James M. Caruthers

Computer-aided molecular design using genetic algorithms

Abstract Designing new molecules possessing desired properties is an important activity in the chemical and pharmaceutical industries. Much of this design involves an elaborate and expensive trial-and-error process that is difficult to automate. The present study describes a new computer-aided molecular design approach using genetic algorithms. Unlike traditional search and optimization techniques, genetic algorithms perform a guided stochastic search where improved solutions are achieved by sampling areas of the parameter space that have a higher probability for good solutions. Moreover, genetic algorithms allow for the direct incorporation of higher level chemical knowledge and reasoning strategies to make the search more efficient. The utility of genetic algorithms for molecular design is demonstrated with some case studies in polymer design. The merits and potential deficiencies of this approach are also discussed.

Sulfur vulcanization of natural rubber for benzothiazole accelerated formulations: From reaction mechanisms to a rational kinetic model

Abstract The chemistry of accelerated sulfur vulcanization is reviewed and a fundamental kinetic model for the vulcanization process is developed. The vulcanization of natural rubber by the benzothiazolesulfenamide class of accelerators is studied, where 2-(morpholinothio) benzothiazole (MBS) has been chosen as the representative accelerator. The reaction mechanisms that have been proposed for the different steps in vulcanization chemistry are critically evaluated with the objective of developing a holistic description of the governing chemistry, where the mechanisms are consistent for all reaction steps in the vulcanization process. A fundamental kinetic model has been developed for accelerated sulfur vulcanization, using population balance methods that explicitly acknowledge the polysulfidic nature of the crosslinks and various reactive intermediates. The kinetic model can accurately describe the complete cure response including the scorch delay, curing and the reversion for a wide range of compositions...

A hybrid genetic algorithm for efficient parameter estimation of large kinetic models

Abstract The development of predictive models is a time consuming, knowledge intensive, iterative process where an approximate model is proposed to explain experimental data, the model parameters that best fit the data are determined and the model is subsequently refined to improve its predictive capabilities. Ascertaining the validity of the proposed model is based upon how thoroughly the parameter search has been conducted in the allowable range. The determination of the optimal model parameters is complicated by the complexity/non-linearity of the model, potentially large number of equations and parameters, poor quality of the data, and lack of tight bounds for the parameter ranges. In this paper, we will critically evaluate a hybrid search procedure that employs a genetic algorithm for identifying promising regions of the solution space followed by the use of an optimizer to search locally in the identified regions. It has been found that this procedure is capable of identifying solutions that are essentially equivalent to the global optimum reported by a state-of-the-art global optimizer but much faster. A 13 parameter model that results in 60 differential-algebraic equations for propane aromatization on a zeolite catalyst is proposed as a more challenging test case to validate this algorithm. This hybrid technique has been able to locate multiple solutions that are nearly as good with respect to the “sum of squares” error criterion, but imply significantly different physical situations.

Thermodynamic constitutive equations for materials with memory on a material time scale

We present a complete, self‐consistent set of thermodynamic constitutive equations for viscoelastic solid and fluid materials which can be applied during arbitrary, three‐dimensional deformations and thermal processes. Deformational and thermal histories are measured using a fading memory norm in a material time which provides a quantitative indication of the constitutive models’ ability to represent the dynamic response. The free energy constitutive equation is a Frechet expansion about the deformation and temperature histories of arbitrarily large but sufficiently slow departures from equilibrium in material time. The kinetic relationship between the laboratory and material time scales does not depend on equilibrium considerations. This approach greatly extends the applicability of low‐order memory expansions to nonequilibrium polymer states. Constitutive equations for stress, internal energy, entropy, enthalpy, and heat capacity are derived. All the required material properties can be evaluated unambig...

