Chains potential function

A complete set of intermolecular potential functions has been developed for use in computer simulations of proteins in their native environment. Parameters have been reported for 25 peptide residues as well as the common neutral and charged terminal groups. The potential functions have the simple Coulomb plus Lennard-Jones form and are compatible with the widely used models for water, TIP4P, TIP3P and SPC. The parameters were obtained and tested primarily in conjunction with Monte Carlo statistical mechanics simulations of 36 pure organic liquids and numerous aqueous solutions of organic ions representative of subunits in the side chains and backbones of proteins... 

Our model is based on a polyethylene-like chain similar to that used by Helfand, et. al.(i) The potential function... 

To explore this issue, Monte Carlo computer simulations were run using the protocol outlined in the previous section. In these simulations, however, a peptide of sequence Ac-Ala-Xaa-Ala-Ala-NMe was employed (Xaa = Gin or Asn), the backbone was not constrained to the PPII conformation, and a side chain-to-backbone hydrogen bond was constrained using a potential function previously used to constrain a-helical backbone-to-backbone hydrogen bonds (Tun and Hermans, 1991 Creamer and Rose, 1994). 

Values in the industry value chain are subjects of financial accounting, profit and cost controlling as well as value-based management research. Out of the scope is the value chain support function of corporate finance concerned with getting required or investing excess financial resources in financial markets, which is not a core activity in the industry value chain and out of the scope in this work. The integration of value chain management with corporate finance is a potential area for further research. 

A second, and potentially more useful feature is the stability of these unimolecu-lar initiators to a wide variety of reaction and polymerization conditions which is in sharp contrast to traditional initiators for anionic procedures, such as n-butyl lithium. This allows the initiators to be fully characterized, purified and handled by normal techniques, thus simplifying the polymerization process. It also permits a variety of chemical transformations to be performed on the initiator prior to polymerization, which greatly facilitates the preparation of chain end functionalized macromolecules. For example, the chloromethyl functionalized al-koxyamine, 18, can be readily converted in high yield to the corresponding aminomethyl derivative, 19, followed by polymerization to give well-defined linear polymers, 20, with a single primary amine at the chain end (Scheme 12). 

The method of Section 7.6 can be used to find the potential functions corresponding to the boson Hamiltonians of Chapter 2. According to Eq. (2.30), one has in this case two possible chains... 

The potential function corresponding to this chain can be easily evaluated and is given by... 

The application of these functionalization reactions to polymers has been catalogued in the anionic polymer review literature (4-6). Unfortunately, many of the reported applications of these functionalization reactions to anionic chain-ended polymers have not been well characterized (7). In order to exploit these functionalization reactions to their potential, well-defined procedures for quantitative chain end functionalization must be available. 

Atom-atom potentials have been used extensively for the study of molecular crystals, and many useful empirical parameters sets have been designed. The interaction energy of the two chains is considered to be the sum over all pairwise interactions. In the present work, such interaction is considered according to the 6-12 potential functions. The energy of an atom pair is given by an expression of the form ... 

Conformational energies are calculated for chain segments in poly(vlnyl bromide) (PVB) homopolymer and the copolymers of vinyl bromide (VBS and ethylene (E), PEVB. Semlempirical potential functions are used to account for the nonbonded van der Waals and electrostatic Interactions. RIS models are developed for PVB and PEVB from the calculated conformational energies. Dimensions and dipole moments are calculated for PVB and PEVB using their RIS models, where the effects of stereosequence and comonomer sequence are explicitly considered. It is concluded from the calculated dimensions and dipole moments that the dipole moments are most sensitive to the microstructure of PVB homopolymers and PEVB copolymers and may provide an experimental means for their structural characterization. 

Hindered rotation is studied for the disaccharides composed of basic p-glucopyranose units. The van der Waals Interactions are calculated for the Lennard-Jones, Buckingham, and Kitaygorodsky interatomic potential functions. Values of the ratio of unperturbed to free-rotation root-mean-square end-to-end distance are calculated for chains composed of the unsolvated disaccharide repeating units. 

In our paper we are concerned with a potential energy function which is somewhat more realistic than one implied by the excluded volume effects. This potential function allows indirectly bonded chain elements which occupy adjacent lattice sites to interact with a finite energy . We call these interactions nearest-neighbor interactions, which should not be confused with interactions between near-neighbor pairs along the chain. 

In open chain molecules the torsional angles are the obvious independent variables for the potential function. But even in the simplest case, that is ethane, the origin of the torsional barrier is not fully understood, though ab initio calculations represent the experimental barrier fairly well26 For larger molecules theoretical predictions for the potential functions are often based upon semiempirical molecular mechanics calculations27,2S ... 

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