Bending constant

Discuss the quantitative differences among enhies in your table. Why are some entries larger than other comparable entries What are the torsional bending constants for C=C and C—C Why do they assume the values you find What is a torsional angle, anyway ... 

MMh- is SF = 7.0 x 10". The constant 0.043828 converts the MMh-bending constants expressed in millidyne-Aper radian to... 

Usually the constants involved in these cross terms are not taken to depend on all the atom types involved in the sequence. For example the stretch/bend constant in principle depends on all three atoms. A, B and C. However, it is usually taken to depend only on the central atom, i.e. = k , or chosen as a universal constant independent of atom type. It should be noted that cross tenns of the above type are inherently unstable if the geometry is far from equilibrium. Stretching a bond to infinity, for example, will make str/bend go towards — oo if 0 is less than If the bond stretch energy itself is harmonic (or quartic) this is not a problem as it approaches +oo faster, however, if a Morse type potential is used, special precautions will have to be made to avoid long bonds in geometry optimizations and simulations. 

Note 2 fri low molar mass nematics composed of rod-like molecules, the bend constant is the largest while the twist constant Ki is the smallest. Typical values of K are 10 " - lO Nm l... 

FC = force constant EQV =equilibrium value stretch constants in kcal/mol/A bend constants in kcaVmol/rad ... 

For all three systems the HF and DF complex had the same N. .. F distance. The more interested Reader will certainly like to consult papers89) and 90) for the complete set of force constants obtained for the first time for H-bond systems, including the H-bond stretching and bending constants. 

When C2D2 frequencies are used, in should be replaced by /Hq. The force constants for acetylene can be calculated from these relations using the measured vibrational frequencies, and the bond lengths can be determined from the rotational analysis described below. If one expresses the frequencies in cm units and the masses in appropriate isotopic mass units, the factors 4t7 should be replaced by 4t7 c 10 NY = 5.8918 X 10 (this includes a factor of 10 kg/g mass conversion). This substitution gives the force constants Y, kg, and Yr in N m units and the bending constants kg and kgg in units of N m. 

The overwhelming problem in developing force fields is the lack of enough high quality reference data. As illustrated above, there are literally millions of possible parameters in even quite simple force fields. The most numerous of these are the torsional parameters, followed by the bending constants. As force fields are designed for predicting properties... 

Problem 10.8 You are measuring the elasticities and viscosities of a room-temperature nematic at reduced temperatures and you find that below about 10°C the twist and bend constants K2 and become very large, while the splay constant Ki retains a modest value. Also, the Miesowicz viscosity t], becomes enormous while r) goes up only modestly. What could explain this behavior ... 

Because of the difficulty with which polymeric nematic monodomains are prepared, there are few measurements of Leslie viscosities and Frank constants for LCPs reported in the literature. The most complete data sets are for PBG solutions, reported by Lee and Meyer (1990), who dissolved the polymer in a mixed solvent of 18% dioxane and 82% dichloromethane with a few percent added dimethylformamide. Some of these data, measured by light scattering and by the response of the nematic director to an applied magnetic field, are shown in Figs. 11-19 and 11-20 and in Table 11-1. While the twist constant has a value of around K2 0.6 x 10 dyn, which is believed to be roughly independent of concentration and molecular weight, the splay and bend constants ATj and K3 are sensitive to concentration and molecular weight. 

Figure 11.20 The bend constant 3 as a function of molecular aspect ratio, obtained for the same solutions as in Fig. 11-19. (From Lee and Meyer 1990, by permission of Taylor Francis.)...

O—C—O bending constant (all-atom and united-atom) Klewinghaus 1997... 

M. Gradzielskl, Bending Constants of Surfactant Monolayers, in Curr. Opinion Colloid Interface ScL 3 (1998) 478. 

Usually the constants involved in lliese cross terms are not taken to depend on all the atom types involved in the sequence. For example the stretch/bend constant in principle depends on all three atoms. A, B and C. However, it is usually taken to depend only on the central atom, i.e. or chosen as a universal constant independent of atom... 

Units mdyn/A for stretch and stretch, stretch constants mdyn for stretch, bend constants and mdyn A for all others. 

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