Improvement of the synthesis of lutetium bisphthalocyanineusing the Taguchi method

Margarita Linaje,a Ma Cruz Quintanilla,a Ana González,a Jose Luis del Valle,a GloriaAlcaideb and María Luz Rodríguez-Méndez*b

a Máster en Gestión de Calidad Total, E.T.S. Ingenieros Industriales, University ofValladolid, Po del Cauce s/n. 47011, Valladolid, Spain. Fax: 34 983 423310;Tel: 34 983 423399

b Departamento de Química Inorgánica, E.T.S. Ingenieros Industriales, Universidad deValladolid, Po del Cauce s/n. 47011, Valladolid, Spain. Fax: 34 983 423310;Tel: 34 983 423540

Received 20th October 1999, Accepted 30th November 1999

In this work, a Taguchi experimental design has been used to identify important factors that influence theprocedure of synthesis and purification of the lutetium bisphthalocyanine (LuPc2). The working conditions havebeen improved using an L8 (27) experimental design. A statistical analysis of the experimental data revealed thatthe most influential factor in the yield is the amount of the starting material (AR), with a 34.4% contribution,followed by the way of performing two chromatographies (C), sequentially or in parallel (26.8%), the temperatureof the reaction T (17.8%), the type of chromatography TC, standard or flash (9.1%), and lastly, the volume of thesample injected in the column (5.4%). The time of the reaction (t) and the length of the column (LC) had littleeffect on the yield. Noise (N) was found to have a negligible influence on the throughput. Maximum yield(20.0%) was obtained when the synthesis was carried out at 280 °C (T) during 1 h 30 min (t) using 0.5 g oflutetium acetate (AR) and performing a standard chromatography (TC) on neutral alumina, injecting 30 ml (V) ofthe reaction mixture in two columns performed in parallel (C). This yield represents an increase of 186% inrelation to the 7% obtained before the application of the Taguchi method. Under these conditions the yield is notsignificantly influenced by variability of external factors, which validates the proposed procedure.

Introduction

Phthalocyanine (Pc) compounds are of great interest becausethey possess well known electronic, electrochemical andphotophysical properties which are responsible for theirpotential applications in electronic devices.1–4 These devicesare usually prepared by depositing the phthalocyanine mole-cules as thin films on to appropriate substrates, using differentmethods (LB technique, high vacuum evaporation, spin coating,etc.).5–8

Among the Pc compounds, the bisphthalocyanines (LnPc2)are of especial interest. These molecules are sandwich typecomplexes where a lanthanide metal is co-ordinated with twophthalocyanine rings. LnPc2 have particularly interestingproperties such as a high intrinsic conductivity (s = 1026–1023

S cm21 at T = 300 K)9–12 and a rich electrochromism.13–15

The procedure for the synthesis of the LnPc2, has beenpreviously published,16–18 but the literature is fairly empiricaland, as has been noticed by other authors, it is practicallyimpossible to find exact technical details.19 Moreover, even ifyields of 40–50% are reported, these values correspond tobisphthalocyanines on which little purification has beenattempted.

The unwanted impurities make the preparation of thin films(either by evaporation, spin coating or by the LB technique)very difficult, resulting in films of poor quality and in thecontamination of the instruments used for the preparation of thefilms. If better results are desired, the bisphthalocyanines haveto be further purified. Moreover, the fabrication of reproducibledevices requires the availablility of a reproducible purificationmethod.

To obtain bisphthalocyanines of high purity is difficult forseveral reasons.17–18,20 First during the reaction, there isextensive formation of by-products and of mono- and bis-phthalocyanines other than that desired. Secondly, the highreactivity of the bisphthalocyanines causes the easy transforma-tion of the neutral green LnPc2 to the reduced form, which isblue. Finally, as bisphthalocyanines exhibit strong aggregationeffects, it often happens that bands eluting from a column,which are supposedly due to the pure green lutetium phthalo-cyanine, may incorporate hydrogen phthalocyanine, lutetiummonophthalocyanine, blue LnPc2 or other polymeric phthalo-cyanines.

