Fg

GCa

b

a

ARRAA

KTNRt

1

qmicetpd

ms

aaan

c

0d

Thermochimica Acta 521 (2011) 26– 36

Contents lists available at ScienceDirect

Thermochimica Acta

journa l h o me page: www.elsev ier .com/ locate / tca

errocene derivatives thermostability prediction using neural networks andenetic algorithms

abriela Lisaa,∗, Daniela Apreutesei Wilsona,b, Silvia Curteanua, Catalin Lisaa,∗,iprian-George Piuleaca, Victor Bulacovschia

“Gh.Asachi” Tehnical University, Faculty of Chemical Engineering and Environmental Protection, 71D. Mangeron Blv, 700050 Iasi, RomaniaInstitute for Molecules and Materials (IMM), Radboud University Nijmegen Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands

r t i c l e i n f o

rticle history:eceived 21 November 2010eceived in revised form 29 March 2011ccepted 31 March 2011vailable online 16 April 2011

eywords:hermostability predictioneural networks

a b s t r a c t

A database containing the thermal stability of 100 new liquid crystalline ferrocene derivatives and similarphenyl compounds is reported. The experimental determination of the thermal stability was undertakenin inert atmosphere using a Mettler Toledo derivatograph. Both initial temperature when the thermaldecomposition starts (Ti) and the temperature at which the decomposition rate is maximum (Tm) wereconsidered as thermal stability criteria. The thermostability was predicted using models of multilayer feedforward neural networks, having one or two hidden layers with four up to 36 neurons. The input param-eters taken into consideration were: the molecular mass, molecular polarization, number of aromaticunits, number of ferrocenyl units, number of cholesteryl units, number of C O bonds in the molecule,

elationship between structure andhermostability

number of N C bonds, number of N N bonds, and melting temperature. These parameters were selectedby establishing a hierarchy for the available molecular descriptors using genetic algorithms. During thevalidation stage of the models, the average percentage errors were smaller than 12%. These neuronalmodels were included into optimization procedures based on genetic algorithms with the goal to findideal molecular structures with the highest thermal stability (Ti = 420, 430, 440 ◦C and Tm = 460, 470,

◦

480 C).

. Introduction

The study of chemical, physical and biological phenomena fre-uently requires tedious experiments, which are both time andaterial consuming. Recent efforts are now focused on reduc-

ng the number of these experimental trials by introducing newomputational techniques capable of predicting the output of thexperimental research. Beside the economic advantages, theseechniques are expected to bring vital information regarding thehysical properties of materials and will certainly contribute to theesign of new-programmed structures.

By finding the quantitative relation between structure and ther-al stability for different structures could become a research

ubject of primary importance in computational chemistry.The prediction methods of a certain property can be evalu-

ted according to their classification into empirical, half-empirical,

nd theoretical or hybrid approaches. The empirical methods usu-lly require the presence of an expanded database and lead toon-linear relations between structure and property. Although the

∗ Corresponding authors.E-mail addresses: gapreot@yahoo.com, gapreot@ch.tuiasi.ro (G. Lisa),

lisa@ch.tuiasi.ro (C. Lisa).

040-6031/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.tca.2011.03.037

© 2011 Elsevier B.V. All rights reserved.

estimations are quickly made, however the precision of the pre-diction is reduced. Theoretical methods require a specific model,which cannot be always available, and its parameters are usuallydetermined by regression, on the basis of the experimental data.These methods are also expensive from computational point ofview, but they ensure excellent estimations of the characteristics.Most of the approaches allow a compromising method by the useof certain simplifying hypotheses, half-empirical and hybrid meth-ods fall into this category. These methods make possible the bestcompromise between the effort given to the development of themodel, the estimation time and the precision of the prediction oftheir characteristics. Hence, the methods based on the use of arti-ficial neuronal networks (ANN) and genetic algorithms (GA) offerthe advantages of an easy approach regarding their developmentand implementation, execution speed, maintaining in the sametime the accuracy of the prediction [1–6]. Different algorithms suchas: “machine learning”, including hierarchical clustering, “nearestneighbors” decision trees, “support vector machines” and baggingcould be also used for the prediction of the structure–characteristicrelation [7–9].

Liquid crystals containing metals in the molecule, known asmetallomesogens, combine the properties of liquid crystals withthe variety of characteristics of the coordination metals (color,electronic density, magnetism and polarization). This appeal-

imica

irrder

ccpcrtgt

l[ulet

ddtasere0

at

pipe

mosmttapdccmaphoBmi

f[

ka

G. Lisa et al. / Thermoch

ng combination of properties generated a great interest amongesearchers to synthesize and study the properties of these mate-ials. Obtaining liquid crystals with a wide mesomorphic domainepends on the careful combination of the important structurallements, respectively linear shape, rigidity and high values of theatio length/diameter [10,11].

Good thermal stability is an important property when theseompounds are used for applications that require heating, espe-ially in the fields where high temperature is demanded forrocessing [12]. In the case of liquid crystals, apart from the physi-al characteristics which are necessary (fluidity, optical anisotropy,educed viscosity), the compounds should be thermally stable inhe mesophase state. When the isotropic transition temperatureets higher than the decomposition temperature, a study of thehermal stability of these compounds is required.

The thermal stability of some ferrocene derivatives was ana-yzed in the literature, in the most cases, for polymer materials13–16]. For ferrocene derivatives, which are small molecular liq-id crystals, the analysis of the thermal stability is performed much

ess [17]. Due to its molecular simplicity, this type of moleculesnables a better understanding of the degradation processes and ofhe structure–thermal stability relation.

