Strain from molecular mechanics

Table 3.3. Correlation between Intramolecular Strain from Molecular Mechanics (MM) Calculations and Activation Energies for Dissociation of C—C Bonds in Substituted Ethanes"...

Before dealing with reinforcement of elastomers we have to introduce the basic molecular features of mbber elasticity. Then, we introduce—step-by-step—additional components into the model which consider the influence of reinforcing disordered solid fillers like carbon black or silica within a rabbery matrix. At this point, we will pay special attention to the incorporation of several additional kinds of complex interactions which then come into play polymer-filler and filler-filler interactions. We demonstrate how a model of reinforced elastomers in its present state allows a thorough description of the large-strain materials behavior of reinforced mbbers in several fields of technical applications. In this way we present a thoroughgoing line from molecular mechanisms to industrial applications of reinforced elastomers. 

The calculations described here have been called strain calculations, molecular mechanics, or force field calculations. We prefer the latter term. For a discussion of historical developments and a literature survey of earlier work, which are not given here, the reader is referred to a number of other reviews (1-3). The present paper deals with the description of force field types, techniques of energy minimisation, and procedures for the determination of force field parameters, and with some applications, preferentially taken from our own field of interest. In accordance with the experiences of the author, the work of Lifson and coworkers is given special attention other authors are nevertheless well represented in the context of critical comparisons. We hope that this selection, although inevitably biased, will help to improve the consistency of the presentation of the subject. 

Estimates of the ultimate shear strength r0 can be obtained from molecular mechanics calculations that are applied to perfect polymer crystals, employing accurate force fields for the secondary bonds between the chains. When the crystal structure of the polymer is known, the increase in the energy can be calculated as a function of the shear displacement of a chain. The derivative of this function is the attracting force between the chains. Its maximum value represents the breaking force, and the corresponding displacement allows the calculation of the maximum allowable shear strain. In Sect. 4 we will present a model for the dependence of the strength on time and temperature. In this model a constant shear modulus g is used, thus r0=gyb. 

Several approaches are being explored and developed using new methods in biotechnology to eliminate pre-harvest aflatoxin contamination of food and feed. These approaches resulted from recent information acquired on 1) non-aflatoxigenic A. flavus strains that prevent aflatoxin contamination of cottonseed when co-inoculated with aflatoxigenic strains, 2) molecular mechanisms governing aflatoxin biosynthesis, and 3) plant-derived metabolites that inhibit aflatoxin biosynthesis. 

The parameterization can be based on any type of experimental data that are directly related to the results available from molecular mechanics calculations, i. e., nuclear coordinates, nuclear vibrations, or strain energies. Most of the force fields available, and this is certainly true for force fields used in coordination chemistry are at least partially based on structural data. The Consistent Force Field (CFF)[43,49,601 is an... 

The presence of a double bond at a bridgehead position (as in 101 and 102) leads to strained olefins. From molecular mechanics (MM1) calculations (Z)-bicyclo[3.3.1]non-l-ene (101) should exist preferentially in a chair-boat conformation (the alternative boat-boat conformation is 1.18 kcal mol-1 higher in energy) while (E)-bicyclo[3.3.1 ]non-1 -ene (102) would be expected to adopt a chair-chair conformation (the strain energy of 102 is 29 kcal mol-1 higher than of 101 and the chair-boat conformation is 3.34 kcal mol"1 above the chair-chair one) (78). 

For details on the calculation of heats of formation from molecular mechanics, molecular orbital theory, or bond/group increments, see the discussion in Allinger, N. L. Schmitz, L. R. Motoc, 1. Bender, C. Labanowski, J. K. /. Am. Chem. Soc. 1992,114,2880. The strain energy of a conformation can be calculated from values of heats of formation from these sources also. The relationships in Figure 3.39 among heat of formation, T/R, strainless increments, and strain energy hold no matter what the source of the heat of formation value. 

For molecules with many bonds about which rotation can occur and many conformations that might be populated at room temperature, the POP and TOR corrections can be significant. For relatively rigid molecules, however, these terms are less important, and the strain energies calculated from molecular mechanics can more closely approximate those that would be determined with consideration of POP and TOR. For example, consider the results of a molecular mechanics calculation for puckered cyclobutane, the final portion of which is reproduced here. 

Computational methods are now used extensively by experimental chemists. Information that can be calculated includes the equilibrium geometry of a molecule, transition state geometries, heats of formation, composition of molecular orbitals, vibrational frequencies, electronic spectra, reaction mechanisms and (from molecular mechanics calculations) strain energies. The last 20 years have witnessed a huge increase in the use of computational methods in chemistry. Two factors have revolutionized the ways in which computational chemistry may be applied. The first is that calculations can now be performed on small computers (including laptops) or small clusters of computers, instead of on a mainframe computer. The second is the development of the computational methods themselves. The importance of... 

Perea S, JL Lopez-Ribot, WR Kirkpatrick, RK McAtee, RA Santillan, M Martinez, D Calabrese, D Sanglard, TP Patterson (2001) Prevalence of molecular mechanisms of resistance to azole antifungal agents in Candida albicans strains displaying high-level fluconazole resistance isolated from human immunodeficiency virus-infected patients. Antibicrob Agents Chemother 45 2676-2684. 

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