Preparation and characterization of monodisperse polymer microspheroids

Abstract An original scheme for producing monodisperse polymer microspheroids of precise size and shape was developed. Graft-copolymer-stabilized poly(methyl methacrylate) (PMMA) microspheres with diameters of 0.5 to 1.4 μm were prepared by dispersion polymerization. The microspheres were embedded in a matrix of poly(dimethylsiloxane) (PDMS) normally containing 1 to 10% PMMA particles. The matrix was subsequently crosslinked. The composite elastic material was deformed under uniaxial extension, at a temperature well above the glass transition temperature Tg of the particles, to produce prolate microspheroids with aspect ratios up to 8. The microspheroids were physically set by cooling below Tg and were then recovered after selective chemical degradation of the PDMS matrix. The particles were characterized by scanning electron microscopy and by a previously developed method of transmission electron microscopy with metallic double shadow casting (Keville et al., J. Microsc. 142, 327 (1986)). Deviations in the dimensions and aspect ratios were typically less than 5%. Uniaxial deformation of properly synthesized materials produced a smooth prolate shape when the particles were less stiff than the matrix, even when they were uncrosslinked. Stable dispersions of spheroids were prepared in alkanes and PDMS. These novel dispersions of model particles are well suited for elucidating the effects of shape and orientation on various properties of colloidal dispersions.

Catalyst design: knowledge extraction from high-throughput experimentation

We present a new framework for catalyst design that integrates computer-aided extraction of knowledge with high-throughput experimentation (HTE) and expert knowledge to realize the full benefit of HTE. We describe the current state of HTE and illustrate its speed and accuracy using an FTIR imaging system for oxidation of CO over metals. However, data is just information and not knowledge. In order to more effectively extract knowledge from HTE data, we propose a framework that, through advanced models and novel software architectures, strives to approximate the thought processes of the human expert. In the forward model the underlying chemistry is described as rules and the data or predictions as features. We discuss how our modeling framework—via a knowledge extraction (KE) engine— transparently maps rules-to-equations-to-parameters-to-features as part of the forward model. We show that our KE engine is capable of robust, automated model refinement, when modeled features do not match the experimental features. Further, when multiple models exist that can describe experimental data, new sets of HTE can be suggested. Thus, the KE engine improves (i) selection of chemistry rules and (ii) the completeness of the HTE data set as the model and data converge. We demonstrate the validity of the KE engine and model refinement capabilities using the production of aromatics from propane on H-ZSM-5. We also discuss how the framework applies to the inverse model, in order to meet the design challenge of predicting catalyst compositions for desired performance.  2003 Elsevier Science (USA). All rights reserved.

High fidelity mathematical model building with experimental data: A Bayesian approach

Abstract Mathematical models of physicochemical systems are usually built in an iterative fashion during the course of an experimental investigation. In this paper, a novel Bayesian approach to model building is presented. This approach is now feasible because of breakthroughs in Monte Carlo sampling procedures and high performance computing, that make it possible to deal directly with the nonlinear mathematical models themselves instead of their linear approximations. By including an error model for experimental data, it is further possible to use nonlinear statistical concepts to test a given model for adequacy against experimental data and prior knowledge, and to place realistic confidence limits on the resulting model parameters. In this paper a model building work flow that takes advantage of these recent advances to enable high fidelity mathematical modeling is proposed. A set of models and their parameters are needed to initiate the process. Probability distributions for the models and their parameters based on available quantitative and subjective information must also be supplied. Finally, an error model describing the heteroscedasticity in the data along with probability distributions for the error model parameters must be generated from exploratory data. Then experiments are designed and data collected. Using Bayes’ theorem, Monte Carlo (MC) or Markov Chain Monte Carlo (MCMC) methods are used to generate a sequence of samples of parameter values for each postulated model. These sets of samples are then used to discriminate among the models using the criteria introduced in this paper. Once discrimination is achieved, a global lack of fit test is introduced to determine model adequacy. After a single adequate model is selected, highest probability density (HPD) intervals are determined for the individual parameters and HPD density regions are constructed for all model parameter pairs. Experiments are then designed to reduce the uncertainty in the joint posterior probability HPD regions. Finally, a sampling procedure is described to properly represent uncertainties in predictions made from the model. The proposed approach is demonstrated by an illustrative problem where three simple models are discriminated and the parameters in the most suitable ones are estimated rigorously.

