has been reported for emulsion polymerization. The ... emulsion polymerization makes, generally speaking, ... withdrawn from the reactor using the experimental.
Copyright © IFAC Dynamics and Control of Process Systems, Corfu . Greece. 1998
ON-LINE CONTROL OF MOLECULAR WEIGHT DISTRIBUTION IN SEMIBA TCH EMULSION POL YMERIZA TION USING CT A
Antonio Echevarria, Jose R. Leiza, Jose C. de la Cal and Jose M. Asua
Crupo de Illgellieria Quimica, Depanamento de Quimica Aplicada, Facultad de Ciencias Quimicas, Universidad del Pais Vasco , Apdo. 1072, 20080 Sail Sebastian, Spain.
Abstract: Polystyrene latexes having a well defined molecular weight distribution (MWD) were prepared by means of an on-line control strategy that uses the measurements of both unreacted monomer and chain transfer agent (CT A) . Based on a mathematical model for the prediction of the MWD and an off-line optimization algorithm , optimal trajectories of styrene and CTA (CCI 4 in this work) as a function of conversion that ensure the production of polystyrene of the desired MWD were obtained. The control strategy used a non linear model based controller to calculate the feed flow rates of styrene and CCI 4 to track the optimal conversion based trajectories. The control strategy was first assessed by numerical simulation and then experimentally verified to produce polystyrene latexes of widely different MWDs. Copyright © 1998 IFAC. Keywords: On-line Control, Molecular Weight Distribution, Polymerization, Optimization, State Estimation, Model Based Control
Emulsion
lack of hardware sensors might be overcome by software sensors, namely by estimating the MWD from available on-line measurements of other variables. Although some success has been obtained in solution polymerization systems (10 and Bankoff, 1976; Schuler and Suzhen, 1985 ; Schuler and Papadopoulou, 1986; ElIis et al. 1988; Adebekun and Schork, 1989) the compartmenta1ized nature of emulsion polymerization makes, generally speaking, the MWD non-observable from usually available online measurements (monomers conversion and temperature) . Nevertheless, under some conditions of practical significance, the MWD of the emulsion polymer is not affected by the compartmentalization of the system. A typical example is when chain transfer agents (CT A) are used and hence the kinetic length of the growing chain is controlled by the chain transfer reaction to the CT A instead of by the bimolecular termination. This feature was utilized by Canu et al. (1994) to keep constant the MWD through the polymerization in an open-loop control scheme.
I . INTRODUCTION Many. applications of the polymer latexes, e.g. adheSIves, paper coating, paints, varnishes and carpet backing, require the formation of a continuous film with high mechanical strength. Both the film formation process and the mechanical properties of the film strongly depend on the molecular weight distribution of the polymer. Thus, latexes including a proper balance of high molecular weight polymer (which provides adhesive strength and high temperature cleavage) and low molecular weight polymer (which imparts legginess and compatibility) have been reported to be particularly useful for contact adhesives (Baus and Swift, 1985). Therefore, there is a strong incentive for the development of strategies for molecular weight distribution (MWD) control. On-line measurement of the MWD would be possible through the use of automated gel permeation chromatography (GPC), but although experimental setups capable to perform this task for solution polymerization have been reported (Ponnuswamy et al., 1988; Budde and Reichert, 1988; Ellis at al., 1988, 1994), to our knowledge not such application has been reported for emulsion polymerization . The
This work is an anempt to obtain emulsion polymers with well defined MWD by means of a control strategy based on on-line gas
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withdrawn from the reactor using the experimental setup developed by Leiza et al. (1993) and the unreacted monomer and CTA measured by on-line gas chromatography. In order to estimate the amounts of monomer and CTA in the polymer particles from these experimental results, a state estimation technique based on non linear optimization (Jang et aI., 1986) was used. This algorithm allows the estimated states
chromatographic measurements of the unreacted monomer and the chain transfer agent. Several MW Os were considered : i) Polymer with a given weight average molecular weight (Mw) and minimum polydispersity index (PI=2 , because chain growth is controlled by chain transfer reactions) ; ii) Polymer with arbitrary Mw and PI; and iii) Polymer with a given bimodal MWO.
of [M]p, [CCI4] p and n X
Np
to be calculated.
2. CONTROL STRATEGY The goal of this work is to obtain emulsion polymers with well defined MWO by means of a control strategy based on on-line measurements of the unreacted monomer and CT A. As pointed out above, the transfer reaction to CTA might control the kinetic length of the growing radical chain in emulsion polymerization processes. In such circumstances the ratio of the instantaneous weight and number average chain lengths, X wi / X ni, namely the polydispersity index, is equal to two and the instantaneous number average chain length is given by
Slln·lincar Mlld~1
Ba.wd
Cun'roll~r
StY"M
(I)
Fig. I. Control Scheme were kp and kr are the rate constant of the propagation and and transfer to CT A reactions, and [M]
These values are used to update the estimated states to compensate for the delay due to sampl ing, G .c. analysis and computer calculation. The updated values are compared with the set-point calculated by means of an off-line optimization and then a nonlinear model based controller was used to calculate the control actions for the next time interval.
p
[CCI4lp the concentration of mono mer and CTA in the polymer particles, respectively . Besides, the instantaneous molecular weight distribution can be calculated by using the Schulz-Flory distribution (Bilmeyer, 1962) which for X wi / X ni = 2 reduces to:
Wen) =
~
2.1 Optimization Algorithm
Xni
ex p(- n
Xm
J
(2)
The goal of the optimization algorithm is to calculate the set-point trajectories of the controlled variables that ensure the production of an emulsion polymer of the desired MWD in a minimum process-time. This optimization algorithm reduces to the minimization of the following objective function :
being n the chain length. The cumulative molecular weight distribution , W (n), can be calculated as c follows :
1 X Wc(n)=-X TW(n)dX T
i
(3)
T 0
(4) where X
is the monomer conversion. From the T combination of equations (I), (2) and (3), it can be concluded that the cumulative molecular weight distribution of a polymerization process, whose termination mechanism is mostly by chain transfer reaction to CTA, depends on the evolution of the monomer and chain transfer agent concentration ratio in the polymer particles. This feature was used in this work to attempt to control the molecular weight distribution of polystyrene latexes using carbon tetrachloride as chain transfer agent. Figure I summarizes the control scheme. Samples are
where Rp is the polymerization rate and X T the overall conversion defined as the ratio between the polymer in the reactor and the monomer in the recipe. The minimization of Eq. 4 must be subjected to the following constraints: i) The polymer produced must have the desired final MWD
(wg (n)).
It is convenient to reformulate
this constraint in terms of the instantaneous MWD that has to be produced at each value of XT.
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ii) The maximum amounts of monomer and chain transfer agent that can be in the reactor are the total amount in the recipe Mmax and CCI 4 m... iii) The monomer and CTA already charged into the reactor cannot be removed. The concentration of monomer in the latex particles should be equal or less than the concentration of saturation, namely monomer droplets are not allowed . The optimization provides the amounts of both monomer and CTA in the reactor at any Xr. This result is independent of the polymerization rate of the process and can be regarded as master curves.
The controller is based on the linealization of the material balances.
M." ,
CCI, •• , = cci,,,
+(F,n ,
-k
(7)
,[CCI,l ":: ]