Fayet et al. [18,19] used the QSPR methodology for the pre-iction of the thermal stability of a number of 22 nitro-aromaticerivatives. The decomposition enthalpy, determined experimen-ally via calorimetry with differential scanning, was used asn indicator of the thermal stability for these compounds. Theemi-empirical models obtained by these authors, which containquations with three, four or six parameters, provide a good cor-elation between the computed values and the ones determinedxperimentally, respectively correlation coefficients bigger than.9.

The artificial intelligence tools (neural networks and geneticlgorithms) are appropriate methods to investigate these proper-ies reducing therefore the experimental demand.

Neural networks have been much studied for their massivearallel computing capability, the possibility of mapping the

nput/output relationships, and for investigating the course of arocess without modeling the physical and chemical laws that gov-rn the system [20].

Additionally, genetic algorithms can perform well for opti-ization of complex nonlinear systems. The solution of an

ptimization problem can be found through deterministic ortochastic approaches. The former contains the traditional opti-ization methods (direct and gradient-based methods) and has

he disadvantage of requiring the first and/or second-order deriva-ives of the objective function, and/or constraints. Therefore, thispproach is not efficient in non-differentiable or discontinuousroblems. Furthermore, the deterministic methods are depen-ent on the selection of the initial solution and usually tend toonverge towards local extrema of the fitness function, which islearly unsatisfactory for problems where the fitness varies non-onotonously with the parameters. The stochastic methods, such

s genetic algorithms, do not possess these drawbacks. GAs areart of the so-called evolutionary algorithms. They do not need toave any information about the search space and require only anbjective/fitness function that assigns a value to any solution [21].ecause of their own characteristics (flexibility, ease of operation,inimal requirements and global perspective), GAs have been used

n a wide variety of multiobjective problems [22,23].The combination of ANN with GA is widely used in a variety of

orms, from the optimization procedures including a neural model

24] to the genetic evolution of neural networks [25].

Many examples of modeling and optimization techniques arenown in the literature that benefit from the advantages of ANNnd GA [26], but they have not been yet applied to predict the ther-

Acta 521 (2011) 26– 36 27

mostability of organic structures. For instance, our group used GAoptimization accompanied by neural network models for differentchemical processes [27–29].

This paper reports the prediction of thermostability of certainorganic compounds, using different instruments of artificial intelli-gence (ANN + GA), coupled with the modeling of an ideal molecularstructure, in order to obtain the required physical characteristics—abetter thermostability. The relevant elements of the optimizationprocedure applied in this article are the following: obtaining theadequate structural descriptors for the thermal stability propertythrough molecular modeling, establishing the main parameterswhich influence this property with GA methods, quantifying thethermostability through significant temperatures for the process,ANN modeling of this property depending on structural charac-teristics and determining the optimal structures which lead to animposed thermostability with a procedure based on GA.

2. Experimental

2.1. Materials

The database we have created includes information on 100 newcompounds and their general structure is presented in Fig. 1 wherethe notations have the following meanings: I – ferrocene deriva-tives with the cholesteryl unit and the ferrocene rigidly connectedto the mesogen unit; II – ferrocene derivatives with the ferrocenerigidly connected to the mesogen unit; III – compounds with thecholesteryl unit rigidly connected to the mesogen unit; IV – com-pounds with the cholesteryl unit rigidly connected to the phenylunit; V – ferrocene derivatives with the ferrocene rigidly connectedto the cholesteryl unit; VI – ferrocene derivatives with the fer-rocene flexibly connected to the mesogen unit and the cholesterylunit rigidly connected to the mesogen unit; VII – ferrocene deriva-tives symmetrically substituted by ferrocene flexibly connectedto the mesogen unit and the cholesteryl unit rigidly connectedto the mesogen unit; VIII – Ferrocene derivatives asymmetricallysubstituted by ferrocene flexibly connected to the mesogen unitand the cholesteryl unit rigidly connected to the mesogen unitand a flexible chain; IX – ferrocene derivatives with the ferroceneflexibly connected to the mesogen unit; X – phenyl derivativessimilar to the phenyl flexibly connected to the mesogen unit andthe cholesteryl unit rigidly connected to the mesogen unit; XI– ferrocene derivatives symmetrically substituted with ferroceneflexibly connected to the cholesteryl unit; XII – ferrocene deriva-tives with the ferrocene flexibly connected to the cholesteryl unit;XIII – ferrocene derivatives with the ferrocene rigidly connectedto the mesogen unit and the cholesteryl unit flexibly connected tothe mesogen unit; XIV – ferrocene derivatives with the ferrocenerigidly connected to the mesogen unit and a flexible side chain;XV – symmetrical diferrocene derivatives with a flexible centralpart; XVI – symmetrical diferrocene derivatives with a flexible sidepart.

The compounds were obtained either through reactions of ester-ification of the ferrocenyl or phenyl units with the mesogen block,using the DCC/DMAP method or through reactions of condensationof the ferrocenyl or phenyl amine with aldehydes which containcholesterol. The confirmation of the synthesized structures wasperformed using spectroscopic methods (1H-RMN, 13C-RMN, IR,mass spectroscopy) as well as elemental analysis [30–34].

The variety of the structures presented in this study offersthe possibility to establish the relationship between structure and

thermostability and to generate a large database for the network.Several parameters that affect the thermal stability of these com-pounds can be studied such as the influence of ferrocene, thepresence of cholesterol, the length of the flexible bond, the posi-

28 G. Lisa et al. / Thermochimica Acta 521 (2011) 26– 36

Fe

mu Choles t

IFe

mu

II

mu Chole st

III

mu Chole st

IV

Fe

Cholest

V

Fe

mu Cholest

VI

Fe

mu Chole st

VIImuCholestFe

mu Cholest

VII I

Fe

mu

IX

mu

X

Fe

Cholest

XICholest

Fe

Cholest

XII

Fe

mu Chole st

XII I

Fe

mu

XIV

Fe

mu

XV

mu

Fe Fe

mu

XVI

Fe

N N

N C

muX

X = 1, 2, 3

Cholest

Cholest

ructur

tb

2

lT2prt

H X

Fig. 1. General chemical st

ion of the flexible bond, the mesogen unit, the influence of theond groups and the number of benzenic units.

