Computer-aided And Predictive Models For Design Of .

Computer-aided and predictive models for design ofcontrolled release of pesticidesNúria Muro Suñé and Rafiqul Gani*CAPECDanish Technical University, Søltofts Plads, 2800 Lyngby, DenmarkGordon Bell and Ian ShirleySYNGENTAJealotts Hill Research Station-BracknellBracknell, Berkshire RG42 6E4, UKAbstractIn the field of pesticide controlled release technology, a computer based model that canpredict the delivery of the Active Ingredient (AI) from fabricated units is important forpurposes of product design and marketing. A model for the release of an AI from amicrocapsule device is presented in this paper, together with a specific case studyapplication to highlight its scope and significance. The paper also addresses the need forpredictive models and proposes a computer aided modelling framework for achieving itthrough the development and introduction of reliable and predictive constitutive models.A group-contribution based model for one of the constitutive variables (AI solubility inpolymers) is presented together with examples of application and validation.Keywords: Controlled release, Microcapsule, Solubility prediction, Pesticide, Polymer1. IntroductionThere are many applications in agriculture, where protection from pests is required forextended periods of time. If control is required for periods of a year or more, then theconventional methods of delivering the pesticide compound (for instance, spraying asolution of the pesticide over the crop) may not be good enough because the pesticidemight not be delivered at the specific desired site and also because it does not last longenough to accomplish the protection of the crop. Considerable improvement can beachieved by using controlled release systems for the pesticide delivery to theenvironment. Through the sustained release of the pesticide from these devices, theamount of pesticide used, as well as, the number of times it needs to be applied on thecrop, is reduced. As the pesticide is usually encapsulated within a polymer membrane,there is also a reduction with respect to environmental hazards and human toxicity.A great number of models exist for describing the wide variety of controlled releasedevices available, due to the attention that the sustained delivery of drugs has receivedin the past years. Our purpose at this level is to try and apply these models into the field*Author to whom correspondence should be adressed : rag@kt.dtu.dk

of pesticide controlled release technology and to make them available through acomputer aided system. As the controlled release devices consist basically of a pesticide(AI) that is encapsulated or incorporated within a polymer membrane, the mostimportant properties in these models are the ones that relate to the pesticide and thepolymer. It is then appropriate to say that the solubility of the pesticide in the polymerand its diffusivity through the polymer membrane have a significant influence in therelease of a pesticide from a controlled release device. This is where the models forprediction of the solubility of pesticides in polymers become important.The main objective in this work is to make the current models predictive, flexible androbust so that they can be used to design and evaluate AI formulations and theirdelivery, rapidly and reliably. This implies being able to predict the properties that arecritical to the controlled release mechanism through specially developed predictiveproperty (constitutive) models. These property models when incorporated into thegeneric controlled release models will allow the study of the release of the pesticidemolecule through the polymer. Thus, these computer models would be a valuableaddition to the tools for both polymer and product design and analysis.2. Model for controlled releaseControlled release technology presents several advantages over the conventionalapplications of pesticides; they are illustrated in Figure 1. A comparison of the pesticideconcentration in the environment over time obtained from a conventional pesticideapplication ( ) with the concentration from a controlled delivery system ( -) ispresented in this figure. It can be observed that with a conventional application a veryhigh concentration is obtained initially, that can even be greater than the allowedtoxicity level. This concentration decreases fast and is soon below the minimumeffective level. On the other hand, the benefits of having a sustained pesticide deliveryare immediately observed in the other concentration plot ( -), due to the quickachievement of the desired concentration that is then maintained over time, this isobviously a more desirable scenario.OverdosingToxic concMin.eff.conc.Under dosingTimeFigure 1.Common pesticide application ( ) versus controlled release application ( -)

2.1 Model descriptionThe field of controlled release technology offers a wide variety of devices with a similarfinal effect, one of the most common types being the microcapsules. A microcapsule isa reservoir system where the AI is enclosed within a polymer membrane, as is shown inFigure 2. Several examples can be found in the market of microencapsulated pesticides(TopNotch, Fultime, etc.) with different properties and functionalities (Scher et al.,1998).MembraneCoreriReleasemediumCdroCrFigure 2. Microcapsule schematic representationThe process of AI release from a polymer can be described in most cases by Fickiandiffusion, with the appropriate initial and boundary conditions. In the present work, acomputer based model has been developed for the delivery of AI from microcapsuledevices. This model accounts for the number of microcapsules and their size differencesthrough a normal distribution function (Eq. 1). The controlled release is modelled withthe equations for non-constant activity source (Eqs. 2 and 3, Comyn, J., 1985), that arederived from Fick’s law of diffusion and provide the concentration dependence withtime.This model applies for systems where the AI is available in solution below thesolubility limit. In the microcapsules diffusion occurs through a thin film (of thicknessh), thus the equation of diffusion can be considered in one dimension only with respectto space.f (r; µ ;σ ) r dCd DA Km / ddtVb h (r µ ) 2 exp 2σ 2 2πσ (1) K m / r Vb DA Vd K m / r Vb K m / d Cd ,initial exp 1 t VbVd K m / d Vd h (2)1 DAK m / d K m / r Vb dCr DA K m / d Cd ,initial exp dtVb hVb h K m / d Vd t (3)

