. For example, the magnitude of the negative axial thermal expansion coefficient in polyethylene is a direct result of the quantum mechanical nature of the heat capacity at room temperature. At still higher temperatures, near a phase transition, e.g., the assumption of strictly vibrational dynamics of atoms is no 

Equation (1) expresses the crystal polarization (P, C/m ). as a function of the dipole moment (p. Cm) and the unit cell volume (V, m ). In PVDF, it suffices to express Eq. (1) in scalar form, where it is understood that P and p represent the components of the polarization and dipole moment vectors parallel to the -crystal axis. This arrangement of dipoles produces a significant local electric field in the 

From Eq. (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the 3-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory or Lorentz field sums of dipole lattices static, atomic level modeling of the intrinsic bond polarity atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

Equation (2) expresses the model of the crystal polarization used in the molecular modeling of PVDF reported in this chapter, where is the dipole of each repeat unit of the single chain in vacuum, Ap is the change in dipole moment of the repeat unit of the chain in going from the vacuum environment to the environment of the packed crystal and (cos cp) is the attenuation of the dipole moment of the repeat unit along the -axis due to thermally stimulated oscillations about thec-axis. Ap is directly related to the local electric field ( ioc, V/m) through the repeat unit polarizability (a, m )  

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Laughton CA, Zvelebil MJ, Neidle S. A detailed molecular model for human aromatase. J Steroid Biochem Mol Biol 1993 44 399-407. 

This scenario for molecular packing leading to biased chiral symmetrybreaking is quite speculative. However, it makes an important point for molecular modeling of lipid membranes The unusual feature of diacetylenic lipids does not have to be associated with the stereocenter of the molecules but rather may be a broken symmetry in the packing of the kinks in the acyl chains. This speculation needs to be investigated by detailed molecular modeling calculations. 

The interplay between oscillations and bistability has been addressed in detailed molecular models for the cell cycles of amphibian embryos, yeast and somatic cells [138-141]. The predictions of a detailed model for the cell cycle in yeast were successfully compared with observations of more than a hundred mutants [142]. Other theoretical studies focus on the dynamical properties of particular modules of the cell cycle machinery such as that controlhng the Gl/S transition [143]. 

The chemical and physical properties of ribosomes are well characterized (for reviews see The exact understanding of their function, however, still lacks a detailed molecular model. Appropriate methods such as image reconstruction from electron micrographs of two-dimensional sheets, or X-ray structure analysis, all depend on the crystallizability of the material. 

In brief, obtaining a detailed molecular model of the unit-cell contents entails calculating p(x,y,z) from Eq. (6.7) using measured intensities from the native... 

The second publication detailed molecular modeling studies on the reaction of sulfur trioxide with a series of fluoroalkenes and found that the reaction proceeds via formation of stable 7t-complexes prior to transition state formation <1999J(P2)1819>. 

The initial stages of the solid-state decomposition have been studied by Cordes and Smith84 between 330 and 440°C. An Arrhenius plot was linear to 390°C. Above this temperature, the slope of the plot increased. This result, as well as the low preexponential factor, was accounted for by a detailed molecular model (discussed under KC104) in which 02 is abstracted from two neighboring perchlorate ions ... 

In this particular example, estimates for both free energy parameters g and ga of the coarse-grained model are obtainable from more detailed molecular models albeit that strictly speaking they depend not only on the chemical composition and structure of the molecular building blocks but in principle also on the solvent properties. It is important to stress again for it is often ignored, the solvent molecules not only drive the assembly but have been shown to play an active role in structural reorganizations of supramolecular assemblies (Bouteiller et al., 2005 Jonkheijm et al., 2006). Ideally, their influence should not be absorbed in adjustable parameters as is almost always done. 

It seems to the author that a detailed molecular model for the solution using only near neighbor interactions is no more complex and would probably yield more interesting and useful information. The parameters for such a model would be only the dipole moments and radii of the solute and solvent species. 

The basis for thermodynamic calculations is the adsorption isotherm, which gives the amount of gas adsorbed in the nanopores as a function of the external pressure. Adsorption isotherms are measured experimentally or calculated from theory using molecular simulations. Potential functions are used to constmct a detailed molecular model for atom-atom interactions and a distribution of point charges is used to reproduce the polarity of the solid material and the adsorbing molecules. Recently, ab initio quantum chemistry has been applied to the theoretical determination of these potentials, as discussed in another chapter of this book. 

Pace and Datyner (64-66) have proposed a more detailed molecular model which provides an expression for the activation energy that is free of adjustable parameters. This model was successfully applied to polymer/penetrant systems both above and below Tg (64-66). The glassy state is accounted for only by its lower thermal expansivity. 

These are promising approaches, which incorporate a detailed molecular model in which groups can be differentiated. In this way, they benefit from advantages of the successful UNIFAC approach, and overcome the difficulties associated with its underlying lattice model. They are accurate over large pressure ranges and can be used consistently for liquid and vapour phases. In addition, as mentioned above, their formulation as continuum fluid theories means that the binary interaction parameters can be determined from pure component data. 

In summary, the use of atomistically detailed molecular models provides a level of fidelity and thus confidence that cannot be matched by the other models described here. Thus, if one wishes to state with confidence that one s simulations describe a particular experimental system, there is no substitute. However, the use of such models is not without cost, which, in this case, is the dramatically larger computational time required. 

Sobell HM, Jain SC (1972) Stereochemistry of actinomycin binding to DNA. II. Detailed molecular model of actinomycin-DNA complex and its implications. J Mol Biol 68(1) 21-... 

While there may have been controversy in other quarters, Haworth, Meyer and Mark were doing polymer science. Careful experiments were interpreted in terms of detailed molecular models. All the best concepts of structural chemistry and all the best experimental methods from X-ray diffraction to detailed synthetic analyses were employed. Eventually a much larger community would join them. 

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