Molecular modeling unsolved problems

Theoretical considerations based upon a molecular approach to solvation are not yet very sophisticated. As in the case of ionic solvation, but even more markedly, the connection between properties of liquid mixtures and models on the level of molecular colculations is, despite all the progress made, an essentially unsolved problem. Even very crude approximative approaches utilizing for example the concept of pairwise additivity of intermolecular forces are not yet tractable, simply because extended potential hypersurfaces of dimeric molecular associations are lacking. A complete hypersurface describing the potential of two diatomics has already a dimensionality of six In this light, it is clear that advanced calculations are limited to very basic aspects of intermolecular interactions,... 

One can extend the picture to include a process composed of several unit operations, or even the whole factory. When the whole range of scales is included, the problem becomes one of describing the behavior of an entire plant starting from molecular principles. This problem is unsolved at the present time, but given the rapid advancements in modeling and simulation at each individual scale, and the growth in computational power, one can envision that the overall coupled problem will be solvable within the next few decades. 

While tremendous strides have been achieved during the past two decades, there are still a number of unsolved problems and emerging opportunities as noted in Table 17.7. Improved predictability will continue to be desired, and molecular modeling offers the longer range solution to this need. Improved compatibilization techniques to combine immiscible polymer pairs will allow for new and commercially important polymer blends, some of which have been highlighted in this section. 

It should be clear from the above that because of sustained efforts over many decades, significant progress has now been achieved in the understanding of the freezing of water into ice. However, there stiU remain many unsolved problems in this area. For example, we do not yet have a quantitative theory of the nucleation of ice in supercooled water. The molecular models we use in simulations are perhaps too primitive, as most of them do not include the polarizabihty of water molecules. The polarizability of water is large due to the two lone pairs of electrons on the lone oxygen atom. Perhaps one would need to consider quantum simulations to fully understand the freezing of ice. 

The aim of molecular spectrum analysis is to reduce the vibrations observed in the infra-red, visible and ultra-violet band spectrum as well as in the Raman spectrum to a definite model locating exactly the individual atomic centers of mass on the one hand, and specifying quantitatively the forces between the constituent atoms on the other. The former object is relatively easy to attain from data on inter-nuclear distances and valence angles, while the latter is a difficult problem as yet unsolved. In interpreting band spectra, we have assumed that, among all the atoms of a molecule, including even those not directly united, forces interact which depend only upon the distances separating the atoms. 

At present, the lack of any universal model allowing an exact evaluation of viscometric properties of pure liquids and liquid mixtures is mainly due to two unsolved questions 1) no comprehensive theory describing the interactions at the molecular level between similar and/or unlike species is known 2) deviations from ideality are not predicted neither in sign nor in intensity by the common thermodynamic liquid solution principles [14-19]. Both problems are unlikely to be solved in the very near future, even if there is much interaction information. 

The question about the conformations of main chains in many side-chain and main-chain LC polymers remains unsolved for various types of mesophases. Without a doubt, this problem is of prime importance for the consideration of an adequate model treating the packing of all structural elements of such LC polymers. This model is necessary for optimization of the molecular design and synthesis of LC polymers with desired optical and other physicochemical properties. 

Thus far we have only introduced the pure-fluid corresponding-states principle which, as mentioned above, has a rigorous basis in molecular theory. The extension of this theory to mixtures cannot, however, be made without further approximation and the problem of rigorous, yet tractable, prediction of mixture properties remains unsolved. These approximations take the form of mixing rules which are the topic of Chapter 5 in this volume. We will only discuss mixing rules from an illustrative basis to show problems that can arise in the implementation of a corresponding-states model. In that regard, we will focus our discussions on the one-fluid theories and primarily the van der Waals one-fluid theory proposed by Leland et The essence of this model... 

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