.2. Equipment

The thermal stability of the ferrocene derivatives was ana-yzed using a Mettler Toledo derivatograph, type TGA-SDTA851e.he records were made in nitrogen environment, with a flow of

0 ml/min and a heating speed of 10 ◦C/min. The weight of the sam-les was 3–5 mg and the study was undertaken in a temperatureange between 25 and 900 ◦C. For comparable data, the opera-ional parameters were maintained constant for all the samples.

e of ferrocene derivatives.

STAR software was used for curve processing to obtain the thermalcharacteristics of the samples.

2.3. Methods

The most important characteristic of the neural networks is theirability to implicitly synthesize a certain model of the problem start-ing from a great number of examples. We could say that a neural

network creates the algorithm to solve a problem on its own, ofcourse if a representative number of particular cases are offered(training examples). The neural network extracts the informationpresented in the training examples (learns from the examples—the

imica

ttwoteh

wpanbssneo

msitcdr

bdaanpbfnfa

x

wgt

trvcp

lctbcnas

iibpupe

G. Lisa et al. / Thermoch

raining stage). In this situation, we could say that the network israined. During the working stage – or the reference stage – the net-ork will use the information acquired during the training stage in

rder to apply it to the new situations, but similar to the ones inhe training examples. This actually represents the ability to gen-ralize, meaning that ANN could correctly operate with data whichad not been presented during the training process.

The feed-forward neural networks represent a group of net-orks which are frequently used. They are characterized by theresence of a layer of input neurons, a number of hidden layers and

layer of output neurons. A generic notation for a layered neuraletworks is MLP(i:x:y:o)—multi-layer perceptron with i the num-er of input variables, x and y number of neurons in the first andecond hidden layers, and o the number of output variables. Thepecial interest shown by the researchers to this type of neuraletworks is generated, among other things, by their ability to gen-ralize well, namely to operate with data which differs from thenes presented during the training stage.

In this paper, neural networks are used to predict the ther-al stability of the ferrocene derivatives depending on a series of

tructural characteristics determined through molecular mechan-cs. These structural descriptors represent the input variables forhe neural model. The thermostability was quantified by two spe-ific parameters: the initial temperature at which the thermalegradation begins and the temperature at which the degradationate is maximum. These are the two outputs of the neural network.

The training algorithm chosen for the prediction of thermosta-ility of a series of ferrocene derivatives and phenyl analogouserivatives was a sort of supervised training, namely the back prop-gation algorithm. It is usually considered as the most importantnd the most frequently used algorithm for the training of neuraletworks. The mathematic optimization algorithm used in back-ropagation was the gradient descent algorithm. It was chosenecause it is the simplest optimization algorithm and has beenound to usually provide very satisfactory results. It updates theetwork weights and biases in the direction in which the per-

ormance function decreases most rapidly. One iteration of thislgorithm can be written:

k+1 = xk − akgk (1)

here xk is a vector of current weights and biases, gk is the currentradient, and ak is the learning rate. This equation is iterated untilhe network converges.

The modeling based on neural networks was accomplished withhe commercial simulator called Neurosolutions produced by Neu-odimension. The number of iterations during the training stagearied between 1000 and 20,000 epochs, the duration of data pro-essing was between 1 and 3 min and there was used a Pentium4ersonal computer with a 2 GHz processor.

In the case where neural networks are used for prediction prob-ems, the genetic algorithms could be used for searching the correctombinations of input data, the most suitable prediction horizon,he structures and the percentages of the optimum interconnectionetween the neurons, based on the training data and the predefinedriteria. The genetic algorithms, as well as the neural networks, doot always guarantee a perfect solution, but, in most cases, gener-tes decent solutions without the time and costs of an exhaustiveearch.

GA mimics the mechanics of natural selection and natural genet-cs to find the solution of optimization problems. Starting from annitial population (an initial set of solutions), generated on a randomasis, new populations are created repetitively from the parent

opulation until a solution is determined. Each solution in the pop-lation is called a chromosome (or individual) and represents aoint in the search space. In a GA, a fitness value is assigned toach individual according to a problem-specific objective function.

Acta 521 (2011) 26– 36 29

Generation by generation, the new individuals, called offspring,are created and survive with chromosome in the current popu-lation, called parents, to form a new population. Based upon theDarwinian theory of survival of the fittest, only individuals well fitfor the environment (i.e. optimization problem) proceed to the nextgeneration.

In this work, genetic algorithms are used with two goals: to esti-mate the minimum set of input parameters for the neural modelsand the design compounds with a pre-established thermostability,that means to determine the structural characteristics which lead toan imposed thermostability. A simple genetic algorithm was used,with a scalar function where the partial objectives were combinedweightily.

The optimization procedure is implemented in Matlab with orig-inal software, as specific functions were programmed for eachphase of the genetic algorithm.

3. Results and discussion

3.1. Thermogravimetrical analysis

The thermogravimetric study undertaken led to a series of con-clusions regarding the thermostability of the similar ferrocene andphenyl derivatives. Firstly, the thermal decomposition of thesecompounds takes place in two or several stages of degradation, theinitial temperature when degradation starts (Ti) reaching valueshigher than 200 ◦C, except only for some symmetrical diferrocenederivatives with a lateral flexible part. All the samples analyzed inthis study do not degrade completely to small gas molecules andgenerate a certain residuum, which depends on the chemical struc-ture of the samples. Additionally, the increase in the number ofaromatic rings induced a decrease of thermostability. This behav-ior could be explained by the increase in the number of connectinggroups between the aromatic chains that determine a decrease inthe thermal stability, as they can easily release free small moleculessuch as N2, CO2, CO or CH2O, by breaking the azo-type, iminic oresteric bonds. It was also noticed that the azo-junction induces alower stability than the esteric one.