Equation 1 represents the normal distribution function that is applied to themicrocapsule radius (r) in order to get a representation of the various sizes ofmicrocapsules found in solution. This distribution is applied with a certain meandistribution value (µ) and a specific standard deviation (σ). Equation 2 represents therate at which the concentration changes with time (t) in the donor compartment (Cd,g/cm3), that is the “core”, as it is defined in Figure 2. This concentration is affected bytwo properties related to the AI and the polymer: the diffusion coefficient (D, cm2/s) ofthe AI within the polymer and the partition coefficients between the polymer membraneand the donor (Km/d) and the one between the release medium and the polymermembrane (Km/r). The geometric parameters of the microcapsule also have an effect onthe release; these are the surface area through which diffusion takes place (A, cm2), thevolume of the microcapsule or donor volume (Vd, cm3), and the thickness of themicrocapsule wall (h, cm). Finally, the initial concentration in the core (Cd,initial , g/ cm3)and the volume of the release medium, or bulk volume (Vb, cm3) are also present in theequation. In Eq. 3 the variation of the concentration in the receiver or release medium(Cr, g/cm3) is represented over time and having mainly the same variables present in Eq.2. In the total model, the radius distribution from Eq. 1 is used to calculate microcapsulevolume and surface areas that appear in Eqs. 2 and 3.2.2 Model solutionIn this section the model presented above is tested with some experimental data in orderto assess its performance and suitability. The case study is selected so that the values ofthe model parameters and known variables required for the model equation solution areavailable from experiment. Shao et al. (1993) have studied the release of a disperse dyesolution from a microcapsule. This microcapsule is prepared by complex coacervation(i.e., phase separation in colloidal systems) and the dye solution is encapsulated with agelatin and gum acacia membrane.0.180.160.140.12-ln ((Cr,f -Cr)DhKm/dKm/r0.1/(Cr,f -Cr,init)) 0.080.060.04Exp. data0.02Simulation resultsInput Data1.75e-14 m2/s27.2 µm110020406080100time (min)Figure 3. Comparison of model results with literature data (Shao et al. (1993)); whereCr,init is the concentration of the receiver at time zero (g/cm3) and Cr,f is theconcentration of the receiver at 24h (g/cm3).

The model equations (Eqs. 2 and 3) are solved by setting values for the diffusioncoefficient (D), the wall thickness (h) and the two partition coefficients (Km/d , Km/r)obtained from Shao et al. (1993). The available apparent diffusion coefficient includesthe partitioning effect, therefore in our simulations the partition coefficients have beenset to unity in order to avoid accounting for them more than once. The calculated valuesobtained from the simulation with the microcapsule release model are plotted togetherwith the experimental values from the literature in Figure 3. It can be observed that themodel reproduces the release of the dye solution from the microcapsules reasonablywell, even though the simulated values are somewhat lower than the experimental data.This small disagreement can be due to differences in the donor volume arising from thedistribution of microcapsules sizes, which affects the amounts of AI released.3. New developmentsAnalyzing the microcapsule model presented in the previous section we observe thatthere are two parameters that are critical for the applicability of the model to a widerange of microcapsules and pesticides. These two parameters are the partitioncoefficient (related to the solubility of the pesticide in the polymer) and the diffusioncoefficient. The first attempt, therefore, has been to select and implement a model forthe prediction of the thermodynamic partition coefficient (Kpol/c) through activitycoefficient calculations (Eq. 4). The challenge here is to use a simple model that ispredictive and can then be extended to handle a wide range of complex molecules. Theselected model is the “GC-Flory Equation of State” by Bogdanic et al. (1994), which isa simple activity coefficient model based on a group contribution approach, with anexisting parameter table that provides accurate and predictive results.K pol / c Ω cΩ pol(4)In order to illustrate the possibility of having a completely predictive model for thecontrolled release of pesticides, some preliminary calculations related to the predictionof the partition coefficient are presented. In Table 1 the experimental values of activitycoefficients at infinite dilution (Ω ) of two solutes in a polymer (Polystyrene, PS) arecompared with the ones calculated with the GC-Flory EoS. It can be noted that goodagreement has been obtained. After this initial test, the next validation test involved thecalculation of partition coefficients of complex molecules in selected polymers. Table 2highlights some of these results for three complex molecules (drugs are used aspesticide molecules being studied cannot be disclosed for reasons of confidentiality).These examples are selected so that the available parameter table of the GC-Flory EoSmodel can be used and the results compared with literature data (Pitt et al., 1988).Although there are some differences between the experimental and calculated valueswe have to keep in mind that this has been pure prediction, that is, without anyadjustment of parameters. We would like to note though, the qualitative goodness of theresults.