Property constraints

Many physical and process constraints limit the cycle time, where cycle time was defined as the time to the maximum exotherm temperature. The obvious solution was to wind and heat the mold as fast and as hot as possible and to use the polymer formulation that cures most rapidly. Process constraints resulted in a maximum wind time of 3.8 minutes where wind time was defined as the time to wind the part plus the delay before the press. Process experiments revealed that inferior parts were produced if the part gelled before being pressed. Early gelation plus the 3.8 minute wind time constrained the maximum mold temperature. The last constraint was based upon reaction wave polymerization theory where part stress during the cure is minimized if the reaction waves are symmetric or in this case intersect in the center of the part (8). The epoxide to amine formulation was based upon satisfying physical properties constraints. This formulation was an molar equivalent amine to epoxide (A/E) ratio of 1.05. 

Klein, J. A., Wu, D. T. Gani, R. (1992) Computer aided mixture design with specified property constraints, Computers and Chemical Engineering, 16, S229. 

The basic GC-model of the Constantinou and Gani method (Eq. 1) as presented above provides the basis for the formulation of the solvent replacement problem as a MILP-optimization problem. For purposes of simplicity, in this chapter, only the first-order approximation is taken into consideration (that is, W is equal to zero). In this way, the functions of the target properties of the generated molecules (solvent replacements) are written as monotonic functions of the property values, thereby, leading to a linear right hand side of the property constraints (property model equation), as follows,... 

The above conditions limit the search space by removing candidates that are most likely not to satisfy the property constraints. 

This sub-problem considers the pure component properties. This sub-problem is also a function of binary variables alone (because these constraints only handle primary structure based properties). The feasible molecular structures from Subproblem 1 are solved for the pure component properties. Those molecules, which satisfy the pure component property constraints, are then passed into subproblem 3. 

This sub-problem considers the mixture properties. Mixture properties can be categorized into two types. Properties such as selectivity, solvent power etc., are based on infinite dilution activity coefficients, which are independent of composition and hence only structural information is needed for their calculation. Properties such as complete or partial miscibility of solvent with another constituent is handled by discritizing the composition range from 0 to 1 into n divisions and verifying the miscibility criterion at those points. The difference between pure component property constraints and mixture property constraints is that the former are linear and the latter are non-linear. Those satisfying the mixture property constraints are further analyzed in sub-problem 4. 

Sub-problem 2M considers the pure component property constraints where the compounds from sub-problem 1M are evaluated for the pure component properties. All the molecules satisfying these constraints are passed onto subproblem 3m... 

Sub-problem 3M considers the mixture property constraints. The molecules from sub-problem 2M are considered in this sub-problem. The starting point is a list of promising solvents. From this list of solvents, the optimal mixture and the compositions of the constituents are identified by solving sub-problem 4M and sub-problem 5M. Since the first three sub-problems in the mixture design involves designing pure component solvents, these sub-problems are essentially the same as the first three sub-problems in single compound design. 

Molecules that satisfy pure property constraints... 

This CAMD single compound problem is formulated as an MINLP model as shown below. The performance objective function and the various property constraints in the model are discussed subsequently. 

Since we do not have any mixture property constraints related to single compound design this sub-problem was ignored. 

If all candidates are rejected, an analysis of the constraints must be done. Constraints may be too tight or in conflict with one another. Constraints which are too tight can be easily identified by examining the result of applying the individual constraint. Conflicting physical property constraints can be difficult to identify because of the interrelationships between physical properties. A standard technique in statistical analysis to find such interrelationships is to create plots of all pairs of variables. 

The tester module checks each candidate molecule for satisfaction of the design constraints. Three types of constraints are used (a) physical property constraints, (b) structural constraints, and (c) chemical constraints. 

The next step of the search algorithm is to reduce the level of abstraction. Groups were abstracted into metagroups to reduce the combinatorics of the problem. However, this same abstraction reduced the effectiveness of property constraints. As the abstraction is reduced, this effectiveness is regained. Metagroup 1 is divided into two new metagroups ... 

T, is estimated for each meta-molecule and the property constraint is applied. Table IX shows estimated T, values for the 13 metamolecules. 

Applying the property constraint prunes metamolecules [(2 0) 0 0 0] [(1 1) 0 0 0] and [(2 0) 1 0 0]. Additionally, the estimate of T, for metamolecule (0 3 0 1 0) shows that all the molecules it contains have T, values that satisfy the property constraint. None of the metamolecules resulting from further expansion of metamolecule [(0 3) 0 1 0] need to be checked. 

Two approaches can be used to add back detail expansion and division. Expansion adds back knowledge about the metagroups, which is used by the structural constraints. Division focuses on reducing the width of metacontributions, thus improving the screening power of physical property constraints. 

The permeability of the polymer to oxygen should be <1.0 cm -mil 100 in. day atm . Diffusion of oxygen and water through the polymer to the microelectronic circuitry could cause corrosion and is thus undesirable. To establish a value for this physical property constraint, we examined polymers used as barriers. Polymers with a permeability to oxygen of <1.0 cm -mil 100 in. day atm are considered high-barrier materials. 

The following heuristics on group selection are often helpful in selecting groups that satisfy the physical property constraints and are structurally feasible. 

The dimension of the design space is equal to the number of fundamental physical properties needed to evaluate the property constraints. Using... 

Other groups to yield a feasible molecule. Figure 2b, on the other hand, shows how interactive design can be employed to tighten the specifications of a physical property constraint (e.g., by moving the location of a constraint see dashed-line constraint), requiring the evolution of the initial molecule to a new one (satisfying the new set of constraints). 

To design in a 2D space, the factor relationships shown in Table XVI are used to reduce the fundamental properties to the factors F, and Fj. Each physical property constraint, which is a function of F, and F3, is plotted in a 2D Fj-Fj design space shown in Fig. 3. The region in which all constraints are satisfied is shaded. The displayed symbols correspond to the constraints as follows ... 

The problem formulation section provides an interface with which the designer can enter physical property constraints. The system displays the properties stored in its database (currently about 40 properties are present) and provides a simple constraint editor for entering and modifying physical property constraints. 

Once physical property constraints are entered in the problem formulation section, it is necessary to instruct the system how to estimate the properties contained in these constraints. This involves the creation of estimation procedures for each physical property used in the design constraints. The target transformation section provides facilities for collecting estimation techniques into estimation procedures. The chosen... 

Gani, R., and Fredenslund, Aa., Computer-aided molecular and mixture design with specific property constraints. Fluid Phase Equilib. 82, (1993). 

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