Electronic effects in the aromatic units played also an importantrole in the thermal stability of these compounds. In the case of theferrocene derivatives containing a group with electron withdraw-ing effects (carbonylic) in the close proximity of ferrocene, the sameeffect of decreasing the thermal stability was observed in compar-ison to the ones which have a ferrocenyl unit connected directlyto the aromatic unit. This effect can be explained by the destabi-lization of the retroactive � bond between the iron atom and thetwo cycles of ferrocene induced by the electron withdrawing group,which is conjugated to the cyclopentadienyl ring of the ferrocene.The destabilization of the retroactive bond results in the decreaseof the thermal stability [35].

A comparison between the degradation temperatures charac-teristic to the derivatives containing ferrocene (type I or VI) andtheir homologous structures without ferrocene (type IV or X) showsclose thermostabilities (Fig. 2). This behavior is probably due to thefact that the thermal degradation starts from the connecting groups–N N– or –N CH– in both type of structures.

The presence of cholesterol in most of cases led to a slightincrease in thermostability. Thus, if the characteristic temperaturesof the compounds without cholesterol (type II or IX) are comparedwith those of the homologous structures which contain cholesterol(type I or VI), an increase in thermostability with approximately

10 ◦C was observed (Fig. 3). When considering the thermal stability,not only one molecule plays important role but also the neighbor-ing molecules, as the intermolecular forces have a very importantcontribution. These interactions influence the melting point and,

30 G. Lisa et al. / Thermochimica Acta 521 (2011) 26– 36

-0.04970-0.04470-0.03970-0.03470-0.02970-0.02470-0.01970-0.01470-0.00970-0.004700.00030

9008007006005004003002001000

Type I (sample 7) Type IV (sample 15)

a

b

-0.02990

-0.02490

-0.01990

-0.01490

-0.00990

-0.00490

0.00010

9008007006005004003002001000

T, ºC

T, ºC

dm/d

t, m

g/ºC

dm/d

t, m

g/ºC

Type VI (sample 29) Type X (sample 39)

Fig. 2. DTG curves (a) for the ferrocene derivatives with cholesteryl unit and fer-rocene rigidly connected to the mesogen unit (type I) and similar phenyl compounds(type IV); (b) for the ferrocene derivatives with ferrocene flexibly connected to themesogen unit and the cholesteryl unit rigidly connected to the mesogen unit (typeVI) and the similar phenyl compounds (type X).

-0.03990

-0.03490

-0.02990

-0.02490

-0.01990

-0.01490

-0.00990

-0.00490

0.00010

9008007006005004003002001000T, ºC

T, ºC

dm/d

t, m

g/ºC

dm/d

t, m

g/ºC

Type II (sample 8) Type I (sample 5)

a

-0.03999

-0.03499

-0.02999

-0.02499

-0.01999

-0.01499

-0.00999

-0.00499

0.00001

9008007006005004003002001000

Type IX (sample 37) Type VI (sample 28)

b

Fig. 3. DTG curves (a) for the ferrocene derivatives with the ferrocene rigidly con-nected to the mesogen unit (type II) and the homologous compounds which alsocontain the cholesteryl unit (type I); (b) for the ferrocene derivatives with theferrocene flexibly connected to the mesogen unit (type IX) and the homologouscompounds which also contain the cholesteryl unit (type VI).

-0.04490

-0.03990

-0.03490

-0.02990

-0.02490

-0.01990

-0.01490

-0.00990

-0.00490

0.00010

9008007006005004003002001000T, ºC

dm/d

t, m

g/ºC

Type XI (sample 40) Type XII(sample 41)

Fig. 4. DTG curves for the bi-substituted derivatives of type XI and mono-substituted derivatives of type XII.

consequently, the aggregation state of the material at a certaintemperature [36–38].

The disubstituted ferrocene derivatives (type XI) present aslightly higher thermostability than the monosubstituted ones(type XII), the initial temperature where the degradation beginsbeing between 260 and 280 ◦C for these compounds (Fig. 4).

As regards the influence of the position of the flexible part in thecase of diferrocene derivatives, the comparison between the degra-dation temperatures for the derivatives which contain the centralflexible part (compounds XV) with the derivatives which have aside flexible part (compounds XVI) showed a higher thermostabilityof those which have a central flexible part (Fig. 5).

The highest thermostability is held by the ferrocene deriva-tives of iminic type with the ferrocene rigidly connected to themesogen unit and with a flexible side chain (type XIV) [39]. Forthese compounds, the initial temperature when the decompos-ing process starts is around 400 ◦C, while the temperature forwhich the degradation rate is maximum is between 460 and 480 ◦C(Fig. 6).

3.2. Molecular modeling

The most difficult problem in modeling with neural networksof the thermostability of these small molecules was to estab-lish the input parameters, as they are represented by moleculardescriptors which should make a connection between the prop-erty under study and the structure of the molecules [40]. TheHyperchem 7.5 software was used to fulfill this goal. In order

to calculate the molecular descriptors, a well-defined structurehave to be created. After drawing the molecules and minimiz-ing the energy of the system in an optimum state, “single point”

-0.00970

-0.00870

-0.00770

-0.00670

-0.00570

-0.00470

-0.00370

-0.00270

-0.00170

-0.00070

9008007006005004003002001000

T, ºC

dm/d

t, m

g/ºC

Type XV (sample 46) Type XVI(sample 84)

Fig. 5. DTG curves for the symmetrical di-ferrocene derivatives with a central flex-ible part (type XV) and for the symmetrical di-ferrocene derivatives with a sideflexible part (type XVI).

