Svetlana Keshtova - PARAMETRIZATION OF FORCE CONSTANTS IN DEPEND ON CHANGE OF INDUCED LOCAL ELECTROSTATIC FIELD BY CHANGE OF ENVIRONMENT IN CLUSTER MODEL AND APPROXIMATE TO BULK MODEL AT MODELING OF IONOMER MEMBRANE

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  PARAMETRIZATION   OF FORCE CONSTANTS IN DEPEND ON CHANGE OF INDUCED LOCAL   ELECTROSTATIC FIELD BY CHANGE OF ENVIRONMENT IN CLUSTER MODEL AND   APPROXIMATE TO BULK MODEL AT MODELING OF IONOMER   MEMBRANE

     

    Fatima. Keshtova and Svetlana V. Keshtova

     

     LMSU,   Skobeltsyn Institute of Nuclear Physics, Leninskie Gory, GSP-2,   Moscow, 119992; Private researcher, Vinokurova st.16,

    Moscow, 117447 Russia.

    Introduction

  Here   suggested scheme for development fitting a polarizable molecular   mechanics model to high quality ab initio quantum   chemical data for the electrostatic charge distribution,   polarization response, and intermolecular interactions. Quantum   chemical method for determination of many-particles effects in   intermolecular interactions used the assumption that the   potential function parameters of many-particles interactions in   an extended molecular system should give a good demonstration of   the many-particles interactions in small molecular   clusters1. Thus, they are partition on terms that   involve from three and more particles. The electrical induction   has an important effect in fluids where the induced dipoles can   be 50% as large as the permanent dipoles2.   Many-particles polarization is a critical factor in constructing   non-pair-wise interaction potentials of large clusters from   information about small clusters. The forces between molecules on   short distance are not purely electrostatic, but a mixture of the   electrostatic and non-electrostatic interactions. The molecular   vibrations are sensitive to the local electrostatic field,   leading to field-induced changes. Molecular vibrations are   affected by a weak electrostatic field the electronic effects   arise from the interaction of the field with the molecular   electron cloud, which perturbs chemical bonds and alters the   charge distribution in the molecule. On the basis of these   theories we propose scheme for parameterization of the standard   force fields (DREDING).

  Model

  In work   have been considered atomistic models, in which to atoms assigned   charges obtained by ab initio method. The complete of   ab initio parameterization was carried out at the   depiction of atom as the harmonic oscillator with point view   fixed of charge on atom. After parameterization the new force   constants considered the many-particles effect, which can be   taken from vibration spectra of molecules in cluster. The   boundary effects of cluster model have been neglected. The   covalent bond consider as spring between oscillators, and force   constants considered as magnitudes, which proportionally to   reciprocal polarizability. The Hartree-Fock potential is scanning   from minimal distance to decay of bond and the cut off on   boundary for not valent interactions. In result the energies    and  are tabulated as a function of    and of  respectively the energies and   forces are calculated by the interpretation scheme during   simulations. The charges are constants and thus cannot change in   response to changing electrostatic fields, which arise from   movement of the atoms during the simulation. These charges   reflect average field charge values for the particular phase.We   consider the valence force field where non-diagonal terms of the   force matrix, does not take account. Within the framework of   harmonious approach, each molecule is considered as system of   connected harmonious oscillators. We implicitly incorporate   many-particles forces by simple way of implant in each atom of   the isotropic harmonic oscillator with the frequency, mass and   polarizability: . Two charges  and  were attached to each other via   a harmonic spring with a force constant, which is proportional   . The normal oscillatory   coordinates corresponding to this force field, have given   approximate description of the fluctuations made by a molecule.   Analogically are considering other force constants. The method of   molecular dynamic is just based on transferability of potential   functions. The energy of system at harmonically approximation is   writing as sum of bonded and non-bonded terms:

   

  The   non-bonding pair potentials are calculated by Lennard-Jones   function. A cutoff radius is created and interactions between   atoms separated by more than are ignored. The electrostatic   interactions evaluated by using the Ewald summation   technique

