# Knowledge-based control of emulsion polymerization: tailoring adhesive properties.

An on-line control strategy to produce copolymer latexes with
desired adhesive properties (resistance to shear and resistance to peel)
has been developed. The strategy required a quantitative model relating
adhesive properties and molecular weight distribution that was built
using partial least squares regression. The model was used to determine
the set-point trajectories of the monomers and chain transfer agent that
are used as manipulated variables in the control strategy. The control
strategy was experimentally verified to produce an n-butyl
acrylate/styrene copolymer latex with a resistance to shear of 1310 s
and resistance to peel of 3.1 N/100 mm.

Keywords: Gel permeation chromatography, acrylics, latexes, colloids, emulsions, process control

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A good control strategy for emulsion polymerization reactions must assure that a product with the desired final properties will be obtained. Unfortunately, most of the control strategies developed until now only allow for the control of the molecular properties of the polymer by manipulation of several process variables, (1-7) without including the final properties of the product in the control strategy.

Historically, end-use and molecular properties of the product have been related using trial and error procedures, which are in most cases, highly time-consuming. This work is an attempt to relate those properties in a quantitative and reliable way and to include such a relationship in a control strategy in order to directly provide a product with the desired end-use properties.

An important application of acrylic latexes is as pressure sensitive adhesives (PSAs), mainly used for labels, tapes, decorative films, protective materials, and wall and floor coverings. Each specific application requires appropriate end-use properties, characterized by a combination of specific values of adhesive properties such as tackiness, resistance to peel, and resistance to shear.

It has been proved that several molecular properties of a latex, such as copolymer composition, average molecular weight and molecular weight distribution, level of branching, content of gel, and crosslinking, strongly affect the values of the adhesive properties. (8-13)

The glass transition temperature ([T.sub.g]) of the copolymer, which depends on the copolymer composition, determines to a very large extent the tackiness of the final product. (8) The adhesive performance is also affected by the composition profile. (9) Dale et al. (10) reported on the effect of crosslinking on the properties of acrylic adhesives, concluding that the crosslinking density should be low for a PSA, because a high degree of crosslinking, which severely affects tack and peel adhesion, may yield to a nontacky product. The gel content also affects the mechanical properties of the final product. (11-13) Generally, the presence of gel increases the resistance to peel and the resistance to shear and decreases the tack, although above certain levels of gel, resistance to both shear and peel dramatically decreased. (12, 13)

Resistance to shear and to peel depend also on the molecular weight of the polymer. (14, 15) Although there are some qualitative studies on the effect of the average molecular weight (MW), the effect of the whole molecular weight distribution (MWD) is more elusive, and therefore, has not been very widely studied. Good tack values are observed for low MW polymers and the tackiness decreases when the MW is raised. With resistance to shear, the behavior is exactly the opposite. Good resistance to shear is obtained with high MW polymers and the value decreases rapidly for lower MWs. High values of resistance to peel are provided by the intermediate MWs, but the value decreases for both high and low MWs. As previously mentioned, each application requires a specific combination of the adhesive properties and this can be achieved by a proper balance of high and low MW polymers, namely, by an appropriate shape of the MWD.

Therefore, to produce a latex with some desired end-use properties, an understanding and quantification of the effect of the molecular properties on the end-use properties is an essential step. In the next section, a qualitative study of the effect of gel content and MWD on the adhesive properties is presented. Thereafter the effect of the MWD of linear polymers on adhesive properties is addressed. In the third section the control strategy developed for controlling resistance to both shear and peel of linear polymer latexes is explained, and the methodology is validated experimentally. This is followed by a study of the effect of several variables on the calculation of the optimal MWD (the MWD that will give the desired adhesive properties) and an analysis of the limitations of the control strategy. The article concludes with final remarks and future perspectives.

EFFECT OF GEL CONTENT AND MWD ON ADHESIVE PROPERTIES

Table 1 presents the effect of the gel content and sol MWD on the adhesive properties of n-butyl acrylate/styrene (n-BA/S) and n-BA latexes. It can be seen that resistance to shear and resistance to peel are particularly affected by the fraction of gel and the soluble [bar.M.sub.w]. When a latex is employed as a PSA, the influence of gel content and [bar.M.sub.w] cannot be underestimated and must be taken into account to obtain the desired product. Both resistance to shear and resistance to peel present a maximum for a fraction of gel of about 32%. The gel, which decreases the free movement of the polymer molecules, provides better cohesion, improving the mechanical properties of the polymer film. However, if the gel fraction increases over a given value, the network becomes so rigid that it limits the particle coalescence during film formation. As a consequence, resistance to shear decreases to values similar to the latexes without any gel, whereas resistance to peel decreases until an intermediate value.

Although Satas (14, 15) studied the effect of the [bar.M.sub.w] on the adhesive properties, for the purpose of controlling the final adhesive properties, it is much more useful to understand the effect of the complete MWD, even if it is much more difficult to capture.

To study the effect of the whole MWD, several n-BA/S latexes with a fixed molar composition of 85/15 and varying MWDs were prepared (see the Appendix for experimental details). This relatively high content of styrene avoids chain transfer to the polymer, and therefore, mostly linear polymers were obtained. (12) This helps to isolate the effect of the MWD on the adhesive performance of the latexes. The desired MWDs were obtained by using an on-line control strategy based on reaction calorimetry. (4, 5)

The characteristics of some of the latexes used in the study and their adhesive properties are presented in Table 2. Figure 1 contains the MWDs of the four latexes employed in this study. It was observed that, in general, broad unimodal latexes had slightly better adhesive properties than bimodal latexes of similar [bar.M.sub.w] (e.g., compare B and C latexes in Table 2). When [bar.M.sub.w] was increased (latex D), the resistance to shear also increased, as mentioned in the literature. (14, 15) An opposite trend was observed for resistance to peel, as can be deduced from Table 2. As a general rule, it can be said that by broadening the MWD, it is possible to produce a more balanced adhesive that can be used in different applications. Unfortunately this general rule gives only a qualitative idea of the MWD that should be produced for each application.

