A Cellular Automata Model of Water

STUDIES OF WATER AND SOLUTION PHENOMENA A Cellular Automata Model of Water... 

In a cellular automata model of a solution, there are three different types of cells with their states encoded. The first is the empty space or voids among the molecules. These are designated to have a state of zero hence, they perform no further action. The second type of cell is the water molecule. We have described the rules governing its action in the previous chapter. The third type of cell in the solution is the cell modeling a solute molecule. It must be identified with a state value separate from that of water. 

Figure 4.1. (a) A cellular automata model of hydrophilic solutes in water, (b) A cellular automata model of hydrophobic solutes in water... 

Figure 4.2. A cellular automata model of a crystal in water...

We have introduced the use of cellular automata modeling of water and possibly some other solvent, and have observed the influence of solutes on the emergence of properties in these complex systems. In this chapter we consider a few, more complex chemical systems that may lend themselves to cellular automata modeling. We will discuss several of these and then suggest some studies for the reader. 

The hydrophobic effect is a term describing the influence of relatively nonpolar (lipophilic) substances on the collective behavior of water molecules in their vicinity. The common expression is that water is more structured or organized when in contact with a lipophilic solute. This behavior was observed in a cellular automata model of a solute in water,42,43 which led to a study in more detail.44 The hydrophobic effect was modeled by systematically increasing the breaking probability, PB(WS), value, encoding an increasing probability of a solute molecule, S, not to associate with water. 

A further illustration of the decreasing hospitality of water and othei polar solvents for ionic species at higher temperatures has been presented in a cellular automata model of acid behavior reported by Kier et al. [546] This model, designed according to heurishc attributes of the acid-watei system, shows that increased temperature of the aqueous solvent alone leads to a decrease in the acid dissociation constant in the absence of any changes in the acid itself. 

Studies described in earlier chapters used cellular automata dynamics to model the hydrophobic effect and other solution phenomena such as dissolution, diffusion, micelle formation, and immiscible solvent demixing. In this section we describe several cellular automata models of the influence of the hydropathic state of a surface on water and on solute concentration in an aqueous solution. We first examine the effect of the surface hydropathic state on the accumulation of water near the surface. A second example models the effect of surface hydropathic state on the rate and accumulation of water flowing through a tube. A final example shows the effect of the surface on the concentration of solute molecules within an aqueous solution. 

A series of studies have been reported modeling the diffusion process in water.49 Using the rules previously defined, we examined several characteristics of a system to determine their influence on diffusion. The first study revealed that solutes of high lipophilicity (low polarity) diffuse faster than those of low lipophilicity (high polarity). This result is not commonly considered or reported. Diffusion studies are numerous in the literature, but comparisons with solute polarity are very scarce. Two such studies, however, support the cellular automata model of this phenomenon.50,51... 

A series of rules describing the breaking, / B,and joining, J, probabilities must be selected to operate the cellular automata model. The study of Kier was driven by the rules shown in Table 6.6, where Si and S2 are the two solutes, B, the stationary cells, and W, the solvent (water). The boundary cells, E, of the grid are parameterized to be noninteractive with the water and solutes, i.e., / b(WE) = F b(SE) = 1.0 and J(WE) = J(SE) = 0. The information about the gravity parameters is found in Chapter 2. The characteristics of Si, S2, and B relative to each other and to water, W, can be interpreted from the entries in Table 6.6. 

In this chapter we address several phenomena involving a solvent, principally water, and a stationary surface. These include various wetting and wall effects, chromatography, and membrane passage. Some of these phenomena have been modeled with cellular automata, and a brief description of those studies will be presented. Each of these examples opens up a wealth of possibilities for future work, and the reader is urged to pursue some studies that these may inspire. 

Using cellular automata we have an opportunity to model the flow of water from each compartment into the membrane, when a solute is present on one side of the membrane. By design, the membrane in our model is composed of 31% empty cells. At iteration zero, in our dynamics, the membrane contains no water. After several iterations, there will be flows of water from the two compartments into the membrane. If we monitor the early stages of this process, we may detect a possible preference for water to flow from one of the compartments. Such a condition would model the early stages of the osmotic effect. 

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