The objective of this work is to discuss the factors thatinfluence the synthesis and purification of a compound of theLnPc2 family, lutetium bisphthalocyanine (LuPc2), in a system-atic manner. An attempt has been made to improve the yield ofthe process and to attain good levels of reproducibility. Thelarge number of variables involved in the process makes itrather difficult to perform a traditional optimisation by studyingthe effect of one variable at a time. For this reason, the Taguchimethod has been used. As has been reported, this method can beof great help to improve the quality of processes where theperformance depends on many factors.21,22 It can be used toarrive at the best parameters for the improvement of the systemwith the least number of analytical investigations. It also allowsthe design of robust systems, that is, systems insensitive to dailyenvironmental variations, and to external factors. This methodwill allow higher yields to be obtained with good reproduci-bility.

In this particular case, the Taguchi method has been appliedto improve the synthetic procedure of the LuPc2 described by

This journal is © The Royal Society of Chemistry 2000

DOI: 10.1039/a908398g Analyst, 2000, 125, 341–346 341

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Tomilova et al.,18 and the subsequent purification methoddeveloped in our laboratory.

Methods

Apparatus and chemicals

Both, phthalonitrile and lutetium acetate [Lu(OAc)3·4H2O]were purchased from Aldrich (Madrid, Spain). As-receivedphthalonitrile and lutetium acetate were stored in a desiccatorchamber and used without further purification. All solventsused (Panreac Química S.A., San Fernando de Henares, Spain)were of analytical grade. Neutral aluminium oxide (Activitygrade I) from J. T. Baker (Deventer, Holland) was used as thestationary phase for the chromatography. A Shimadzu ScientificInstruments (Columbia, MD, USA) UV-1603 UV–VIS spec-trophotometer was used to record the electronic absorptionspectra of the LuPc2 chloroform solutions eluted from thecolumn. FTIR spectra were run as KBr pellets in a NicoletInstrument Corp. (Madison, WI, USA) Magna 760.

Synthesis of the LuPc2

According to the method previously reported by Tomilova etal.,18 the synthesis of LuPc2 involves the reaction of phthaloni-trile with lutetium acetate at an 8 + 1 ratio.

The particular details of the synthetic procedure used in thiswork are as follows. Prior to use, the reactants were desiccatedat 110 °C for 2 h, and pulverised and mixed in an agate mortar.A slight excess of phthalonitrile was added in order tocompensate for the losses due to the sublimation of thephthalonitrile. Phthalonitrile was fused with lutetium acetate atthe temperature indicated in the respective trial (280 or 290 °C)and was kept at this temperature for a period of time (11⁄2 or 2 h)to give a mixture of compounds including different phthalocya-nines, which can be separated by chromatographic methods.The progressive formation of the metal complex was monitoredthrough UV–VIS spectroscopy. The unreacted phthalonitrile(which sublimes) was collected from the cooled reactionmixture as needles deposited in the Vigreux column.

Purification of the LuPc2

In this work, a purification method has been developed. Thesample was first purified by heating at 140 °C for 1 h, to removesome low-molecular-weight starting materials (phthalonitrile)and by-products (phthalic anhydride and phthalimide). Theresidue was dissolved in chloroform using an ultrasonic bath,then further purified by column chromatography on neutralalumina to separate other by-products, such as H2Pc, themonophthalocyanine lutetium complex, small amounts of theblue form of the LuPc2 and trace amounts of a polymeric formof LuPc2. UV–VIS spectra of the fractions eluted from thecolumn were recorded. The pure green LuPc2 shows two intensebands, a B band at 320 nm and a Q band at 658 nm. The reducedform can easily be distinguished by its blue color, whichproduces a shift of the Q band to 645 nm.18 The fractionscontaining the pure green LuPc2 were unified and dried. Thesolid residue was washed with heptane and dried again. In orderto eliminate the remaining impurities, a final purification stepusing vacuum sublimation was carried out. The purity of theresulting LuPc2 was evaluated by vibrational spectroscopy,since this technique allows the presence of the reduced LuPc2

and of unwanted impurities to be detected.23 The vibrationalspectra showed four intense bands at 727, 1114, 1324 and 1452cm21 confirming that pure LuPc2 was obtained. This dark greenproduct was weighed and the yield calculated.

Results

In the first step of this work, the LuPc2 was synthesised andpurified as described above, without further optimisation. Ayield of 5–7% was obtained.

Taguchi methodologies were followed to plan the experi-ments and analyse the test results.