Another aspect that should be considered is the optimal way to produce a latex with the desired MWD, once the shape of the optimal MWD (the one that will give the desired adhesive performance) is known. A previous paper (17) included a comparison between the adhesive performance of latexes with similar bimodal MWDs prepared by blending unimodal latexes or by producing the bimodal MWD in-situ during a controlled experiment, the so-called in-reaction method. It was concluded that the in-reaction bimodal latex, prepared using the previously mentioned online control strategy, (4, 5) presented better adhesive properties than the bimodal MWD latex prepared by blending two unimodal MWD latexes. Therefore all the latexes used in this work were prepared by using the on-line control strategy that allows the in-reaction production of the desired MWD, and also the control of copolymer composition.

From this study we can conclude that there is not a perfect adhesive, and that the desired properties depend on the specific application. A good control of polymer microstructure helps to improve the adhesive performance of the latex, but it does not assure that the desired properties will be obtained. This leads to the need for adding a further step: to relate quantitatively polymer and end-use properties and implement this relationship in the optimization and control of the desired adhesive performance. This is explained in detail in the following section.

MWD-ADHESIVE PROPERTIES QUANTITATIVE RELATIONSHIP: PLS-R

All the works previously mentioned considered the relationship between molecular and final properties in a qualitative way. This study is necessary as a preliminary step to understand the effect of several properties, but it is not enough to develop a control strategy for the final properties of the latex.

By applying partial least squares regression (PLS-R) (18, 19) to a set of 13 calibration samples of n-BA/S of fixed molar composition (85/15) and very different MWDs, a quantitative relationship between the adhesive properties (resistance to peel and resistance to shear) and the MWD was established. (17) As a result, a model with one principal component (PC) was built and experimentally validated. The model gave satisfactory results for predicting resistance to shear and resistance to peel values of different latexes knowing their complete MWD. According to the model, shear had large and positive values on the first and unique PC, and peel had large but negative values. Therefore, resistance to shear and to peel were related in an inverse way by the model. It related intermediate MW values to high peel values and high MW values to high shear values.

CONTROL STRATEGY FOR THE ADHESIVE PROPERTIES

With the previously developed calibration model, (17) adhesive properties of a given latex can be predicted if the MWD is known, but the model cannot be directly used to achieve the control of the adhesive properties. To do so, the MWD required to obtain some desired adhesive properties must be calculated first. In this section the procedure developed to solve this problem is explained.

[FIGURE 1 OMITTED]

Once the optimal MWD that ensures the production of latex with the desired properties is known, this can be synthesized employing the on-line control strategy developed by Vicente et al. (4, 5) In this strategy the optimal trajectories of monomers and chain transfer agent (CTA) that allow the production of a given MWD and copolymer composition are first determined. Then, these trajectories are tracked by on-line monitoring the heat of reaction (20, 21) and using a nonlinear model based controller to fulfill the target trajectories.

If the whole procedure is analyzed globally--the calculation of the optimal MWD and the control strategy employed to produce that MWD--we reach a control scheme that allows the direct control of the adhesive properties (resistance to shear and resistance to peel) by the manipulation of process variables (feed rates of monomers and CTA).

MWD Required to Obtain the Desired Adhesive Properties

The calibration model described above is useful to predict the adhesive properties of different latexes from MWD measurements, but it cannot be directly used for control purposes. In practice, only the desired adhesive properties of the latex will be known, and the MWD that will give those properties must be calculated in order to produce it experimentally and obtain the desired final product. However, for this objective, the inversion of the calibration model is not possible because it is ill-conditioned.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The solution to this problem was found using an optimization algorithm that calculates the MWD that minimizes the following objective function:

[J.[(MWD)]] = [2.summation over (i=1)][[alpha].sub.i](([y.sub.i.sup.d] - [y.sub.i.sup.pred])/[y.sub.i.sup.d])[.sup.2] i = 1(Shear),2(Peel) (1)

where [y.sub.i.sup.d] are the desired adhesive properties, [y.sub.i.sup.pred] the predictions of the model and [[alpha].sub.i] the weighing factors chosen to compensate for the different absolute values of the shear and peel measurements. The MWD was assumed to be composed of m Schultz-Flory distributions of equal mass and having a polydispersity index equal to 2.

X(n) = [m.summation over (i=1)] [n/[bar.X.sub.nk.sup.2]]exp(-[n/[bar.X.sub.nk]])[1/m] (2)

where X(n) is the weight fraction of polymer chains of length n. In order to apply the X(n) values of equation (2) in the quantitative relationship between MWD and adhesive properties to calculate [y.sub.i.sup.pred], they first must be transformed to a gel permeation chromatography (GPC) distribution, because the quantitative relationship was built using GPC data for the MWD.

[FIGURE 4 OMITTED]

The optimization reduces to determining the m values of [bar.X.sub.nk] that minimize equation (1). This was carried out by means of a Nelder and Mead algorithm using the DBCPOL routine of the IMSL library.

EFFECT OF THE INITIAL MWD GUESS: In the Nelder and Mead algorithm, an initial guess for the MWD (what we wish to optimize) is required. Using previously acquired qualitative knowledge on the MWD-adhesive performance relationship, it is possible to have a rough idea of a possible initial MWD, but this is not straightforward in all cases. In addition, in order to develop a robust optimization process, one must make sure that different initial guesses will lead to the same final result, namely that a global optimum is obtained.

To assess the robustness of the optimization, the MWDs given in Figure 2 were used as initial guesses in an attempt to obtain a resistance to shear of 1310 s and a resistance to peel of 3.1 N/100 mm. The first initial guess was a bimodal MWD, with two peaks of polydispersity 3 for each of them; the low molecular weight peak had 10% of the total polymer, and the high molecular weight one had the other 90% of the polymer. The second guess was a monomodal one, of rather low molecular weight with a polydispersity of 3.

Figure 3 shows the optimal MWDs obtained with the two initial guesses and Table 3 the values of the adhesive properties predicted for them. Both optimizations gave almost the same MWD, as well as the same resistance to shear and peel values. This proves that the procedure is robust, and that a change in the initial guess does not affect the final result. This is also very helpful when a user with no or limited knowledge on the subject uses the optimization program, because even if the initial guess is poor, the optimal MWD will be achieved.

EFFECT OF THE NUMBER OF SHULTZ-FLORY DISTRIBUTIONS: Another parameter that should be chosen during the optimization is the number of Shultz-Flory (S-F) distributions for which the MWD is decomposed. The larger this number is, the better the MWD is described, but a larger number of parameters should be estimated. The effect of the number of S-F distributions used to decompose the desired distribution was checked by performing three optimizations, using the same initial guess, and an increasing number of S-F distributions (20, 50 and 100). As in the previous section, a latex with a resistance to shear of 1310 s and a resistance to peel of 3.1 N/100 mm was sought.

