Polymer force fields

We have adopted a strategy similar to that used in our development of polymer force fields in parameterization of an atomistic potential function for HMX. Specifically, we have undertaken a systematic investigation of conformational and intermolecular binding energies in model nitramine compounds (i.e., those containing the C2N-NO2 moiety ) using high-level QC calculations. In the case of HMX, a QC-based force field is the only realistic option due to insufficient spectroscopic data that would facilitate force field parameterization. 

The parameterization of nonbonded interactions for these force fields has received special attention in the form of efforts to improve the predictive ability of polymer force fields for properties that depend on the cohesion of polymer systems.ii The extensive use of molecular dynamics calculations in the parameter derivation process has been a hallmark of such work, and the resulting force field parameter set can provide computed properties that rival experimental accuracy for many... 

The Boltzmann factor depends on the positions of all atoms that interact with the penetrant. For a pairwise additive penetrant polymer force field, such as the Lennard-Jones expression... 

Our goal is to model quantitatively 7r-electronic contributions to both vibrational and electronic spectra. The general e-ph analysis introduced in Section II combines the microscopic AM formalism [18,19] with the spectroscopic ECC model [22]. The reference force field F for PA provides an experimental identiHcation of delocalization effects. Transferable e-ph coupling constants are presented in Section III for polyenes and isotopes of trans- and a s-PA. The polymer force field in internal coordinates directly shows greater delocalization in t-PA, while coupling to C—C—C bends illustrates V(/ ) participation and different coupling constants a(/ a) and a(Jis) in Eq. (3) support an exponential r(/ ). NLO spectra of PDA crystals and films are presented in Section IV, with multiphoton resonances related to excited states of PPP models and vibronic contributions included in the Condon approximation. Linear and electroabsorption (EA) spectra of PDA crystals provide an experimental separation of vibrational and electronic contributions, and the full tt-tt spectrum is needed to model EA. We turn in Section V to correlated descriptions of electronic excitations, with particular attention to theoretical and experimental evidence for one- and two-photon thresholds of centrosymmetric backbones. The final section comments on parameters for conjugated polymers, extensions, and open questions. 

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

United Atom force fieldsare used often for biological polymers. In th esc m oleciiles, a reduced ii nm ber of explicit h ydrogen s can have a notable effect on the speed of the calculation. Both the BlOn and OPLS force fields are United Atom force fields. AMBER con tain s both aU nited and an All Atom force field. 

For biological polymers, molecular mechanics force fields arc not well substantiated by experirn eri tal data. You should be cautious about relying on predictions from thesc calculations. 

Ah initio calculations of polymer properties are either simulations of oligomers or band-structure calculations. Properties often computed with ah initio methods are conformational energies, polarizability, hyperpolarizability, optical properties, dielectric properties, and charge distributions. Ah initio calculations are also used as a spot check to verify the accuracy of molecular mechanics methods for the polymer of interest. Such calculations are used to parameterize molecular mechanics force fields when existing methods are insulficient, which does not happen too often. 

It is important to mention that for most applications the special form of the force field is not as important as the actual values of the parameters. These parameters are determined in a number of ways, mainly by comparison with experiments, e.g., vibrational spectroscopy. Torsional potentials, which are crucial for polymer configurations and dynamics of polymers, can... 

In addition to the MD method, a wealth of Monte Carlo methods is used also at the atomistic level [6]. They use essentially the same models, force fields, for polymers. Their main advantage, however, is that by introduction of clever moves one can beat the slow physical dynamics of the systems and can run through phase space much faster than by MD. These methods are still in their infancy, but will certainly become more important. 

Fig. 3a-e. Supermolecular structures of polymers crystallized in various force fields a structure of the shish-kebab type, b structure formed during crystallization in a capillary with a conical inlet and c structure of a polymer crystallized at hydrostatic compression at 4 x 108 Pa... 

The reliability of molecular mechanics calculations hinges entirely on the validity and range of applicability of the force field. The parameterisation of these functions (the force field) represents the chemistry of the species involved. Many force fields have been developed and the one used in any application usually depends on the molecular mechanics package being used. The force field itself can be validated against experimental and ab initio results. Because of the relative speed of molecular mechanics calculations, it is possible to consider routine calculations of a large number of atoms, certainly tens of thousands, which makes the method amenable to calculations on polymers. To remove surface effects, calculations of bulk properties are normally carried out employing 3D periodic boundaries. In this way it is possible to perform calculations on both amorphous and crystalline systems. 

Having established the validity of the force field for such a wide range of properties the authors go on to extend and apply the force field to electrolyte systems [141]. In particular the diffusion of Li+ in the polymer medium is treated, which is one of the key properties for understanding ionic conduction in the... 

One tool for working toward this objective is molecular mechanics. In this approach, the bonds in a molecule are treated as classical objects, with continuous interaction potentials (sometimes called force fields) that can be developed empirically or calculated by quantum theory. This is a powerful method that allows the application of predictive theory to much larger systems if sufficiently accurate and robust force fields can be developed. Predicting the structures of proteins and polymers is an important objective, but at present this often requires prohibitively large calculations. Molecular mechanics with classical interaction potentials has been the principal tool in the development of molecular models of polymer dynamics. The ability to model isolated polymer molecules (in dilute solution) is well developed, but fundamental molecular mechanics models of dense systems of entangled polymers remains an important goal. 

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. 

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