The steps for implementing the Taguchi experimental designare as follows. 1. To define clearly the problem to be solved. 2.To select a measurable variable which will be the qualitycharacteristic to be improved. 3. To identify all the controlfactors that can influence the output variable selected above. 4.To identify the possible interactions between the factors that canaffect the output parameter. 5. To identify the noise factors. 6.To choose the levels to be tested. 7. According to the previousanalysis, to select the adequate inner and outer orthogonal array.8. To assign the control factors and interactions to the columnsof the inner array. 9. To perform the experiments. 10. To carryout a statistical analysis of the data and the signal-to-noise ratioanalysis and determine the best factor levels. 11. Conduct aconfirmatory experiment.

Since the yield (Y) obtained after the purification of the LuPc2

is directly related to the efficiency achieved in the process, thisvariable was chosen as the measurable parameter that will be thequality characteristic to be optimised.

YW

W= ¥obtained

theoretical

100

A high yield is desired and the quality characteristics can bedescribed as ‘the higher the better’.

Before designing the experiments, an exhaustive evaluationof the factors that could influence the yield obtained was carriedout.

The yield depends on controllable experimental conditions(the so-called control factors) such as the temperature (T) andthe time (t) of the reaction, the volume injected in thechromatographic column (V) the stationary phase (SP), thesolvent used as eluent (E) used in the chromatography, etc. Thenoise factors are those factors that affect the output variable butwhose levels cannot be controlled; for instance, the seasonalvariations or the instrumental errors. Table 1 shows a completelist of the factors that can influence the yield of the processunder study.

From the 19 control factors, seven of them were included inthe Taguchi design of experiments for testing their influence inthe yield. The remaining control factors (twelve) were fixed ata value that was given by the previous experiences. Theinfluence of the seven control factors included in the Taguchidesign and the conditions used for the fixed control factors aredescribed below.

Control factors

Key points in the synthesis of the LuPc2 are the temperature (T)and the time (t) of the reaction. In previous works the synthesisof the LuPc2 has been carried out at temperatures ranging from280 to 300 °C and times varying from 11⁄2 to 3 h.16–18

Nevertheless, it is well known that low temperatures and shortreaction times do not allow the formation of the requiredproduct. In contrast, high temperatures and long reaction timesfavour the transformation of the neutral green form to the blueform.17,18 It is important to point out that whatever conditionsare used, a certain amount of the blue form is alwaysobtained.

In order to study the influence of the temperature and the timeon the yield, two levels for each control factor were chosen. Theobjective was to find those levels that maximise the yield andoptimise its robustness. The levels chosen for each control

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factor are shown in Table 2. In the case of T, previousexperience of our laboratory indicate the convenience ofworking at temperatures below 300 °C and times no longer than2 h to avoid the formation of the reduced form. Temperatures of280 and 290 °C and times of 11⁄2 and 2 h have been used in therespective trials.

The chromatographic separation is at the heart of thepurification procedure and hence several factors related to thechromatography can influence the yield. For instance, inpreparative chromatography, the sample capacity is often thefactor of major importance. To determine the loading capacityof the stationary phase, it is necessary to increase the amount ofsample per injection until resolution just begins to suffer. Thevolume injected onto the column will also possibly affect theeffectiveness of the separation achieved by the chromatography.Similarly, the yield can also be related to the amount ofstationary phase: increasing the amount of adsorbent canimprove the resolution of the column. Lengthening the columncan affect the output variable.

In our case, the sample capacity of the chromatography wastested as follows. The reaction was carried out using differentamounts of reactants (AR) (0.3 g or 0.5 g of Lu(OAc)3·4H2O).After the synthesis, the reaction mixtures were dissolved in 500ml of chloroform using an ultrasonic bath as mentioned above.Once complete solubilisation had been reached, the solutionwas concentrated until a volume (V) of 30 ml (level 1) or 60 ml(level 2) was attained. The length of the column and hence theamount of stationary phase (LC) was tested at two levels,measured as the level of the adsorbent reached in the column (15cm and 25 cm).

Due to the similar characteristics of the neutral and reducedforms, the resolution of the chromatography is not enough toseparate quantitatively both compounds (resolution < 1.2). Thebands corresponding to the blue and the green phthalocyanineselute almost together, then, only a very small number offractions contain the pure green compound and the resultingyield is very low. To improve the yield it has been proposed toperform two chromatographies as follows (C). One possibilityis to unify the fractions of pure LuPc2, then the fractionscontaining small amounts of blue form can be further purified ina second (sequential) alumina column. A second option is tosplit the reaction mixture into two batches and perform twoparallel chromatographies where only the extremely purefractions were put together.