Figure 4 presents the resultant MWDs for the three cases. It can be seen that the optimization result is not sensitive to changes in the number of Shultz-Flory distributions and that in all the cases very similar results were obtained, with no differences on the predicted adhesive properties. Therefore, 20 S-F distributions were used in this work to calculate the optimum MWD for a given desired resistance to shear and resistance to peel.

[FIGURE 5 OMITTED]

Practical Limitations of MWD Control Strategies Using Chain Transfer Agents

In a free-radical polymerization, the instantaneous number average molecular weight of linear polymers is given by the ratio between propagation ([R.sub.p]) and termination rates ([R.sub.t]) (23):

[bar.X.sub.n] = [R.sub.p]/[R.sub.t] (3)

For a "zero-one" system, the termination rate is:

[R.sub.t] = ([k.sub.tr,CTA] [CTA][.sub.p] + [k.sub.tr,M][M][.sub.p] + [k.sub.a][R][.sub.w]) * [[bar.n][N.sub.p]]/[N.sub.A] (4)

where the first term of the right side takes into account the termination by chain transfer to CTA, the second the termination by chain transfer to monomer, and the last one the instantaneous bimolecular termination with radicals entering the particle from the aqueous phase. In equation (4), [k.sub.tr,CTA] and [k.sub.tr,M] are the chain transfer rate constants to CTA and monomer, respectively; [CTA][.sub.p] is the concentration of the chain transfer agent in the polymer particles; [k.sub.a] is the rate coefficient for radical entry into the particles; and [R][.sub.w] the radical concentration in the aqueous phase.

If a chain transfer agent is going to be used as the sole variable to control the MWD, chain growth should be controlled by chain transfer to CTA, namely:

[[[k.sub.tr,CTA][CTA][.sub.p]]/[[k.sub.tr,M][M][.sub.p]]] > 10 (5)

[[[k.sub.tr,CTA][CTA][.sub.p]]/[[k.sub.a][R][.sub.w]]] > 10 (6)

Under these conditions, the MWD is not affected by the compartmentalization of the system, and it can be controlled using the appropriate monomer to CTA ratio in the polymer particles. (2,22)

[bar.M.sub.ni] = [[[k.sub.p][M][.sub.p]]/[[k.sub.tr,CTA][CTA][.sub.p]]] X [P.sub.m] (7)

A consequence of equations (5-7) is that, for each particular system, there is a maximum molecular weight that can be controlled using chain transfer agents. For the copolymerization of styrene/n-butyl acrylate using the recipe in the Appendix, this maximum value is [bar.M.sub.n] = 700,000 g/mol.

On the other hand, because the CTA have strong odors, their maximum concentration is limited to about 1 wt% based on the total amount of monomer. For t-dodecyl mercaptan and the formulation in the Appendix, this leads to a minimum value of [bar.M.sub.n] of 20,000 g/mol.

Figure 5 presents the MWD calculated by means of the optimization procedure to obtain an adhesive with a resistance to shear of 1310 s and a resistance to peel of 3.1 N/100 mm (Table 4). In the optimization, the attainable [bar.M.sub.n] values were limited to the range 20,000-700,000 g/mol in order to account for the practical limitations.

EXPERIMENTAL VALIDATION

The approach developed by Echevarria et al. (2) was used to calculate the monomer and CTA feed policies aimed at producing the MWD calculated by the optimization (Figure 5). These policies were implemented in an on-line control strategy based on calorimetry. (4,5) The MWD of the polymer obtained is also presented in Figure 5.

Table 5 shows the values of the adhesive properties; the desired values, the predicted values for the optimal MWD (obtained with the PLS model), and the experimentally measured values for the produced latex are reported. When comparing the desired and the predicted adhesive properties, it can be seen that a suboptimal solution is obtained; namely, that it is not possible to find an MWD that gives exactly the desired adhesive properties. Therefore, according to the model, there is no MWD that can give exactly the desired adhesive properties. The suboptimal MWD (predicted) was used therefore as the target in the controlled experiment. It can be seen that the measured adhesive properties are in good agreement with the predicted ones, showing the good prediction capability of the model.

CONCLUDING REMARKS AND FUTURE PERSPECTIVE

In this work, a control strategy for the end-use properties of polymer latexes was developed and experimentally validated. A previous control strategy for copolymer microstructure (MWD and copolymer composition) was upgraded to directly control adhesive properties (resistance to shear and resistance to peel). In order to do so, it was first necessary to establish a quantitative relationship between the adhesive properties and the microstructure of the polymer (the MWD in this particular case). A model that satisfactorily predicts adhesive properties from the MWD of a latex was built using partial least squares regression.

The MWD required to produce the desired adhesive properties cannot be determined by model inversion because it is ill-conditioned. Therefore, this MWD was calculated by carrying on an optimization that minimizes the square difference between the desired adhesive properties and the predicted properties, calculated by the PLS-R model. Different initial guesses led to the same final results, showing that the optimization is robust. The optimization results were not sensitive to changes in the number of Shultz-Flory distributions of which the MWD is decomposed.

The optimal MWD that will lead to the desired adhesive properties can be synthesized employing an on-line control strategy that was previously developed and uses a chain transfer agent to control the MWD. However, as has been pointed out in this work, there are practical limitations to control MWD using strategies with CTA as the sole manipulated variable. For a given comonomer system, CTA, and recipe, the attainable [bar.M.sub.n] values are limited to a certain range in order to account for practical limitations. This requires setting constraints in the calculation of the optimal MWD. The limitations of using CTA as the manipulated variable might be overcome if an initiator is used to control the high molecular weights and the CTA for the low molecular weights.

Taking into account the mentioned practical limitations, the complete control strategy was experimentally validated, producing a latex of n-BA/Sty of composition 85/15 with some desired adhesive properties, proving that the approach can be implemented.

In this work, it has been demonstrated that the described methodology works well in the case of linear polymers. However, there are many other microstructural properties that also affect adhesive performance. In the case of nonlinear polymers, for example, apart from the MWD, gel fraction and branching level also play an important role on the adhesive properties. Therefore, to achieve a good and robust control of the end-use properties, other microstructural properties must be added to the quantitative relationship. Work is in progress to develop adhesive properties-microstructural properties models that also consider other relevant microstructural properties, such as gel fraction and branching level.