  Calculation

  The models   were built from three different molecular fragments: sulfonate of   side chain, water and hydroxonium ion. In this case was used a   conglomerate of such fragments rather than a fully connected   polymer chain in order to produce higher molecular mobility’s, so   that a model could undergo significant structural reorganization   at the simulation. The molecular fragments use by means the   constraining influence of chain-bending forces on ionic   aggregation is less significant than in real polymer. The   omission of the fluorocarbon links between ion exchange groups   will be result in an effective increase in the ratio of polar to   non-polar material in the model compared to the real polymer. The   sulfonic acid group was embodied as completely ionized. Thus, the   dissociated hydrogen ion can move freely between different   sulfonate fragments in the cluster. The net charge of the   combination is been zero. Lone protons proved very destructive to   the simulations due to their small size and the extremely high   charge to mass ratio. Therefore, each proton was associated with   a water molecule, to form a hydroxonium ion. The hydroxonium ion   was built from a water molecule with a net charge of, and uniformly distributed   charges on each hydrogen. The partial atomic charges of the   molecular fragments calculated by quantum-chemical package GAMESS   with using ab inito calculation with 6-311G* basis. The   partial charges for atoms in water molecules were used TIP3P   model. The parameters of valent force field have been calculated   on the basis of the HF/ 6-311G*.

  Table 1. The list of   parameters the generating force field for simulation of   perfluorinated ionomer membrane.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
         

            Valence Parameters             for perfluorosulfonic acid         

       
         

                        Bond type         

       
         

                                             

       
         

                                             

       
         

                        C_F         

       
         

                        1.34         

       
         

                        1514.00         

       
         

                        Oc_C         

       
         

                        1.40         

       
         

                        2928.80         

       
         

                        C_C         

       
         

                        1.61         

       
         

                        1360.00         

       
         

                        C_S         

       
         

                        2.10         

       
         

                        480.00         

       
         

                        S_Os         

       
         

                        1.45         

       
         

                        863.00         

       
         

                        H_Oh         

       
         

                        1.00         

       
         

                        3989.00         

       
         

                        Lenard-Jones parameters         

       
         

                        Atom         

       
         

                                             

       
         

                                             

       
         

                                             

       
         

                        F_F         

       
         

                        3.093         

       
         

                        0.304         

       
         

                        0.0         

       
         

                        Os_Hh         

       
         

                        Tabul.poten.         

       
         

                        0.0         

       
         

                        H_H         

       
         

                        2.960         

       
         

                        0.342         

       
         

                        +0.417         

       
         

                        C_C         

       
         

                        3.473         

       
         

                        0.398         

       
         

                        0.000         

       
         

                        S_S         

       
         

                        3.550         

       
         

                        1.047         

       
         

                        +1.530         

       
         

                        Os_Os         

       
         

                        3.350         

       
         

                        0.850         

       
         

                        -0.690         

       
         

                        Oh_Oh         

       
         

                        3.151         

       
         

                        0.650         

       
         

                        -0.833         

       
         

                        Oh_Hh         

       
         

                        Tabul.poten.         

       
         

                        0.0         

       

  These data show the coordination between results of wave number   for harmonically oscillator for experiment results of water   molecule and of perfluorinated ionomer and results of quantum   chemical calculations for cluster. By spectral   analysis determined the stretches constant for C-S and O-H bonds,   which equal 480.0 and 3989.0 kJ/mol/A2 that not closer   to the DREDING analogy values 2926.0 kJ/mol/A2. For   obtained force constants have been taken clusters where consider   the influence of change environment on vibration frequencies of   the valent (C-S) and non-valent (H-O) interactions. The results   of calculation listed in Table 1.

  Molecular dynamic simulation of per-fluorinated ionomers was   carried out in the NVT/NPT/Andersen-Nose-Hoover ensemble.  The   temperature control was carried out by Nose-Hoover algorithm,   which used when pressure-stress is controlled by the extended   Hamiltonian methods. For the not   tabulated potential, the cutoff distance of the Lennard-Jones   potentials was the 2.5. In the NPT ensemble, the   amount of each component in the simulation cell is fixed. The   volume of the system is allowed to fluctuate satisfy a given   pressure. The benchmark model consisted of 16 sulfonate   fragments, 16 hydroxonium ions and 64 water molecules. For this   system has been found that it tends to aggregate to form of water   channel like of cylindrical form with expansion in some places   tend to formation of sphere (Fig. 1).

   

  Figure 1.  Snapshot of   MD simulation of per-fluorinated ionomer membrane in first time.   After NVT simulation about 100 ps, we performed a 200 ps   simulation in NPT ensemble simulation at P = 1.0 atm. The density   and different contributions to the potential energy of the system   were constant after the 200 ps of the simulation. After the   equilibration, statistics were collected over 350 ps. The   periodic boundary conditions calculated so out to minimize   finite-size effect.