Finally, as a result of the high retention times of thephthalocyanines in column, the conventional liquid chromatog-raphy is a long procedure. Exhaustive flash chromatographyalso affords samples of almost pure bisphthalocyanine in shortertimes. The influence of the type of chromatography (TC)standard or flash, will be tested in the respective trials. Table 2shows the control factors and their selected levels.

Fixed control factors

The humidity of the reactants (H) was eliminated by using fixeddrying conditions; the reactants were kept in an oven at 110 °Cfor 2 h immediately prior to the experiment. The excess ofphthalonitrile (Ph) was fixed using a ratio of phthalonitrile tolutetium acetate of 8.8+1. This proportion ensures the completereaction of the acetate even if the losses due to phthalonitrilesublimation are of importance. The selected ramp for heating(R) from ambient temperature to the temperature of thesynthesis was the fastest allowed by the heating system.

In order to proceed to the chromatography, the solid LuPc2

formed in the reaction has to be dissolved. The compound israther insoluble even in organic solvents. The best solubility hasbeen found in chloroform, benzene or toluene. In this case,chloroform was chosen as solvent (S). The reaction mass wasdissolved in 500 ml (Vs) of chloroform using an ultrasonic bathfor 30 min (U). Under these conditions complete solubilisation

Table 1 List of the factors that can influence the final yield of thereaction

Control factors Fixed control factors Noise factors

Step 1. Preparation of the reactants—Purity of the reactants

Humidity of the reactants(H)

Amount of the reactants(AR)

Excess of phthalonitrile(Ph)

Homogenisationprocess

Step 2. Synthesis—Temperature of the

reaction (T)Ramp of the heating (R)

Time of the reaction (t)Ramp of cooling

Step 3. Solubilisation and concentration—Type of solvent (S)

Purity of the solventsVolume of the solvent

(Vs)Solubilisation method

(U)Final volume (V)

Waiting conditionsStep 4. Preparation of the column—

Size of the column (Col)Eluent (E)Stationary phase (SP)

Packing of thecolumn

Type of chromatography(TC)

Length of the column(LC)

Step 5. Chromatography—Volume of the fractions

(Fr)Repetitions of

chromatography (C)Step 6. Purification process—

Washing with heptane:conditions (Hp)

Purification bysublimation: conditions(Sb)

General factors—Instrumental errorsHuman errorsSeasonal variations

(T, Humidity)Losses in

manipulations

Table 2 Control factors and their levels

Factors Level 1 Level 2

Time of reaction (t) 1 h 30 min 2 hTemperature of the

reaction (T) 280 °C 290 °CAmount of the reactant

(AR) 0.3 g of Lu acetate 0.5 g of Lu acetate0.9 g of phthalonitrile 1.6 g of phthalonitrile

Type of chromatography(TC) Flash Normal

Succesivechromatographies (C) Two in series Two in parallel

Length of the column(LC) 15 cm 25 cm

Volume of the injectedsample (V) 30 ml 60 ml

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of the LuPc2 was achieved. The solid impurities were filteredand discarded.

Tests performed in the past by our group showed that the useof basic alumina or kiesselgur as stationary phase (SP), did notgive good results. The best separation was always obtained byusing neutral alumina. Previous experience led us to usechloroform as eluent (E). A column (Col) of 13.5 cm ofdiameter was used. It was also decided to collect fractions every3 ml (Fr) and to register a UV–VIS spectra of every fraction.The electronic absorption spectra were used as the criteria forthe unification of fractions.17,18 The fractions showing a B bandat 320 nm, and a single Q band at 658 nm, indicating thepresence of pure LuPc2 green form, were brought together. Thefractions whose UV–VIS spectra showed a shoulder in the Qband at 645 nm, indicating the presence of blue form, or/andbroad peaks at the B band region, indicating the presence ofother impurities were discarded.

The fractions containing the green LuPc2, were evaporated todryness and the dark green residue was washed with 50 ml ofheptane (Hp) in order to eliminate soluble impurities. Thismethod leaves other insoluble impurities behind that wereremoved using vacuum sublimation for 20 min (Sb).