APPENDIX

The experimental setup employed to run the reactions was a commercial calorimetric reactor (RC1, Mettler-Toledo) equipped with a stainless steel HP60 reactor and modified in order to calculate on-line the heat of reaction as presented elsewhere. (20,21) All the reactions were carried out at 60[degrees]C and with an agitation speed of 400 rpm. All the n-BA/S latexes had a solids content of 33% and a molar composition of 85/15.

Doubly deionized water was used in all polymerizations. All reactants, monomers (n-BA and S, Quimidroga), CTA (tert-dodecyl mercaptane, Fluka), emulsifier (SLS, Sigma), initiator ([K.sub.2][S.sub.2][O.sub.8], Fluka) and buffer (NaHC[O.sub.3], Panreac) were used as supplied, without further purification. Table 6 contains the formulation that was employed in the different reactions.

The molecular weight distribution of the latex was determined by size exclusion chromatography (SEC, Waters). The equipment has a pump (Waters 510), a differential refractometer (Waters 2410), and two columns in series (Styragel HR4 and HR6; with a pore size of [10.sup.4] and [10.sup.6] [Angstrom], respectively). The analysis was performed at 30[degrees]C (detector and columns) and tetrahydrofuran (THF) was used as solvent at a flow rate of 1 ml/min.

The adhesive properties (resistance to shear and resistance to peel) of the copolymers were measured using the European AFERA 4001 and 4012 norms and the Ameri-can PSTC-1 and PSTC-7 norms, as detailed in reference 9.

ACKNOWLEDGMENTS

O. Elizalde and M. Vicente acknowledge Ministerio de Educacion y Ciencia and C. Plessis acknowledges Rhodia for the scholarships. The authors acknowledge the financial support from the University of the Basque Country (Grant UPV 00221.215-13594/2001), CICYT (project PPQ 2000-1185), Basque Government (project EX1999-67), and Rhodia.

References

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(4) Vicente, M., Ben Amor, S., Gugliotta, L.M., Leiza, J.R., and Asua, J.M., "Control of Molecular Weight Distribution in Emulsion Polymerization Using On-Line Reaction Calorimetry," Ind. Eng. Chem. Res., 40, 218 (2001).

(5) Vicente, M., Leiza, J.R., and Asua, J.M., "Simultaneous Control of Copolymer Composition and MWD in Emulsion Polymerization," AIChE J., 47, No. 7, 1594 (2001).

(6) Flores-Cerrillo, J. and MacGregor, J.E., "Control of Particle Size Distributions in Emulsion Semibatch Polymerization Using Mid-Course Correction Policies," Ind. Eng. Chem. Res., 41, No. 7, 1805 (2002).

(7) Prasad, V., Schley, M., Russo, L.P., and Bequette, B.W., "Product Property and Production Rate Control of Styrene Polymerization," J. Process Control, 12, No. 3, 353 (2002).

(8) Aubrey, D.W., Pressure Sensitive Adhesives--Principles of Formulation. Developments in Adhesives, Wake, W.C. (Ed.), Applied Sci., Publishers, Barking, England, 1977.

(9) Laureau, C., Vicente, M., Barandiaran, M.J., Leiza, J.R., and Asua, J.M., "Effect of the Composition Profile of 2-ethylhexyl acrylate/methyl methacrylate Latex Particles and Adhesion," J. Appl. Poly. Sci., 81, No. 5, 1258 (2001).

(10) Dale, W.C., Hayne, J.K., Paster, M.D., and Alstede, E.F., Tech. Seminar. Proc., Pressure Sensitive Tape Council, Itasca, 1987.

(11) Zosel, A. and Ley, G., "Influence of Crosslinking on Structure, Mechanical Properties, and Strength of Latex Films," Macromolecules, 26, 2222 (1993).

(12) Plessis, C., Arzamendi, G., Leiza, J.R., Schoonbrood, H., Charmot, D., and Asua, J.M., "Kinetics and Polymer Microstructure of the Seeded Semibatch Emulsion Copolymerization of n-butyl Acrylate and Styrene," Macromolecules, 34, No. 15, 5147 (2001).

(13) Plessis, C., Arzamendi, G., Alberdi, J.M., Leiza, J.R., Schoonbrood, H., Charmot, D., and Asua, J.M., "Seeded Semibatch Emulsion Polymerization of Butyl Acrylate: Effect of Chain Transfer Agent on the Kinetics and the Structural Properties," J. Polym. Sci., Part A: Polym. Chem., 39, No. 7, 1106 (2001).

(14) Satas, D., Handbook of Pressure Sensitive Adhesive Technology, Van Nostrand Reinhold, New York, 1989.

(15) Satas, D., "Tayloring Pressure-Sensitive Adhesive Polymers," Adhesives Age, 15, No. 10, 19 (1972).

(16) Plessis, C., Ph.D. Dissertation, The University of the Basque Country (Spain), 2000.

(17) Elizalde, O., Vicente, M., Leiza, J.R., and Asua, J.M., "Control of the Adhesive Properties of n-butyl Acrylate/Styrene Latexes," Polym. React. Eng., 10, No. 4, 265 (2002).

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(19) Esbensen, K.H., Multivariate Data Analysis--In Practice, CAMO ASA, Oslo, Norway, 2000.

(20) Saenz de Buruaga, I., Arotcarena, M., Armitage, P.D., Gugliotta, L.M., Leiza, J.R., and Asua, J.M., "On-Line Calorimetric Control of Emulsion Polymerization Reactors," Chem. Eng. Sci., 51, 2781 (1996).

(21) Saenz de Buruaga, I., Echeverria, A., Armitage, P.D., de la Cal, J.C., Leiza, J.R., and Asua, J.M., "On-Line Control of a Semibatch Emulsion Polymerization Reactor Based on Calorimetry," AIChE J., 43, No. 4, 1069 (1997).

(22) Storti, G. and Morbidelli, M., "Open-Loop Control of Polymerization Reactors," in Polymer Dispersions. Principles and Applications, Asua. J.M. (Ed), Kluwer Academic Publishers, Dordretch, 1997.