G. Lisa et al. / Thermochimica Acta 521 (2011) 26– 36 31

Table 13D structures for a series of ferrocene derivatives and homologous phenyl compounds.

Sample code (S) 3D structure for the minimum potential energy Sample code (S) 3D structure for the minimum potential energy

1 43

7 57

11 74

25 84

29 96

32 100

cgtbloblpm[

Ft

haracteristics of a molecule were estimated. More examples areiven in Table 1 which presents some of the optimal structures ofhe compounds studied in this work. The optimum structure cane used in the simulations of molecular dynamics. The Molecu-

ar Mechanic Force Field (MM+) was used in order to obtain theptimum preliminary structure and to study the conformationalehavior of each ferrocene derivative and its thermostability ana-

yzed in this paper. It has been proved that molecular mechanicsroduces more realistic geometric values for most of the organicolecules due to the fact that it is expressed only in parameters

40].

T, ºC

dm/d

t, m

g/ºC

-0.00064

-0.00054

-0.00044

-0.00034

-0.00024

-0.00014

-0.00004

0.00006

9008007006005004003002001000

Type XIV (sample 24) Type XIV(sample 26)

ig. 6. DTG curves for the ferrocene derivatives with ferrocene rigidly connected tohe mesogen unit and a side flexible chain (type XIV).

The molecular descriptors estimated for the compounds fromthe database are presented in Table 2.

3.3. Neural network modeling

The selection of the descriptors used as input data in the neuralmodels was made with genetic algorithms.

The problem of the parameter estimation is to find the mini-mum subset of parameters which lead to similar results as the onesobtained with the entire set of data. The problem of optimizationwas resolved by using genetic algorithms. The result is a hierarchicsetting of the input parameters and, for the case study presentedherein, this hierarchy is presented in Table 2.

From the 20 potential input parameters, can be effectively takeninto consideration the first five to eight, whose weight values aresignificantly higher than the other ones, eliminated from the set ofinput data.

The molecular descriptors selected as input data were: themolecular weight (M), polarization of the molecule (P) and a seriesof structural characteristics: the number of aromatic cycles (NA),number of ferrocene units (NF), number of cholesteryl units (NC),number of C O bonds in the molecule (C O), number of N C bondsin the molecule (N C), number of N N bonds in the molecule

(N N).

The analysis of the experimental results regarding the ther-mostability of the ferrocene derivatives and the homologous phenylcompounds led to the conclusion that the compounds with a melt-

32 G. Lisa et al. / Thermochimica Acta 521 (2011) 26– 36

Table 2Values of the weights estimated for the molecular descriptors.

No. Structural parameter Description Values of theweights

1. P Polarizability 1.21742. NA Number of aromatic cycles in the molecule 1.10103. NF Number of ferrocene units in the molecule 0.94254. NC Number of cholesteryl units in the molecule 0.81425. M Molecular weight 0.80506. C O Number of C O bonds in the molecule 0.72537. N C Number of N C bonds in the molecule 0.64328. N N Number of N N bonds in the molecule 0.60889. C–O Number of C–O bonds in the molecule 0.099510. C–N Number of C-N bonds in the molecule 0.071711. C–C Number of C-C bonds in the molecule 0.052012. C–H Number of C-H bonds in the molecule 0.008913. Ltot Total length of the molecule 0.007714. S Surface of the molecule 0.002415. V Total volume 0.001916. C Number of carbon atoms in the molecule 0.0007717. Fe Number of iron atoms in the molecule 0.0005618. H Number of hydrogen atoms in the molecule 0.00033

umbeumbe

idmao

ImTmdamdmuiatatw

bff

wwooc

ttriaineat

19. N N20. O N

ng temperature smaller than the temperature when the thermalecomposition starts have a very good thermostability. Thus, theelting temperatures of the studied compounds were also included

s input parameters for the neural models and their values werebtained from the DTA curves.

For a neural model, two problems were formulated and solved.n Problem 1, there were taken into consideration the first five

olecular descriptors that have weights higher than 0.8 (Table 2).he output parameters were the initial temperature when the ther-al decomposition starts (Ti) and the temperature at the highest

egradation rate (Tm). The second approach, Problem 2, considerss output parameter only the initial temperature when the ther-al decomposition starts (Ti) and the following eight molecular

escriptors (Table 2): molecular weight (M), polarization of theolecule (P), number of aromatic cycles (NA), number of ferrocene

nits (NF), number of cholesteryl units (NC), number of C O bondsn the molecule (C O), number of N C bonds in the molecule (N C)nd number of N N bonds in the molecule (N N). The meltingemperature (Tt) was taken into account as input variable in bothpproaches. Hence, two variants that combine different parame-ers as input data for the neural models and different output dataere considered.

After the data collection for characterization of the thermosta-ility of ferrocene derivatives and the selection of the ones suitableor the neural networks, another equally important stage is per-ormed, namely creating the data sets for training and testing.

The available experimental data reached a number of 100 fromhich 80 were used during the training stage of the neural net-orks and 20 were kept for the testing stage. Then, the architecture

f the networks is established and the training and testing phasesf the neural network begins by modeling of the thermostability forertain ferrocene derivatives and homologous phenyl compounds.

The optimum number of hidden layers depends on the problemo be solved. Generally, one hidden layer is enough to solve most ofhe problems, however up to three hidden layers can be used. As aule, the number of neurons in the input layers, respectively output,s established by the nature of the application (the number of inputnd output variables). The neurons in the hidden layers have themportant role to detect the rules in the training patterns. A great

umber of hidden neurons, respectively intermediate layers, influ-nce in a negative way the generalization ability of the ANN and,lso, increases the volume of data to be processed, increasing theime of the training stage. A too small number of hidden neurons

r of nitrogen atoms in the molecule 0.00006r of oxygen atoms in the molecule 0.00003

could be insufficient to adequately represent the data and couldlead to a high mean squared average during the training and test-ing phases. The most used method to find the optimum numberof hidden layers and neurons (that means the topology of neuralmodels) is by successive trials. Consequently, in order to find thebest topology, several neural models of MLP type, with six or nineinput neurons, one or two hidden layers and one or two outputswere developed, corresponding to the two approached problems.

