SPC model

More realistic treatment of the electrostatic interactions of the solvent can be made. The dipolar hard-sphere model is a simple representation of the polar nature of the solvent and has been adopted in studies of bulk electrolyte and electrolyte interfaces [35-39], Recently, it was found that this model gives rise to phase behavior that does not exist in experiments [40,41] and that the Stockmeyer potential [41,42] with soft cores should be better to avoid artifacts. Representation of higher-order multipoles are given in several popular models of water, namely, the simple point charge (SPC) model [43] and its extension (SPC/E) [44], the transferable interaction potential (T1PS)[45], and other central force models [46-48], Models have also been proposed to treat the polarizability of water [49],... 

A bioprocess system has been monitored using a multi-analyzer system with the multivariate data used to model the process.27 The fed-batch E. coli bioprocess was monitored using an electronic nose, NIR, HPLC and quadrupole mass spectrometer in addition to the standard univariate probes such as a pH, temperature and dissolved oxygen electrode. The output of the various analyzers was used to develop a multivariate statistical process control (SPC) model for use on-line. The robustness and suitability of multivariate SPC were demonstrated with a tryptophan fermentation. 

Atomistic MD models can be extended to the coarse-grained level introduced in the previous section, which is determined by the dimension of the backbone chain and branch. For the precise description of water molecular behavior, simple point charge (SPC) model was adopted (Krishnan et al., 2001), which can be used to simulate complex composition systems and quantitatively express vibrational spectra of water molecules in vapor, liquid, and solid states. The six-parameter (Doh, o , fi, Lye, Lyy, and Lee) SPC potential used for the water molecules is shown in Equation (24) ... 

Figure 5.2 Assessment of electrostatic contributions to the excess chemical potential of water, following Eq. (5.15) redrawn from Hummer et at. (1995). The temperature is T = 298 K and the density is p = 0.03333 A The SPC model of water was used and the reference system interactions are those interactions with all partial charges given the value zero.

The PN-TrAZ potential [15] is used to describe interactions between water and substrate, and the SPC model for water-water interaction. Adsorption isotherm, and isosteric heat of... 

The water adsorbed on the surface is described by the SPC model [16]. This fast computable model is well suited for very large systems, as it reproduces quite well the thermodynamical properties around ambient temperature, like vapor pressure (0.044 bar against 0.035 bar experimentaly) and enthalpy of vaporization [17]. The extended SPC/E model [18] is not adapted to study adsorption properties since the polarization correction that it introduces cannot be well defined in the highly inhomogeneous environment of a molecule adsorbed on a surface. Furthermore, the predicted vapor pressure is only half the experimental value [19]. 

The interaction between water molecules and silica substrate is described in the framework of the PN-TrAZ model [15] which has proven to model successfiilly the adsorption of simple adsorbates on various zeolites [20]. In this model, the pair potential decomposes in two parts a repulsion term Ae" due to electronic clouds and the attractive dispersion terms. The repulsive parameters (A,b) for silica atoms (Si, O, H) are those obtained from studies of adsorption of simple gazes on various zeolites [20] and mesoporous glass [21]. Those for water oxygen are chosen to fit the repulsive part of Lennard-Jones from SPC model in the range around equilibriiun distance, and those for water hydrogen are taken equal to the parameters for surface hydrogen of vycor. The cross repulsive parameters A and b are obtained by Bohm and Ahlrichs [22] combination mles. The dispersion terms are calculated from polarizabilities and effective niunber of electron Neff according to the PN-TrAZ model up to order r °. Values are listed in table 1. 

At full saturation, corresponding to a vapor pressure of 0.044 bar at 300 K (determined by Gibbs Ensemble Monte Carlo [24] for SPC model), the total number of water molecules in the pores is around 10200, which corresponds to a density aroimd 0.90 g/cm, close to the density of SPC saturating water at 300 K (0.97 g/cm, by GEMC method). The discrepancy between both values is probably due to the slow convergence caused by a very low acceptance level of insertion of water molecules in liquid phase. 

The amount of water adsorbed, normalized to full saturation, is given in figure 3 (right part) as a fiinction of pressure normalized to the saturating pressure for SPC model (0.044 bar). The isotherm is of type IV in lUPAC classification, showing a rapid increase at low... 

As an example of the solvent dynamics calculated from SSSV, F(k,t) for the SPC model of water is shown in Fig. 1, compared with the simulation results. Only ose for the H-H pair are shown for the dif mt values of k. The simulation results were obtained from the 200 ps trajectory for a stem of 216 water molecules by directly taking the average,... 

The overall performance of the TIP4P and SPC models, however, is to be considered remarkably good, also in view of their simplicity. That explains their widespread usage, larger than for other computationally more expensive potentials such as ST2, MCY, RWKl and RWK2, see Table 3. 

The decomposition of the interaction energy of a molecule in the liquid, allowed by the nature of the NEMO potentials, shows a larger contribution of the polarization term with respect to the electrostatic one, compared to the dimer case. Diffusion coefficient, 2.3-10 cm /s, is in a good accord with experiment, but Tp and Xnmr are larger than experimental and also than the corresponding data calculated with the SPC model. 

Among the different two-phase liquid/crystal systems, ice/water interfaces are of great interest because of their fundamental presence in nature and importance in chemical, biological, environmental and atmospheric processes [14]. Systematic studies of ice/water interfaces by molecular dynamics simulations began in 1987, when Karim and Haymet [15] simulated for the first time the two-phase coexistence using the SPC model of water molecules. Since 1987, ice/water interfaces were studied with TIP4P [16], CF1 [17], SPC/E [18, 19] and six-site [20] models of water molecules. 

Trypsin in aqueous solution has been studied by a simulation with the conventional periodic boundary molecular dynamics method and an NVT ensemble.312 340 A total of 4785 water molecules were included to obtain a solvation shell four to five water molecules thick in the periodic box the analysis period was 20 ps after an equilibration period of 20 ps at 285 K. The diffusion coefficient for the water, averaged over all molecules, was 3.8 X 10-5 cm2/s. This value is essentially the same as that for pure water simulated with the same SPC model,341 3.6 X 10-5 cm2/s at 300 K. However, the solvent mobility was found to be strongly dependent on the distance from the protein. This is illustrated in Fig. 47, where the mean diffusion coefficient is plotted versus the distance of water molecules from the closest protein atom in the starting configuration the diffusion coefficient at the protein surface is less than half that of the bulk result. The earlier simulations of BPTI in a van der Waals solvent showed similar, though less dramatic behavior 193 i.e., the solvent molecules in the first and second solvation layers had diffusion coefficients equal to 74% and 90% of the bulk value. A corresponding reduction in solvent mobility is observed for water surrounding small biopolymers.163 Thus it... 

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