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Oihana Elizalde, Matias Vicente, ([dagger]) Christophe Plessis,** Jose R. Leiza, and Jose M. Asua ([double dagger]) -- Institute for Polymer Materials (POLYMAT), The University of the Basque Country*

*Dept. de Quimica Aplicada, Apdo. 1072, 20080, Donostia-San Sebastian, Spain.

([dagger]) Current address: mvicente@eiasa.es, Aiscondel Division Quimica, ctra. nac. 240, km 147, 22400 Monzon, Huesca, Spain.

**Current address: christophe.plessis@ucb-group.com, UCB Chemicals, Anderlecht Str. 33, B-1620 Drogenbos (Belgium).

([double dagger]) Authors to whom correspondence should be addressed: jmasua@sq.ehu.es; O. Elizalde: qpbeloro@sq.ehu.es; and J.R. Leiza: jrleiza@sq.ehu.es, fax: 34 943 21 22 36.

Keywords: Gel permeation chromatography, acrylics, latexes, colloids, emulsions, process control

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A good control strategy for emulsion polymerization reactions must assure that a product with the desired final properties will be obtained. Unfortunately, most of the control strategies developed until now only allow for the control of the molecular properties of the polymer by manipulation of several process variables, (1-7) without including the final properties of the product in the control strategy.

Historically, end-use and molecular properties of the product have been related using trial and error procedures, which are in most cases, highly time-consuming. This work is an attempt to relate those properties in a quantitative and reliable way and to include such a relationship in a control strategy in order to directly provide a product with the desired end-use properties.

An important application of acrylic latexes is as pressure sensitive adhesives (PSAs), mainly used for labels, tapes, decorative films, protective materials, and wall and floor coverings. Each specific application requires appropriate end-use properties, characterized by a combination of specific values of adhesive properties such as tackiness, resistance to peel, and resistance to shear.

It has been proved that several molecular properties of a latex, such as copolymer composition, average molecular weight and molecular weight distribution, level of branching, content of gel, and crosslinking, strongly affect the values of the adhesive properties. (8-13)

The glass transition temperature ([T.sub.g]) of the copolymer, which depends on the copolymer composition, determines to a very large extent the tackiness of the final product. (8) The adhesive performance is also affected by the composition profile. (9) Dale et al. (10) reported on the effect of crosslinking on the properties of acrylic adhesives, concluding that the crosslinking density should be low for a PSA, because a high degree of crosslinking, which severely affects tack and peel adhesion, may yield to a nontacky product. The gel content also affects the mechanical properties of the final product. (11-13) Generally, the presence of gel increases the resistance to peel and the resistance to shear and decreases the tack, although above certain levels of gel, resistance to both shear and peel dramatically decreased. (12, 13)

Resistance to shear and to peel depend also on the molecular weight of the polymer. (14, 15) Although there are some qualitative studies on the effect of the average molecular weight (MW), the effect of the whole molecular weight distribution (MWD) is more elusive, and therefore, has not been very widely studied. Good tack values are observed for low MW polymers and the tackiness decreases when the MW is raised. With resistance to shear, the behavior is exactly the opposite. Good resistance to shear is obtained with high MW polymers and the value decreases rapidly for lower MWs. High values of resistance to peel are provided by the intermediate MWs, but the value decreases for both high and low MWs. As previously mentioned, each application requires a specific combination of the adhesive properties and this can be achieved by a proper balance of high and low MW polymers, namely, by an appropriate shape of the MWD.

Therefore, to produce a latex with some desired end-use properties, an understanding and quantification of the effect of the molecular properties on the end-use properties is an essential step. In the next section, a qualitative study of the effect of gel content and MWD on the adhesive properties is presented. Thereafter the effect of the MWD of linear polymers on adhesive properties is addressed. In the third section the control strategy developed for controlling resistance to both shear and peel of linear polymer latexes is explained, and the methodology is validated experimentally. This is followed by a study of the effect of several variables on the calculation of the optimal MWD (the MWD that will give the desired adhesive properties) and an analysis of the limitations of the control strategy. The article concludes with final remarks and future perspectives.

EFFECT OF GEL CONTENT AND MWD ON ADHESIVE PROPERTIES

Table 1 presents the effect of the gel content and sol MWD on the adhesive properties of n-butyl acrylate/styrene (n-BA/S) and n-BA latexes. It can be seen that resistance to shear and resistance to peel are particularly affected by the fraction of gel and the soluble [bar.M.sub.w]. When a latex is employed as a PSA, the influence of gel content and [bar.M.sub.w] cannot be underestimated and must be taken into account to obtain the desired product. Both resistance to shear and resistance to peel present a maximum for a fraction of gel of about 32%. The gel, which decreases the free movement of the polymer molecules, provides better cohesion, improving the mechanical properties of the polymer film. However, if the gel fraction increases over a given value, the network becomes so rigid that it limits the particle coalescence during film formation. As a consequence, resistance to shear decreases to values similar to the latexes without any gel, whereas resistance to peel decreases until an intermediate value.

Although Satas (14, 15) studied the effect of the [bar.M.sub.w] on the adhesive properties, for the purpose of controlling the final adhesive properties, it is much more useful to understand the effect of the complete MWD, even if it is much more difficult to capture.

To study the effect of the whole MWD, several n-BA/S latexes with a fixed molar composition of 85/15 and varying MWDs were prepared (see the Appendix for experimental details). This relatively high content of styrene avoids chain transfer to the polymer, and therefore, mostly linear polymers were obtained. (12) This helps to isolate the effect of the MWD on the adhesive performance of the latexes. The desired MWDs were obtained by using an on-line control strategy based on reaction calorimetry. (4, 5)

The characteristics of some of the latexes used in the study and their adhesive properties are presented in Table 2. Figure 1 contains the MWDs of the four latexes employed in this study. It was observed that, in general, broad unimodal latexes had slightly better adhesive properties than bimodal latexes of similar [bar.M.sub.w] (e.g., compare B and C latexes in Table 2). When [bar.M.sub.w] was increased (latex D), the resistance to shear also increased, as mentioned in the literature. (14, 15) An opposite trend was observed for resistance to peel, as can be deduced from Table 2. As a general rule, it can be said that by broadening the MWD, it is possible to produce a more balanced adhesive that can be used in different applications. Unfortunately this general rule gives only a qualitative idea of the MWD that should be produced for each application.

