Berthelot potential model

Consider the same model system as above, but where there are attractive tail potentials, i mm C ) between sites of type M and M on different copolymers. In the numerical examples presented later, the shifted Lennard-Jones attraction of Eq. (5.10) is appended to the SFC diblock model of Section VILA. For simplicity, the Berthelot potential model is... 

The parameters in simple potential models for interactions between unlike molecules A and B are often deduced from tlie corresponding parameters for the A-A and B-B interactions using combination mles . For example, the a and e parameters are often estimated from the Lorentz-Berthelot mles ... 

For the more interesting thread model case with statistical segment asymmetry and a Berthelot attractive potential model, Schweizer has derived the following expression for the spinodal temperature [67]... 

The predicted spinodal temperature for the Berthelot A tail potential model is given by ... 

The energetic inhomogeneity of the surface along the x and y directions is not taken into account, but this is not expected to affect the results significantly at 308 and 333 K [39]. The cross interaction potential parameters between different sites were calculated according to the Lorentz-Berthelot rules Oap = aa + and eafi= ( The potential energy t/ due to the walls inside the slit pore model for each atom of the CO2 molecule is given by the expression C/ = + Uw(H-r where H is the distance between the carbon centers across... 

The Cheetah thermochemical code uses assumptions about the interactions of unlike molecules to determine the equation of state of a mixture. The accuracy of these assumptions is a crucial issue in the further development of the Cheetah code. We have tested the equation of state of a mixture of methanol and ethanol in order to determine the accuracy of Cheetah s mixture model. Cheetah uses an extended Lorenz-Berthelot mixture approximation [138] to determine the interaction potential between unlike species from that of like molecules ... 

In most cases, interactions between unlike molecules are treated with Lorentz-Berthelot combination rules [28]. Non-additive pair interactions have been used for N2 and O2 [18]. The resulting N2 model accurately matches double shock data, but is not accurate at lower temperatures and densities [22]. A combination of experiments on mixtures and theoretical developments is needed to develop reliable unlike-pair interaction potentials. 

The first of these relations is the Berthelot rule, and the second is the Lorentz rule. Combining rules are also required for other parameters in the chosen model. For example, the range parameter 2i2 in the unlike hard-core-square-well potential might be estimated as an arithmetic mean of 2n and (Table 3.3)... 

The Lennard-Jones potential includes a strongly repelling term proportional to 1 /r A which represents the excluded volume by an atom, and a long attractive tail of the form — 1 /rfj, which models the effect of attractive interactions between induced dipoles due to fluctuating charge distributions. This potential provides reasonable simulation results for the properties of liquid argon. The parameters aij and Sij, the effective diameter and the depth of the potential well between different atoms, can be calculated by using the combination rules since normally the effective diameter and the depth of the potential well are only available for the atoms of individual elements. The most frequently used combination rule is the Lorentz-Berthelot formula ... 

The fluids are modelled by a truncated and shifted Lennard-Jones (LI) pair potential [7], The potential parameters and eqiutions of state of the fluids are given in Table 1 with the parameters for carbon cross-interaction parametos are obtained by the Lorentz-Berthelot rules. The cut-off radius for simulations in the solid is 2.Sa, whilst that used in generating the single pore isotherms for determining the PSDs is Sag, inline uitfa standard procedure. 33. Simulation details... 

The idealized symmetric blend model is not representative of the behavior of most polymer alloys due to the artificial symmetries invoked. Predictions of spinodal phase boundaries of binary blends of conformationally and interaction potential asymmetric Gaussian thread chains have been worked out by Schwelzer within the R-MMSA and R-MPY/HTA closures and the compressibility route to the thermodynamics. Explicit analytic results can be derived for the species-dependent direct correlation functions > effective chi parameter, small-angle partial collective scattering functions, and spinodal temperature for arbitrary choices of the Yukawa tail potentials. Here we discuss only the spinodal boundary for the simplest Berthelot model of the Umm W t il potentials discussed in Section V. For simplicity, the A and B polymers are taken to have the same degree of polymerization N. 

When the nonbond interactions of a system that contains multiple particle types and multiple molecules are modeled using a Lennard-Jones type nonbond potential, it is necessary to be able to define the values of a and e that apply to the interaction between particles of type I and /. The parameters for these cross interactions are generally found using one of the two following mixing rules. One common mixing rule is the Lorentz-Berthelot rule where the value of o// is found from the arithmetic mean of the two pure values and the value of ej/ is the geometric mean of the two pure values ... 

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