Noise factors

The noise factors influence the yield but cannot be controlled,for instance, the ambient temperature affects the interactionbetween the reaction mixture and the stationary phase. It alsoaffects the solubility of the phthalocyanines. Another noisefactor is the loss of the product produced in the transfers fromone container to another.

The variability introduced by the noise factors can besimulated in some way. Introducing two noise levels allows thestudy of the signal-to-noise ratio, which in turns allows thereduction of the variability of the result, making it robust againstenvironmental variations. Table 3 shows the noise factors andtheir selected levels.

Statistical analysis

Seven control factors at two levels contain 7 degrees of freedomand can be fitted to the L8 (27) orthogonal array. The noise

factors were included as an outer array. The outer arrayexperiments allowed the transformation of the results into asignal-to-noise (S/N) ratio. As the eight experiments from theL8 matrix were performed at two noise levels (N1 and N2) a totalof 16 experiments were carried out to determine the correspond-ing yield (Y). (Y) represents the average of the yields at the noiselevels N1 and N2. As the optimised characteristic is a bigger-is-better response, the equation employed for S/N calculationwas21

S/N = -Ê

ËÁÁ

ˆ

¯˜˜Â10

1 12

1

logn Yn

n

where n is the number of repetitions in each of the eight trials (n= 2) and Y are the two experimental values obtained for eachtrial.

Experimental results of the 16 syntheses are listed in Table4.

The relative significance of the individual factors on the yieldaverage Y and S/N ratio was quantitatively determined by usingthe analysis of variance (ANOVA). The control factor–noisefactor interaction and the S/N ratio were also calculated.

From the calculated variance ratios F (Fisher), it can beinferred that the duration of the reaction t and the amount of thestationary phase LC have no statistically significant effects onthe yield average at a 95% confidence limit (F is smaller thanthe critical value). As the contribution of t and LC is small, thesum of squares for these factors is combined with the error. Thisprocess of disregarding the contribution of a selected factor, andsubsequently adjusting the contributions of the other factors is awell known statistical method called pooling up.24

Table 5 shows the results of the ANOVA with pooled errorsperformed on the experimental data.

The most influential factor is the amount of reactant (AR)used (34.4%). The next most contributing factor is the way ofperforming two chromatographies sequentially or in parallel (C)(26.8%) followed by the temperature of the reaction (T)(17.9%). The type of chromatography (TC) (9.1%), standard orflash, and the volume of the reaction mixture injected in thecolumn (V) (5.4%) have only a minor effect. The three firstfactors AR, C and T explain 79.1% of the overall variance of theexperimental data. With regards to the factor interactions, noimportant interactions are observed between the control factorsand N.

The contribution of the residual error to the yield average (Y)variability (0.4%) indicated the goodness of the experimentaldesign used. As a rule, if this contribution is smaller than10–15%, the variance of the experimental data can be said to beexplained by the effect of factors and interactions. In con-sequence, it can be asserted that the experimental design used inthis work took into account all the variables affecting theresponse to be improved, and the levels tested were fit for thepurpose.

Fig. 1(a) shows the mean values of the yield for each level ofthe factors under study. An increase of the temperature (T)

Table 3 Levels of the noise factors

Noise levels Level 1 Level 2

Homogenisation of thereactants

Agate mortar Mixed

Balance High precision (mg) Low precision (mg)Waiting conditions before

chromatographyStorage in a dark place

and under controlledtemperature

Storage underlight,temperatureuncontrolled

Transfers Careful Not carefulSolvents HPLC grade Analytical gradeTemperature Cold room (19 °C) Warm room (23 °C)Technician Number 1 Number 2

Table 4 Experimental L8 (27) orthogonal array with a two level noise factor. Yield (%) has been determined

Control factors and levels Yield (%)

Trial t T V AR TC LC C N1 N2 Y (%) S/N

1 1 1 1 1 1 1 1 1.9 1.2 1.55 3.142 1 1 1 2 2 2 2 21.7 19.1 20.4 26.143 1 2 2 1 1 2 2 0.1 0.1 0.1 2204 1 2 2 2 2 1 1 4.5 4.7 4.6 13.255 2 1 2 1 2 1 2 12.9 5.2 9.05 16.686 2 1 2 2 1 2 1 6.6 6.1 6.35 16.047 2 2 1 1 2 2 1 0.1 0.1 0.1 2208 2 2 1 2 1 1 2 8.2 12.4 10.3 19.71

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resulted in a strong decrease of the yield and level T1 leads to thebest throughput. This result is in agreement with the previousobservation that the formation of the blue form increases with T.An increase of time (t) from 11⁄2 to 2 h produced a negligibleeffect on the yield. This observation has to be interpretedcarefully and the use of times longer or shorter than those fixedfor levels 1 and 2 could strongly affect the result.