Another aspect that should be considered is the optimal way to produce a latex with the desired MWD, once the shape of the optimal MWD (the one that will give the desired adhesive performance) is known. A previous paper (17) included a comparison between the adhesive performance of latexes with similar bimodal MWDs prepared by blending unimodal latexes or by producing the bimodal MWD in-situ during a controlled experiment, the so-called in-reaction method. It was concluded that the in-reaction bimodal latex, prepared using the previously mentioned online control strategy, (4, 5) presented better adhesive properties than the bimodal MWD latex prepared by blending two unimodal MWD latexes. Therefore all the latexes used in this work were prepared by using the on-line control strategy that allows the in-reaction production of the desired MWD, and also the control of copolymer composition.

From this study we can conclude that there is not a perfect adhesive, and that the desired properties depend on the specific application. A good control of polymer microstructure helps to improve the adhesive performance of the latex, but it does not assure that the desired properties will be obtained. This leads to the need for adding a further step: to relate quantitatively polymer and end-use properties and implement this relationship in the optimization and control of the desired adhesive performance. This is explained in detail in the following section.

MWD-ADHESIVE PROPERTIES QUANTITATIVE RELATIONSHIP: PLS-R

All the works previously mentioned considered the relationship between molecular and final properties in a qualitative way. This study is necessary as a preliminary step to understand the effect of several properties, but it is not enough to develop a control strategy for the final properties of the latex.

By applying partial least squares regression (PLS-R) (18, 19) to a set of 13 calibration samples of n-BA/S of fixed molar composition (85/15) and very different MWDs, a quantitative relationship between the adhesive properties (resistance to peel and resistance to shear) and the MWD was established. (17) As a result, a model with one principal component (PC) was built and experimentally validated. The model gave satisfactory results for predicting resistance to shear and resistance to peel values of different latexes knowing their complete MWD. According to the model, shear had large and positive values on the first and unique PC, and peel had large but negative values. Therefore, resistance to shear and to peel were related in an inverse way by the model. It related intermediate MW values to high peel values and high MW values to high shear values.

CONTROL STRATEGY FOR THE ADHESIVE PROPERTIES

With the previously developed calibration model, (17) adhesive properties of a given latex can be predicted if the MWD is known, but the model cannot be directly used to achieve the control of the adhesive properties. To do so, the MWD required to obtain some desired adhesive properties must be calculated first. In this section the procedure developed to solve this problem is explained.

[FIGURE 1 OMITTED]

Once the optimal MWD that ensures the production of latex with the desired properties is known, this can be synthesized employing the on-line control strategy developed by Vicente et al. (4, 5) In this strategy the optimal trajectories of monomers and chain transfer agent (CTA) that allow the production of a given MWD and copolymer composition are first determined. Then, these trajectories are tracked by on-line monitoring the heat of reaction (20, 21) and using a nonlinear model based controller to fulfill the target trajectories.

If the whole procedure is analyzed globally--the calculation of the optimal MWD and the control strategy employed to produce that MWD--we reach a control scheme that allows the direct control of the adhesive properties (resistance to shear and resistance to peel) by the manipulation of process variables (feed rates of monomers and CTA).

MWD Required to Obtain the Desired Adhesive Properties

The calibration model described above is useful to predict the adhesive properties of different latexes from MWD measurements, but it cannot be directly used for control purposes. In practice, only the desired adhesive properties of the latex will be known, and the MWD that will give those properties must be calculated in order to produce it experimentally and obtain the desired final product. However, for this objective, the inversion of the calibration model is not possible because it is ill-conditioned.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The solution to this problem was found using an optimization algorithm that calculates the MWD that minimizes the following objective function:

[J.[(MWD)]] = [2.summation over (i=1)][[alpha].sub.i](([y.sub.i.sup.d] - [y.sub.i.sup.pred])/[y.sub.i.sup.d])[.sup.2] i = 1(Shear),2(Peel) (1)

where [y.sub.i.sup.d] are the desired adhesive properties, [y.sub.i.sup.pred] the predictions of the model and [[alpha].sub.i] the weighing factors chosen to compensate for the different absolute values of the shear and peel measurements. The MWD was assumed to be composed of m Schultz-Flory distributions of equal mass and having a polydispersity index equal to 2.

X(n) = [m.summation over (i=1)] [n/[bar.X.sub.nk.sup.2]]exp(-[n/[bar.X.sub.nk]])[1/m] (2)

where X(n) is the weight fraction of polymer chains of length n. In order to apply the X(n) values of equation (2) in the quantitative relationship between MWD and adhesive properties to calculate [y.sub.i.sup.pred], they first must be transformed to a gel permeation chromatography (GPC) distribution, because the quantitative relationship was built using GPC data for the MWD.

[FIGURE 4 OMITTED]

The optimization reduces to determining the m values of [bar.X.sub.nk] that minimize equation (1). This was carried out by means of a Nelder and Mead algorithm using the DBCPOL routine of the IMSL library.

EFFECT OF THE INITIAL MWD GUESS: In the Nelder and Mead algorithm, an initial guess for the MWD (what we wish to optimize) is required. Using previously acquired qualitative knowledge on the MWD-adhesive performance relationship, it is possible to have a rough idea of a possible initial MWD, but this is not straightforward in all cases. In addition, in order to develop a robust optimization process, one must make sure that different initial guesses will lead to the same final result, namely that a global optimum is obtained.

To assess the robustness of the optimization, the MWDs given in Figure 2 were used as initial guesses in an attempt to obtain a resistance to shear of 1310 s and a resistance to peel of 3.1 N/100 mm. The first initial guess was a bimodal MWD, with two peaks of polydispersity 3 for each of them; the low molecular weight peak had 10% of the total polymer, and the high molecular weight one had the other 90% of the polymer. The second guess was a monomodal one, of rather low molecular weight with a polydispersity of 3.

Figure 3 shows the optimal MWDs obtained with the two initial guesses and Table 3 the values of the adhesive properties predicted for them. Both optimizations gave almost the same MWD, as well as the same resistance to shear and peel values. This proves that the procedure is robust, and that a change in the initial guess does not affect the final result. This is also very helpful when a user with no or limited knowledge on the subject uses the optimization program, because even if the initial guess is poor, the optimal MWD will be achieved.

