Ind. Eng. Chem. Res. 1996, 35, 627-634
627
CORRELATIONS Computer-Aided Synthesis of Polymers and Blends with Target Properties Ragavan Vaidyanathan† and Mahmoud El-Halwagi* Chemical Engineering Department, Auburn University, Auburn, Alabama 36849
Synthesis of polymers with desired properties is a challenging task which often involves considerable time and resources. Traditionally, polymer synthesis procedures have involved a trial and error approach where different candidate molecules were tested in the laboratory. This procedure is very expensive, is time-consuming, and is not guaranteed to culminate in the selection of the desired molecule. In this paper, a systematic method for the synthesis of polymer molecules with a desired set of properties is described. The problem of synthesizing the desired molecule is formulated as a mixed integer nonlinear program. The program has the potential of designing addition and condensation polymers that may be aliphatic or aromatic. The design procedure is also extended to the synthesis of polymer blends. The use of a global optimization technique to solve synthesis problems of reasonable dimensionality is discussed. Case studies are solved to illustrate the efficacy of the synthesis procedure. 1. Introduction In selecting a polymer for an engineering application, the product engineer has to consider several factors. These factors include polymer characteristics, cost, availability, and processability. For a given application, there are typically numerous potential candidates leading to a selection process that can be tedious and expensive. In order to assist the product engineer in recommending reasonable polymers, resin manufacturers and other organizations have introduced software containing data on numerous resins. For example, GE Plastics has developed a database to access the properties of GE resins over a wide range of conditions and is called the Engineering Design Database (Blackletter, 1988). DuPont introduced Polyfacts, a program to select among the plastics manufactured by their company (Blackletter, 1988). CAMPUS (Computer-Aided Material Preselection by Uniform Standards) is other software that can perform plastic selection (Mod. Plast., 1989). The main limitation of these and other commercial software packages is that they are only as rich as their databanks are. Another concern is that different resin manufacturers employ different testing procedures, making comparison of data inaccurate. While software utilizing databases can provide a quick means of comparing available resins, it cannot aid in the synthesis of new plastics that are not as yet commercially available. The need for a fundamental approach for the selection of materials, old or new, based on well established theory, is imminent. Molecular design is one such approach and should be adopted as a tool to perform preliminary material selection. This should then be followed up with a verification step by conducting experiments in the laboratory and/or using * To whom all correspondence should be addressed. Phone: (334)844-2064. FAX: (334)844-2063. E-mail: mahmoud@ eng.auburn.edu. † Current address: The M. W. Kellogg Company, Houston, TX.
0888-5885/96/2635-0627$12.00/0
published data. It is worth pointing out that molecular design techniques cannot distinguish among different grades of the same material and therefore are not an alternative to plastic selection software. Instead, the molecular design approach should be employed in selecting good initial molecules that can be easily tailored to meet the designer’s specifications. Molecular design for product synthesis is the inverse problem of predicting the properties of a chemical species given its structure. While the techniques for the prediction of properties are well developed (for example, the group contribution methods and the graph-theoretic approach for quantitative structure-property relationships), the work on molecular design is still incipient. Recently, there have been some attempts to develop computer-aided systematic tools for molecular design. These approaches can be classified into knowledgebased methods (Gani et al., 1991; Brignole et al., 1986; Eduardo et al., 1994), enumeration-based method employing mathematical tools (Joback and Stephanopoulos, 1989), mathematical optimization method (Machietto et al., 1990) and combinatorial optimization method (Venkatasubramanian et al., 1994). While all the methods have certain attractive features, they have one or more of the following drawbacks: (1) restriction to generate only certain types of structure (for example, only those structures that are terminated by univalent groups, which has the implication of overlooking some potential candidates for design); (2) possibility of generating structurally-infeasible molecules; (3) computational complexity for large problems which may render the design procedure impractical. In order to respond to the foregoing limitations, Vaidyanathan and ElHalwagi (1994a) developed a new mathematical optimization approach. In this approach, they have devised structural feasibility constraints based on their new classification of the UNIFAC groups. These constraints enable all types of structures to be considered for the design. Furthermore, this procedure guarantees the generation of structurally feasible molecules. The math© 1996 American Chemical Society
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Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996
ematical problem formulation was, however, restricted to the design of addition polymers only. In this paper, a general mathematical problem formulation for the design of both addition and condensation polymers is proposed in the form of an optimization program. Aromatic groups are also included in the design. This formulation is then extended to the design of polymer blends. The main limitation of the mathematical optimization approach is that the solution procedure may be trapped in suboptimal local points within the search space owing to nonconvexity. Therefore, we employ a global optimization algorithm based on interval analysis to solve problems of reasonable dimensionality and identify the global (best) solution. Several case studies are solved to illustrate the usefulness of the proposed approach.