The throughput Y increases strongly when increasing theamount of the reactants (AR) used for the obtention of theLuPc2. This factor (AR) is directly related with the amount ofthe sample injected in the column and its concentration. Anincrease in the loading of the column benefits the throughput.Another possible explanation is that a higher amount of reactantcould alter the reaction conditions (for instance, a gradient oftemperature inside the reaction mixture or a lesser contact withoxygen on the inside of the reaction mixture). These conditionscould avoid the formation of by-products to a large extent. Asexpected, an increase in the volume V of the injected sampledecreases the resolution. This is the reason why the yielddecreases slightly when increasing the volume of sampleinjected onto the column. As observed in Fig. 1(a) the way ofperforming the two chromatographies (C) has an stronginfluence on the yield. Performing the two chromatographies(C) in parallel (C2) gave better results than when performed inseries (C1). The length of the column (LC) between the limitsstudied in this work, has no effect on the yield. Lengthening thecolumn proportionally increases the analysis time, but does notaffect the output variable. Finally, regarding to the type ofchromatography TC, Fig. 1(a) shows how flash chromatog-raphy (TC1) produces a lower yield than the standard chroma-tography (TC2). It can be inferred that high flow rates decreasethe time of the experiment but do not improve the yield.

Fig. 1(b) shows the interactions between control factors T, t,AR, V, TC, C and LC and the noise factor N.

Note that the lines corresponding to N1 and N2 for all thecontrol factors, excepted AR and C, appear almost parallel.Hence, their interaction is negligible. Note also that T and TCintersect, thus they interact but only slightly.

Even if the interactions are small, the level N2 yielded thepoorer yields for levels 1 of control factors T and AR. This resultindicates that the synthesis and purification of the LuPc2 isalmost insensitive to experimental noise. The statistical analysisthus revealed that the optimal combination of factors forobtaining the best yield is: T1–AR2–C2–TC2–V1. As it has beenestablished, t and LC introduce only small changes but the use oft1 (11⁄2 h) instead of t2 (2 h) is preferred since it means a saving

of time. Similarly, the use of LC1 (15 cm of stationary phase)instead of LC2 (25 cm) is preferred because it is economicallymore favourable. The optimal combination then is: T1–AR2–C2–TC2–V1–t1–LC1.

Once the regular analysis has been performed, the influenceof the control factors on the S/N variable has been carried out.The S/N analysis allows the influence of the mean and thevariation of the response around the mean value due toexperimental noise to be evaluated. It also allows the experi-mental conditions that will produce an improved response withthe smallest environmental variability to be predicted. Thecalculated values are listed in the ANOVA, Table 6.

Comparing the standard analysis with the analysis using theS/N ratio, note that the average value of the results is replacedby the S/N ratio. The S/N ratios are then used to compute themain effects as well as the estimated performance under theoptimum conditions. The pooled ANOVA table for the signal-to-noise analysis shows that the three factors which have asignificant effect on the variability of the S/N ratio are AR

Table 5 Pooled ANOVA table for the regular analysis

Source Pool

Degrees offreedom(d.f.)

Sum ofsquares (S) V

Variance ratioa

test, F pSum ofsquares (SA)

Contributionb

(%)

t [Y] 1 0.1806 0.1806T [N] 1 123.7656 123.7656 613.0957 1.579 3 1025 123.5637 17.9V [N] 1 37.5156 37.5156 185.8405 1.677 3 1024 37.3137 5.4AR [N] 1 237.9306 237.9306 1178.632 4.295 3 1026 237.7287 34.4TC [N] 1 62.8056 62.8056 311.1191 6.068 3 1025 62.6037 9.0LC [Y] 1 0.5256 0.5256C [N] 1 185.6406 185.6406 919.6048 7.044 3 1026 185.4387 26.9N [N] 1 3.1506 3.1506 15.6072 1.681 3 1022 2.9487 0.4t 3 N [Y] 1 0.0506 0.0506T 3 N [N] 1 15.8006 15.8006 78.2712 9.012 3 1024 15.5987 2.2V 3 N [N] 1 4.9506 4.9506 24.5238 7.749 3 1023 4.7487 0.6AR 3 N [N] 1 5.8806 5.8806 29.1307 5.702 3 1023 5.6787 0.8TC 3 N [N] 1 10.7256 10.7256 53.1313 1.883 3 1023 10.5237 1.5LC 3 N [Y] 1 0.0506 0.0506C 3 N [N] 1 1.6256 1.62563 8.0528 4.697 3 1022 1.4237 0.2