EFFECT OF THE NUMBER OF SHULTZ-FLORY DISTRIBUTIONS: Another parameter that should be chosen during the optimization is the number of Shultz-Flory (S-F) distributions for which the MWD is decomposed. The larger this number is, the better the MWD is described, but a larger number of parameters should be estimated. The effect of the number of S-F distributions used to decompose the desired distribution was checked by performing three optimizations, using the same initial guess, and an increasing number of S-F distributions (20, 50 and 100). As in the previous section, a latex with a resistance to shear of 1310 s and a resistance to peel of 3.1 N/100 mm was sought.

Figure 4 presents the resultant MWDs for the three cases. It can be seen that the optimization result is not sensitive to changes in the number of Shultz-Flory distributions and that in all the cases very similar results were obtained, with no differences on the predicted adhesive properties. Therefore, 20 S-F distributions were used in this work to calculate the optimum MWD for a given desired resistance to shear and resistance to peel.

[FIGURE 5 OMITTED]

Practical Limitations of MWD Control Strategies Using Chain Transfer Agents

In a free-radical polymerization, the instantaneous number average molecular weight of linear polymers is given by the ratio between propagation ([R.sub.p]) and termination rates ([R.sub.t]) (23):

[bar.X.sub.n] = [R.sub.p]/[R.sub.t] (3)

For a "zero-one" system, the termination rate is:

[R.sub.t] = ([k.sub.tr,CTA] [CTA][.sub.p] + [k.sub.tr,M][M][.sub.p] + [k.sub.a][R][.sub.w]) * [[bar.n][N.sub.p]]/[N.sub.A] (4)

where the first term of the right side takes into account the termination by chain transfer to CTA, the second the termination by chain transfer to monomer, and the last one the instantaneous bimolecular termination with radicals entering the particle from the aqueous phase. In equation (4), [k.sub.tr,CTA] and [k.sub.tr,M] are the chain transfer rate constants to CTA and monomer, respectively; [CTA][.sub.p] is the concentration of the chain transfer agent in the polymer particles; [k.sub.a] is the rate coefficient for radical entry into the particles; and [R][.sub.w] the radical concentration in the aqueous phase.

If a chain transfer agent is going to be used as the sole variable to control the MWD, chain growth should be controlled by chain transfer to CTA, namely:

[[[k.sub.tr,CTA][CTA][.sub.p]]/[[k.sub.tr,M][M][.sub.p]]] > 10 (5)

[[[k.sub.tr,CTA][CTA][.sub.p]]/[[k.sub.a][R][.sub.w]]] > 10 (6)

Under these conditions, the MWD is not affected by the compartmentalization of the system, and it can be controlled using the appropriate monomer to CTA ratio in the polymer particles. (2,22)

[bar.M.sub.ni] = [[[k.sub.p][M][.sub.p]]/[[k.sub.tr,CTA][CTA][.sub.p]]] X [P.sub.m] (7)

A consequence of equations (5-7) is that, for each particular system, there is a maximum molecular weight that can be controlled using chain transfer agents. For the copolymerization of styrene/n-butyl acrylate using the recipe in the Appendix, this maximum value is [bar.M.sub.n] = 700,000 g/mol.

On the other hand, because the CTA have strong odors, their maximum concentration is limited to about 1 wt% based on the total amount of monomer. For t-dodecyl mercaptan and the formulation in the Appendix, this leads to a minimum value of [bar.M.sub.n] of 20,000 g/mol.

Figure 5 presents the MWD calculated by means of the optimization procedure to obtain an adhesive with a resistance to shear of 1310 s and a resistance to peel of 3.1 N/100 mm (Table 4). In the optimization, the attainable [bar.M.sub.n] values were limited to the range 20,000-700,000 g/mol in order to account for the practical limitations.

EXPERIMENTAL VALIDATION

The approach developed by Echevarria et al. (2) was used to calculate the monomer and CTA feed policies aimed at producing the MWD calculated by the optimization (Figure 5). These policies were implemented in an on-line control strategy based on calorimetry. (4,5) The MWD of the polymer obtained is also presented in Figure 5.

Table 5 shows the values of the adhesive properties; the desired values, the predicted values for the optimal MWD (obtained with the PLS model), and the experimentally measured values for the produced latex are reported. When comparing the desired and the predicted adhesive properties, it can be seen that a suboptimal solution is obtained; namely, that it is not possible to find an MWD that gives exactly the desired adhesive properties. Therefore, according to the model, there is no MWD that can give exactly the desired adhesive properties. The suboptimal MWD (predicted) was used therefore as the target in the controlled experiment. It can be seen that the measured adhesive properties are in good agreement with the predicted ones, showing the good prediction capability of the model.

CONCLUDING REMARKS AND FUTURE PERSPECTIVE

In this work, a control strategy for the end-use properties of polymer latexes was developed and experimentally validated. A previous control strategy for copolymer microstructure (MWD and copolymer composition) was upgraded to directly control adhesive properties (resistance to shear and resistance to peel). In order to do so, it was first necessary to establish a quantitative relationship between the adhesive properties and the microstructure of the polymer (the MWD in this particular case). A model that satisfactorily predicts adhesive properties from the MWD of a latex was built using partial least squares regression.

The MWD required to produce the desired adhesive properties cannot be determined by model inversion because it is ill-conditioned. Therefore, this MWD was calculated by carrying on an optimization that minimizes the square difference between the desired adhesive properties and the predicted properties, calculated by the PLS-R model. Different initial guesses led to the same final results, showing that the optimization is robust. The optimization results were not sensitive to changes in the number of Shultz-Flory distributions of which the MWD is decomposed.

The optimal MWD that will lead to the desired adhesive properties can be synthesized employing an on-line control strategy that was previously developed and uses a chain transfer agent to control the MWD. However, as has been pointed out in this work, there are practical limitations to control MWD using strategies with CTA as the sole manipulated variable. For a given comonomer system, CTA, and recipe, the attainable [bar.M.sub.n] values are limited to a certain range in order to account for practical limitations. This requires setting constraints in the calculation of the optimal MWD. The limitations of using CTA as the manipulated variable might be overcome if an initiator is used to control the high molecular weights and the CTA for the low molecular weights.

Taking into account the mentioned practical limitations, the complete control strategy was experimentally validated, producing a latex of n-BA/Sty of composition 85/15 with some desired adhesive properties, proving that the approach can be implemented.