Problem 1. For the first problem, the initial temperature whenthe thermal decomposition starts (Ti) and the temperature at thehighest decomposition rate, during the first stage (Tm), were con-sidered as criteria of thermostability. These temperatures were theoutput parameters for the neural models. The first five moleculardescriptors with weight values higher than 0.8 (Table 2) and themelting temperature (Tt) were considered as input parameters. Thenetworks with one or two hidden layers, with four to 30 neuronswere tested. The main criterion used to find the best topology werethe mean squared error (MSE):

MSE =∑Out

j=1

∑Nri=1(dij − yij)

2

Nr · Out(2)

where Out represents the number of outputs (in this case, Out = 2),Nr is the number of data, yij is the output value for the i elementwith the processing of j element and dij is the output value desiredfor i with the processing of j element.

The correlation coefficient (r2) and the percentage error Ep (%)are also calculated for each training network architecture.

In order to avoid the overtraining of the neural networks, thevariation of the percentage error with the number of trainingepochs was monitored (Fig. 7). It was found that for the valueshigher than 10,000 of the number of epochs, the performances donot improve.

MLP(6:15:2) was selected as the best neural network based onMSE = 0.0105, r = 0.9642 and Ep = 2.2194, with 6000 iterations in thetraining stage. Good predictions obtained in the training phase withthis model prove that the network learned well the behavior of thecompounds.

We noticed that even simple topology of the neural networks

generated very good correlation between experimental and pre-dicted data. After the training, the neural model requires validationin order to verify its generalization capacity. The results obtainedduring this stage for MLP(6:15:2) are presented in Table 3.

G. Lisa et al. / Thermochimica Acta 521 (2011) 26– 36 33

2

2.5

3

3.5

4

4.5

5

180001600014000120001000080006000400020000Number of epochs

Ep(

%)

MLP(6:20:2) MLP(6:12:4:2) MLP(6:30:2)

Ft

t

E

waw

obdc

PptTmbnmN

tb

y = 0.9991x + 0.2642

R2 = 0.9998

100

150

200

250

300

350

400

450

450400350300250200150100

Temperature, ºC

Tem

pera

ture

, ºC

TP

ig. 7. Variation of the percentage error with the number of epochs for differentrained neural models.

Percentage relative error Er (%) was calculated to characterizehe testing phase, using the formula:

r = Yexp − Ynet

Yexp· 100 (3)

here Y are the values of the output data (Ti or Tm), whereas expnd net represent the experimental values and the values obtainedith the neural models.

The average relative errors (10.26% for Ti and 11.43% for Tm)btained with MLP(6:15:2) confirmed the fact that this network cane used for the prediction of the thermostability of the ferroceneerivatives and of the homologous phenyl compounds with liquidrystal properties.

roblem 2. The neural models created in the case of the secondroblem have only the initial temperature when the decomposi-ion of the analyzed compounds begins as output parameter (Ti).he input parameters taken into consideration were the following:olecular weight (M), polarization of the molecule (P), the num-

er of aromatic cycles (NA), the number of ferrocene units (NF), theumber of cholesteryl units (NC), the number of C O bonds in theolecule (C O), the number of N C bonds (N C), the number of

N bonds (N N) and the melting temperature (Tt).Different neural models of multilayer perceptron type were

ested, with 9 inputs, one output and two hidden layers and a num-er of intermediate neurons which varied between four and 36. The

able 3redictions during the validation stage obtained with MLP(6:15:2).

M P NA NF NC Tt

81.76 754.84 3 1 0 140

70.63 647.72 2 1 0 140

96.31 908.01 2 1 1 137

60.6 505.78 1 0 1 200

70.54 633.74 2 1 0 140

44.23 452.34 2 1 0 95

69.11 640.77 0 1 1 157

36.59 365.26 2 1 0 158

94.97 893 2 1 1 194

94.43 871.06 2 1 1 172

61.87 600.54 3 1 0 184

56.05 552.58 0 1 0 160

82.14 768.82 3 1 0 149

71.75 690.62 4 1 0 245

73.88 701.65 4 1 0 237

93.13 878.97 2 1 1 171

97.91 898.02 3 1 1 234

82.56 767.83 3 1 0 125

172.66 1582.92 4 1 2 270

79.79 740.81 3 1 0 135

Fig. 8. Comparison between the results obtained during the training stage withMLP(9:36:36:1) and the experimental data.

performance of the created models was analyzed in the same man-ner as for the previous problem, using mean squared error (MSE),correlation coefficient (r2) and percentage error Ep (%).

The modeling has started with networks with one hidden layerand different number of neurons, but the validation error washigher than 30%. Then, another layer was added and, also, manytrials were made. Finally, some neural networks which balance thesize and performance were chosen for modeling the process, fromwhich MLP(9:36:36:1) registered the best performance.

It was noticed that in this case, for an increase of more than15,000 in the number of epochs, the performance does not growsignificantly. Fig. 8 presents in comparison the experimental val-ues with the answers of the neural model in the training stagefor MLP(9:36:36:1). Correlation coefficient of 0.9998 and the meansquared error of 0.000243, accompanied with gradient (0.9991) andintercept (0.2642) of the fitted correlation, indicate a good perfor-mance of the model. The average relative error obtained during thevalidation stage (Fig. 9) with this neural model was 10.10%.