Most polyamides and polyesters can be prepared from one of the following general reaction schemes (Allcock and Lampe, 1990): alcohol + acid
polyester O
O
HOROH + HOC
COH
R′
H
OROC
O
amine + acid
H
ORC
S(ni) e 0 (P1)
where ni is the number of times the ith group appears in the polymer, f(ni) is a performance criteria for the polymer, P(ni) is the vector of predicted properties for the polymer, Pl is the vector of lower bounds specified on the various polymer properties, Pu is the vector of upper bounds specified on the various polymer properties, S(ni) is the vector of structural feasibility constraints, and D(ni) is the vector of constraints imposed by the designer indicating his/her preferences on the polymer. The properties of the polymer are determined by the groups that occur in its repeating unit using the group contribution theory. The structural feasibility of the designed polymer can be ensured in most cases by choosing structurally feasible monomer(s) that react to form the polymer. While the groups that occur in the monomer are exactly the same as those in the repeating unit of an addition polymer, it is not so in the case of condensation polymers. During the formation of a condensation polymer, the monomer molecules react with the elimination of a molecule (usually water or HCl). The repeating unit of a condensation polymer is therefore quite different from the monomer(s) used. In the formulation, the prediction of properties will be based on the groups occurring in the repeating unit of the polymer while structural and thermodynamic feasibility constraints will be written for the monomer unit(s).
C
n
OH (1)
OH
(2)
OH
(3)
n
O
H2NRNH2 + HOC
–H2O
COH
R′ H N
R
H
O
N
C
O C
R′
O
Pl e P(ni) e Pu
R′
polyamide O
H
2.1. Condensation/Addition Polymer Design. A general problem formulation for the design of both addition and condensation polymers will be developed first. The molecular design problem can be stated as “given a desired range for a set of properties and performance criteria, design the polymer that performs best while possessing properties within the acceptable range”. The problem will be formulated as an optimization program whose objective is to optimize the performance of the polymer by maximizing or minimizing a certain performance function while satisfying constraints on properties and feasibility. Mathematically, the program takes the form of P1: Optimize f(ni) subject to the constraints,
O
O –H2O
HORCOH
2. Problem Formulation
D(ni) e 0
O –H2O
O –H2O
H2NRCOH ester + alcohol
n
H
NRC
n
OH
(4)
polyester O
HOROH + R′′OC
O R′
–R′′OH
COR′′
O H
OROC
acid chloride + amine O H2NRNH2 + ClC
O C
R′
n
OR′′
(5)
polyamide O
R′
–HCl
CCl H
H
N
R
H
O
N
C
O R′
C
n
Cl
(6)
Other condensation polymers like polyethers, polysulfones, polyacetals, and polyurethanes can be prepared from similar reaction schemes. Once a particular reaction scheme is chosen, the design task can be converted into the selection of groups that constitute R and R′ (whenever present). For example, if reaction scheme 3 is chosen, the design must determine R and R′ such that the structure H H
N
R
H
O
N
C
O R′
C
has the desired set of properties while the monomers
H2NRNH2 and O HOC
O R′
COH
are structurally and thermodynamically feasible. The following general form of reaction schemes 1-6 and other similar reaction schemes will be used to develop the optimization program:
S-R-T + U-R′-V f -[-X-R-Y-R′-Z-]-n (7) When this form is used to represent, for example, reaction scheme 2, then
S ≡ {HO-}, T ≡ {-COOH} U ≡ { }, R′ ≡ { }, V ≡ { } X ≡ {-O-}, Y ≡ {-C-}, Z ≡ { } It is to be noted that once a reaction scheme is chosen, the nature of the groups constituting S, T, U, V, X, Y,
Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996 629 Table 1. Classification of UNIFAC Groups Used To Develop the Structural Feasibility Constraints type class
1
1
-CH3, -CH2NH2, CH3CO-, -CONH2, -CONHCH3, -CON(CH3)2, -OH, -CHO, -COOH, -Cl, CH3COO-, -CH2CN, CH2Cl, -Cl, Br, -F, CH3O-, CH3S-, C6H5)CH2, )CHNH2, )CHCl, CH2)C), CH3N)
2 3
≡CH,≡CCl
4
>C
C)C