In this work, it has been demonstrated that the described methodology works well in the case of linear polymers. However, there are many other microstructural properties that also affect adhesive performance. In the case of nonlinear polymers, for example, apart from the MWD, gel fraction and branching level also play an important role on the adhesive properties. Therefore, to achieve a good and robust control of the end-use properties, other microstructural properties must be added to the quantitative relationship. Work is in progress to develop adhesive properties-microstructural properties models that also consider other relevant microstructural properties, such as gel fraction and branching level.

APPENDIX

The experimental setup employed to run the reactions was a commercial calorimetric reactor (RC1, Mettler-Toledo) equipped with a stainless steel HP60 reactor and modified in order to calculate on-line the heat of reaction as presented elsewhere. (20,21) All the reactions were carried out at 60[degrees]C and with an agitation speed of 400 rpm. All the n-BA/S latexes had a solids content of 33% and a molar composition of 85/15.

Doubly deionized water was used in all polymerizations. All reactants, monomers (n-BA and S, Quimidroga), CTA (tert-dodecyl mercaptane, Fluka), emulsifier (SLS, Sigma), initiator ([K.sub.2][S.sub.2][O.sub.8], Fluka) and buffer (NaHC[O.sub.3], Panreac) were used as supplied, without further purification. Table 6 contains the formulation that was employed in the different reactions.

The molecular weight distribution of the latex was determined by size exclusion chromatography (SEC, Waters). The equipment has a pump (Waters 510), a differential refractometer (Waters 2410), and two columns in series (Styragel HR4 and HR6; with a pore size of [10.sup.4] and [10.sup.6] [Angstrom], respectively). The analysis was performed at 30[degrees]C (detector and columns) and tetrahydrofuran (THF) was used as solvent at a flow rate of 1 ml/min.

The adhesive properties (resistance to shear and resistance to peel) of the copolymers were measured using the European AFERA 4001 and 4012 norms and the Ameri-can PSTC-1 and PSTC-7 norms, as detailed in reference 9.

Table 1 -- Structural and Adhesive Properties of the Latexes Used in the Study Latex A B Composition (n-BA/S) 100 97.5/2.5 Gel Fraction (%) 55 32 Characteristics Broad Broad of the sol MWD unimodal unimodal Sol [bar.M.sub.w] 523000 1188000 Tack (cm) 0.5 [+ or -] 0.2 0 [+ or -] 0 Shear (s) 40 [+ or -] 10 1662 [+ or -] 106 Peel (N/100 mm) 16.9 [+ or -] 1.6 26 [+ or -] 0.6 Latex C D E Composition (n-BA/S) 90/10 100 100 Gel Fraction (%) 1 32 1 Characteristics Broad Broad Broad of the sol MWD unimodal unimodal unimodal Sol [bar.M.sub.w] 1580000 430000 340000 Tack (cm) 0.7 [+ or -] 0.3 0 [+ or -] 0 0 [+ or -] 0 Shear (s) 1051 [+ or -] 117 1820 [+ or -] 210 45 [+ or -] 12 Peel (N/100 mm) 6 [+ or -] 1.1 23.4 [+ or -] 3.6 11 [+ or -] 1.1 Table 2 -- Characteristics of the Latexes Used to Study the Effect of the MWD Latex A B Characteristics of the distribution Bimodal Bimodal [bar.M.sub.w] 400000 735000 Tack (cm) 7.4 [+ or -] 0.8 12.1 [+ or -] 2.1 Shear (s) 247 [+ or -] 24 413 [+ or -] 144 Peel (N/100 mm) 9 [+ or -] 3.4 4.4 [+ or -] 0.3 Latex C D Characteristics of the distribution Unimodal Broad Bimodal [bar.M.sub.w] 750000 1220000 Tack (cm) 10.6 [+ or -] 1.0 12.5 [+ or -] 2.3 Shear (s) 1512 [+ or -] 182 3100 [+ or -] 1055 Peel (N/100 mm) 5.3 [+ or -] 0.7 2.7 [+ or -] 0.6 Table 3 -- Adhesive Properties Predicted for the Optimal MWDs Presented in Figure 4 Predicted Predicted Desired Initial Guess 1 Initial Guess 2 Shear (s) 1310 1718.78 1718.81 Peel (N/100 mm) 3.1 3.8 3.8 Table 4 -- Desired and Predicted Adhesive Properties for Optimizations A and B Predicted Predicted Desired (Optimization A) (Optimization B) Shear (s) 1310 1719 1717 Peel (N/100 mm) 3.1 3.8 3.8 Table 5 -- Desired, Predicted, and Produced Adhesive Properties for the Experimental Validation of the Approach Desired Predicted Produced Shear (s) 1310 1719 1740 [+ or -] 720 Peel (N/100 mm) 3.1 3.8 4.4 [+ or -] 0.2 Table 6 -- Formulation of the Emulsion Copolymerizations Ingredients Quantity (g) n-BA 350 Sty 50 [H.sub.2]O 800 TDM (CTA) 0.78 [K.sub.2][S.sub.2][O.sub.8] 1 NaHC[O.sub.3] 1 SLS 8 Temperature 60

ACKNOWLEDGMENTS

O. Elizalde and M. Vicente acknowledge Ministerio de Educacion y Ciencia and C. Plessis acknowledges Rhodia for the scholarships. The authors acknowledge the financial support from the University of the Basque Country (Grant UPV 00221.215-13594/2001), CICYT (project PPQ 2000-1185), Basque Government (project EX1999-67), and Rhodia.

References

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Oihana Elizalde, Matias Vicente, ([dagger]) Christophe Plessis,** Jose R. Leiza, and Jose M. Asua ([double dagger]) -- Institute for Polymer Materials (POLYMAT), The University of the Basque Country*

*Dept. de Quimica Aplicada, Apdo. 1072, 20080, Donostia-San Sebastian, Spain.

([dagger]) Current address: mvicente@eiasa.es, Aiscondel Division Quimica, ctra. nac. 240, km 147, 22400 Monzon, Huesca, Spain.

**Current address: christophe.plessis@ucb-group.com, UCB Chemicals, Anderlecht Str. 33, B-1620 Drogenbos (Belgium).

([double dagger]) Authors to whom correspondence should be addressed: jmasua@sq.ehu.es; O. Elizalde: qpbeloro@sq.ehu.es; and J.R. Leiza: jrleiza@sq.ehu.es, fax: 34 943 21 22 36.

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Date: | Jan 1, 2004 |

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