3.4. Optimization with genetic algorithms

An optimization problem can be formulated in terms of thefollowing elements: an accurate model of the process, a selectednumber of control variables, an objective function and a suitablenumerical method for solving the specified optimization problem.

Ti Tm Ti (network) Tm (network)

320 360 352 388340 370 320 371207 315 216 258370 480 328 419400 430 351 397280 325 248 306316 354 332 390309 324 338 345258 269 290 310317 350 331 362300 309 303 314280 330 342 422270 283 273 302302 313 302 310299 305 313 320247 257 286 319317 371 329 354390 450 398 441240 270 131 138300 340 366 404

34 G. Lisa et al. / Thermochimica

0

50

100

150

200

250

300

350

400

450

2019181716151413121110987654321

Validation data

Tem

pera

ture

, ºC

Ti_exp Ti_net

Ft

ttta

otmta

Ppoomti

nti

f

tat

Mfiibaotocatma

ig. 9. Predictions during the validation stage obtained with MLP(9:36:36:1) andhe experimental data.

Taking into consideration that the thermal stability is an impor-ant factor that determines the practical utility of a new compound,his paper proposes determining and analyzing optimum condi-ions that leads to a programmed thermostability using a geneticlgorithm based procedure.

GA was associated with a scalar objective function containingne or more objectives. In the last case, the weights attached tohe individual objectives are computed within the GA optimization

ethodology, along with the optimum decision variables. Becausehe search space becomes larger, it was considered a reasonablelternative to test a simple variant of GA, with reduced complexity.

roblem 1. The aim of the optimization was to solve the followingroblem: to determine the molecular weight (M), the polarizationf the molecule (P), the number of aromatic cycles (NA), the numberf ferrocene units (NF), the number of cholesteryl units (NC) and theelting temperature (Tt) which lead to imposed values of the initial

emperature and of the temperature when the decomposition rates maximum.

The objectives of the optimization were Ti = Tid and Tm = Tmd,amely the output parameters of the neural model to be equals tohe desired one (Tid, Tmd). In these conditions, the objective functions given by the following equation:

= w1

(1 − Ti

Tid

)2+ w2

(1 − Tm

Tmd

)2(4)

The goal of the optimization was the minimization of the objec-ive function, f. The objective function has a scalar form, and w1nd w2 represent the weights by which each partial objective con-ributes to the function f.

The optimization procedure includes the neural modelLP(6:15:2) and it is solved with a simple genetic algorithm. The

tness function of the GA is the scalar objective function (4). Thiss a multi-objective optimization problem because two goals muste accomplished simultaneously (the two imposed values for Tind Tm). Genetic algorithm provides, after an iterative calculus, theptimal values for decision variables (M, P, NA, NF, NC, Tt, which arehe inputs for the neural network model) and the weights for thebjective function (w1, w2). With these inputs, the neural networkomputes the parameters Ti and Tm which are compared with Tid

nd Tmd. If the two values are identical or the difference betweenhem is very small, we can conclude that the task of the opti-

ization, represented by the minimum of the objective function, ischieved.

Acta 521 (2011) 26– 36

The performance of a GA critically depends on the represen-tation of the solutions, the definition of the genetic operatorsthat transforms the solutions from one generation to another andthe values of the algorithm parameters. In this study, a floatingpoint representation of the parameters was used. Rank-based selec-tion procedure identifies in every generation the individuals to bemanipulated by the GA operators.

Population size (dim), number of generations (gen), crossoverprobability (cross) and mutation probability (mut) are known asthe control parameters of genetic algorithms. The values of theseparameters must be specified before the execution of GA and theydepend on the nature of the objective function.

Different values for the GA parameters were tested and theinfluence of their variation on the prediction of the thermostabil-ity presented by the ferrocene derivatives and by the homologousphenyl compounds was studied (Fig. 10). A careful analysis ofthe obtained results revels that the best predictions are made fordim = 100, gen = 400, cross = 0.9 and mut = 0.003. By keeping con-stant these GA parameters and changing the desired value for Tidand Tmd, optimum values of the decision variables were obtained(Table 4).

Data from Table 4 show that the best results are obtained forthe temperature when the decomposition rate is maximum andfor values of Tid and Tmd closer to the field in which there wereundertaken the experiments.

The obtained results are extremely important as they can offerinformation regarding the way in which the synthesis of suchcompounds should be carry out, in order to obtain structureswith a better thermostability, namely higher Ti or Tm. The resultspresented in Table 4 show that the thermostability rises at thesame time with the molecular weight and the polarization of themolecule. Three aromatic cycles or the presence of one cholesterylunit and one ferrocenyl unit could lead, also, to higher values forTi and Tm temperatures, which are considered criteria required bythe thermal stability.

One obvious problem of the optimization that combines objec-tives into a single function is that it may be difficult to generatea set of weights (w1 and w2 in Eq. (4)) that properly scalesthe objectives when little is known about the problem. Thepresent approach has the advantage of computing the optimalvalues for the weights coefficients of the objectives within thegenetic algorithm, along with the optimal values for decisionvariables.

Problem 2. The neural model MLP(9:36:36:1) was included intothe optimization procedure developed to solve the following prob-lem: finding the input parameters M, P, NA, NF, NC, C O, N C, N Nand Tt, which lead to an imposed value of the initial temperaturewhen the process of thermal decomposition starts. The objectivetaken into consideration was Ti = Tid, and the objective functionwas:

f =(

1 − Ti

Tid

)2(5)

and it requires minimum value.Different values for the GA parameters were tested together

with establishing the influence of their variation on the predic-tion of thermostability of ferrocene derivatives and homologousphenyl compounds. The lowest values of the objective functionwere obtained for dim = 800, gen = 400, cross = 0.7 and mut = 0.008.By keeping these GA parameters constant and by changing thedesired value Tid, optimal values of the decision variables, which

are presented in Table 5, were obtained.