   

  Figure   2. Snapshot of the membrane (left) and   snapshot of water containing channels (right) at T=300 K. water   contents nw =   4 molecules per  group. The equilibrium density   was  at temperature T = 300 K. The   snapshot display well constructed channel in perfluorinated   ionomer membrane that not full contain water molecule about 4   molecules water per  group. On Fig. 3 display the   amplitudes vibrations of side chains in channel in process   simulation.Analogy conclusions   corroborate by our ab initio calculations of rate  dissociation for three fragments of side chain. By   formula: preexponential factors   A(s-1) and rate constants of chemical reactions   [kAr] in side and main chains of Nafion at two   temperatures: 298.15 K and 330 K display in Table 2. The computed   results by ab   initio 3-21G methods and literature values of constant   reactions are in reasonable agreement. The results indicate that   largest rate observed for terminal carboxyl group independently   of temperature. The hydrophilic   groups in channel have some mobility in comparison with  hydrophobic poly-(tetrafluoroethylene) backbone in matrix of membrane.

  Table 2 Arrhenius parameters of the   rate constants at temperature 298.15 (330) K of said and main   chain.

                                                                                                                                                                                                             
       

          Paramet.       

     
       

          Reaction       

     
       

          CF3SO3H       

       

          ·CF3+·SO3H       

     
       

          CF3COOH       

       

          ·CF3CO+·OH       

     
       

          CF3-CF(CF3)-O-CF3       

       

                    *CF3-CF(CF3)-O·           +·CF3       

     
       

          Side       

     
       

          Main       

     
       

          Side       

     
       

          Ea       

       

          kcal/mol       

     
       

          32.1(29.3)       

     
       

          68.4(62.4)       

     
       

          71.6(56.8)       

     
       

          A0, s-1       

     
       

          5.09x1013       

       

          (3.9           x10-8)       

     
       

          8.68x1013       

       

          (1.91x1013)       

     
       

          8.9x1013       

       

          (2.1x1013)       

     
       

          kAr, s-1       

     
       

          1.10x10-9       

       

          (3.9           x10-8)       

     
       

          7.3x10-37       

       

          (9.4x10-29)       

     
       

          3.1x10-39       

       

          (5.3x10-24)       

     

  We defined   that part of water molecules have stronger connection with    group. Another fraction of   water molecule has more mobility then first part of them. This   conclusion confirm the energy of hydrogen bonds for   [(H2O)H--O(H3O)] E = 96 kcal/mol more then   [(SO3)O--H(H2O)] E = 5.1 kcal/mol and   [(SO3)O--H(H3O)] E = 72 kcal/mol. For   quantitatively characterize the perfluorinated ionomer structure   considering the partial correlation function.

 

  Figure 3.  The partial   correlation function g(r) for  for the water-containing system   simulated under NPT conditions at  at the (). (Atomistic model).   Function  is peaked at contact distance   and show well-form coordination shell at short distance ~ 2.15 A,   and second coordination shell at ~ 5.0 A, it is well-form first   coordination shell at distance ~ 2.0 A for . The  function is peaked at contact   distance less than give the DREDING force field. The hydrophobic   sub-phase is formed by the organic backbone. The hydrophilic   sub-phase is formed by largely immobile negative charges of    groups on the side chains,   mobile counteractions, and absorbed water. The water formation of   the first layer on a polar surface of the polar head, with   formation of strong hydrogen connections between molecules of   water and polar group and which is characterized by small   mobility.

    Results and Discussion

  Structural and energetic characteristics of new force field well   are coordinated to results of works of other authors. At creation   of new force fields, we overcome three basic problems at this   process and we refuse labour-consuming quantum calculations for   very big systems, as beforehand we parametrized force field by   quantum chemical methods for the given system. Evidently force   field obtained by quantum chemical method to give the more   compact cluster and it give significant speed up simulation of   big systems.

  References

  1.           Kaminski, G. A.; Stern, H. A.; Berne, B. J.; Friesner, R. A.;   Gao, Y. X.; Murphy, R. B.; Zhou, R.; Halgren, T. A. J. Comput. Chem.  2002, 23, 1515.

  2.           Gao, J.; Berne, B. J. J. Chem. Phys. 1993, 99,   4, 15, 2902.

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