Mechanistic Detail Revealed via Comprehensive Kinetic Modeling of [rac-C2H4(1-indenyl)2ZrMe2]-Catalyzed 1-Hexene Polymerization

Thorough kinetic characterization of single-site olefin polymerization catalysis requires comprehensive, quantitative kinetic modeling of a rich multiresponse data set that includes monomer consumption, molecular weight distributions (MWDs), end group analysis, etc. at various conditions. Herein we report the results obtained via a comprehensive, quantitative kinetic modeling of all chemical species in the batch polymerization of 1-hexene by rac-C(2)H(4)(1-Ind)(2)ZrMe(2) activated with B(C(6)F(5))(3). While extensive studies have been published on this catalyst system, the previously acknowledged kinetic mechanism is unable to predict the MWD. We now show it is possible to predict the entire multiresponse data set (including the MWDs) using a kinetic model featuring a catalytic event that renders 43% of the catalyst inactive for the duration of the polymerization. This finding has significant implications regarding the behavior of the catalyst and the polymer produced and is potentially relevant to other single-site polymerization catalysts, where it would have been undetected as a result of incomplete kinetic modeling. In addition, comprehensive kinetic modeling of multiresponse data yields robust values of rate constants (uncertainties of less than 16% for this catalyst) for future use in developing predictive structure-activity relationships.

Experimental verification of a predictive model of penetrant transport in glassy polymers

Abstract The validity of the Lustig et al . ( Chem. Engng Sci. 47 , 3037–3057, 1992) model for penetrant transport in glassy polymers was investigated by comparing experimental results of dodecane transport in crosslinked polystyrene samples with the model. All parameters of the model were measured independently. The time-dependent concentration profiles at the dodecane/polystyrene interface were predicted at various temperatures. The time-dependent concentration and the polymer stress profiles within the dodecane/polystyrene system indicate a wide range of transport mechanisms at different temperatures. The dodecane transport kinetics was affected by dodecane diffusion coefficient, the discrete viscoelastic relaxation time and the modulus of the dodecane/polystyrene system. The significance of the viscoelastic relaxation contribution on the overall penetrant transport was evaluated by analyzing the temperature dependence of the diffusional exponent, n , of a simple exponential dependence of the dodecane uptake as a function of transport time. The diffusional exponent and the resulting penetrant transport kinetics were correlated to the mean diffusion Deborah number. In general, the transport process was closely characterized as Fickian diffusion far above or far below the glass transition temperature of the system and as anomalous transport close to the glassy/rubbery transition

Effects of Pendant Ligand Binding Affinity on Chain Transfer for 1-Hexene Polymerization Catalyzed by Single-Site Zirconium Amine Bis-Phenolate Complexes

The kinetics of 1-hexene polymerization using a family of five zirconium amine bis-phenolate catalysts, Zr[tBu-ON(X)O]Bn2 (where X = THF (1), pyridine (2), NMe2 (3), furan (4), and SMe (5)), has been investigated to uncover the mechanistic effect of varying the pendant ligand X. A model-based approach using a diverse set of data including monomer consumption, evolution of molecular weight, and end-group analysis was employed to determine each of the reaction specific rate constants involved in a given polymerization process. The mechanism of polymerization for 1-5 was similar and the necessary elementary reaction steps included initiation, normal propagation, misinsertion, recovery from misinsertion, and chain transfer. The latter reaction, chain transfer, featured monomer independent β-H elimination in 1-3 and monomer dependent β-H transfer in 4 and 5. Of all the rate constants, those for chain transfer showed the most variation, spanning 2 orders of magnitude (ca. (0.1-10) × 10(-3) s(-1) for vinylidene and (0.5-87) × 10(-4) s(-1) for vinylene). A quantitative structure-activity relationship was uncovered between the logarithm of the chain transfer rate constants and the Zr-X bond distance for catalysts 1-3. However, this trend is broken once the Zr-X bond distance elongates further, as is the case for catalysts 4 and 5, which operate primarily through a different mechanistic pathway. These findings underscore the importance of comprehensive kinetic modeling using a diverse set of multiresponse data, enabling the determination of robust kinetic constants and reaction mechanisms of catalytic olefin polymerization as part of the development of structure-activity relationships.