Residual error (epooled) 4 0.8075 0.2018 3.0280 0.4

Total [—] 15 690.5994 46.0399 690.5994a Critical variance ratio for a 95% confidence level. b Contribution defined as 100 3 (sum of squares SA/total sum of squares).

Fig. 1 (a) Effect of the control factors T, t, AR, TC, C, LC and V on theyield average. (b) Effect of the interactions control 3 noise factor on themean response: (/) N1 (-) N 2. (c) Effect of the control factors on the S/Nratio.

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(49.4%) T (25.0%) and LC (12.6%). The most robust levels arethose levels with the highest S/N value. As observed in Fig. 1(c)these levels are AR2, T1 and LC1. The remaining factors do nothave a significant effect on the average S/N ratio (calculatedvariance ratio F < F critical value). The most robust levels,AR2 and T1, coincide with the optimal combination obtained inthe regular analysis. The LC factor was not influential on theyield average but the reproducibility of the results increases byusing a shorter column (LC1).

The signal-to-noise analysis shows a residual error of 12.9%,which is smaller than 15% indicating the goodness of theanalysis.

Confirmatory experiment

Assuming that the ‘bigger the better’ characteristic is desired,the improved condition becomes T1–t1–LC1–AR2–C2–TC2–V1.The prediction of the yield average obtained by using theANOVA programme for this combination is 20.0 ± 0.9%. Thiscombination does not belong to the combinations sketched bythe orthogonal array. In order to validate the reliability of theresults, a confirmatory experiment at two noise levels wascarried out. The yield average was found to be 20.01%, whichvalidates the proposed conditions.

Conclusions

The Taguchi method has been successfully applied to improvethe synthesis procedure and the purification of the lutetiumbisphthalocyanine (LuPc2). The working conditions wereimproved using an L8 (27) experimental design. Statisticalanalysis of both the raw data and the S/N ratio showed that thecombination of parameter levels giving rise to the maximumyield Y, independent of uncontrolled variation of noise was T1

(280 °C); t1 (1 h 30 min); LC1 (15 cm); AR2 (0.5 g); C2 (2columns in parallel); TC2 (standard); V1 (30 ml). The ANOVAresults show that the best conditions coincide with the mostrobust levels and with the most economical convenience. Underthese conditions, the yield of the synthesis of extremely pureLuPc2 has been found to be 20.01% which represents anincrease of 186% in relation to the 7% obtained before theapplication of the Taguchi method. In summary, the methodapplied in this work allowed us to improve significantly theyield in a robust manner, giving rise to a process with a highreproducibility.

The process could be further improved by using a super-modified simplex method or by using orthogonal arrays, testinga higher number of levels.

Acknowledgements

We gratefully acknowledge CICYT (OLI96-2172) for financialsupport.

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Paper a908398g

Table 6 Pooled ANOVA table for the signal to noise (S/N) analysis

Source PoolDegrees offreedom (d.f.)

Sum ofsquares (S) V

Varianceratioa test, F p

Sum ofsquares (SA)

Contributionb

(%)

t [Y] 1 12.2465 12.2465T [N] 1 595.5977 595.5977 14.56232 1.579 3 1025 554.6978 25.0V [Y] 1 1.1446 1.1446AR [N] 1 1135.7965 1135.7965 27.77014 6.213 3 1023 1094.896 49.4TC [Y] 1 36.9055 36.9055LC [N] 1 320.0160 320.0160 7.82437 4.895 3 1022 279.1161 12.6C [Y] 1 113.3029 113.3029

Residual error (epooled) 4 163.5996 40.8999 286.2994 12.9

Total (S/N) [—] 7 2215.010 316.4300 2215.010a Critical variance ratio for a 95% confidence level. b Contribution defined as 100 3 (sum of squares SA/total sum of squares).

346 Analyst, 2000, 125, 341–346

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