The analysis of the results in Table 5 shows that the objectivefunction Ti = Tid was reached only in two of the three cases understudy, and that the thermostability can increase in the absence of

G. Lisa et al. / Thermochimica Acta 521 (2011) 26– 36 35

430

440

450

460

470

480

490

120010008006004002000

Dimension of initial population

TiTm

430

435

440

445

450

455

460

465

470

475

480

485

120010008006004002000Number of generations

TiTm

a b

430

440

450

460

470

480

490

2.521.510.50

Cross rate

Tem

pera

ture

,ºC

Tem

pera

ture

,ºC

Tem

pera

ture

,ºC

Tem

pera

ture

,ºC

TiTm

430

440

450

460

470

480

490

1.210.80.60.40.20

Mutation rate

TiTm

c d

Fig. 10. The influence of the GA parameters variation on the prediction of the thermostability presented by the ferrocene derivatives and by the homologous phenylcompounds; (a) dimension of the initial population; (b) number of generations; (c) recombination rate; (d) mutation rate.

Table 4Synthetic table regarding the accomplishment of the objectives for three values Tid/Tmd (Problem 1).

Tid/Tmd Decision variables Values of the weights Neuralmodeloutputs

Values oftheobjectivefunction (f)

M P NA NF NC Tt Ti Tm

440/480 882.96 131.58 3.26 0.88 0.80 77.02 w1 = 0.1601 w2 = 12.1797 436 480 0.000014430/470 829.17 112.42 2.52 1.10 0.96 232.79 w1 = 20.2734 w2 = 12.6214 429 470 0.000000420/460 783.51 92.47 3.20 0.91 1.10 177.56 w1 = 25.1706 w2 = 4.1267 420 459 0.000000

Table 5Synthetic table regarding the accomplishment of the objective for three values of Tid (Problem 2).

Tid Decision variables Neuralmodeloutputs

Values oftheobjectivefunction (f)

M P NA NF NC C O N C N N Tt Ti

440 695.78 127.21 3.32 0.55 0.07 1.80 1.16 0.06 130.75 435 0.0001151.751.44

tpw

eitc

430 689.22 102.18 3.57 0.67 0.33

420 722.36 104.08 3.26 0.89 1.00

he –N N– groups. This observation is similar to the ones from therevious studies on the thermal analysis when this functionalityas the first to decompose [36].

Two cases were approached in this work in order to study differ-nt variants to combine input and output parameters. In additions,

n the second case, is simpler to achieve the goal of the optimiza-ion because a single objective was included in the fitness function,ompared to Problem 1, where the optimization is multiobjectives.

0.91 0.58 128.29 430 0.000000 0.96 1.07 123.28 420 0.000000

4. Conclusions

The case studies analyzed in this paper illustrate very goodpredictability of the thermal stability of several ferrocene deriva-tives and homologous phenyl compounds with promesogenic

properties. The models created here were proven to be of highquality demonstrating the advantages of using a combination ofinstruments of the artificial intelligence (neural networks andgenetic algorithms) in the design of ideal programmed molecular

3 imica

sT

av

A

e6

EPE

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

6 G. Lisa et al. / Thermoch

tructures with higher thermostability: Tid = 420, 430, 440 ◦C andmd = 460, 470, 480 ◦C.

The ANN + GA methodology is quite general and can be alsopplied for other systems and processes with high chances to pro-ide accurate results.

cknowledgements

Lisa G., Wilson Apreutesei D. and Curteanu S. gratefully acknowl-dges for financial support from CNCSIS – UEFISCSU, PNII – IDEI00/2007.

Piuleac C.G. gratefully acknowledges for financial support fromuropean Social Fund and the Romanian Government, projectERFORM-ERA “Postdoctoral Performance for Integration in theuropean Research Area” (ID-57649).

eferences

[1] T.J. Shankar, S. Bandyopadhyay, Trans IChemE, part C, Prediction of extrudateproperties using artificial neural networks, Food Bioprod. Process. 85 (2007)29–33.

[2] P. Wang, Z. Huang, M. Zhang, X. Zhao, Mechanical property prediction ofstrip model based on PSO-BP neural network, J. Iron Steel Res. Int. 15 (2008)87–91.

[3] J.A. Lazzus, Prediction of solid vapor pressures for organic and inorganic com-pounds using a neural network, Thermochim. Acta 489 (2009) 53–62.

[4] J.P. Doucet, A. Panaye, 3D Structural information: from property predictionto substructure recognition with neural networks, SAR QSAR Environ. Res. 8(1998) 249–272.

[5] S. Saini, S.K. Singh, A. Garg, K. Khanna, A. Shandil, D.N. Mishra, Prediction of skinpenetration using artificial neural network, Int. J. Eng. Sci. Technol. 2 (2010)1526–1531.

[6] L.A. Dobrzanski, R. Honysz, Application of artificial neural networks in mod-elling of quenched and tempered structural steels mechanical properties, J.Achiev. Mater. Manuf. Eng. 40 (2010) 50–57.

[7] F. Nigsch, A. Bender, B. van Buuren, J. Tissen, E. Nigsch, J.B.O. Mitchell, Meltingpoint prediction employing k-nearest neighbor algorithms and genetic param-eter optimization, J. Chem. Inf. Model. 46 (2006) 2412–2422.

[8] H. MaXiao, R. Wang, Y. Xue, R. Li Ze, Y. Yang Sheng, Q. Wei Yu, Z. ChenYu, Advances in machine learning prediction of toxicological properties andadverse drug reactions of pharmaceutical agents, Curr. Drug Saf. 3 (2008)100–114.

[9] C.X. Xue, R.S. Zhang, H.X. Liu, M.C. Liu, Z.D. Hu, B.T. Fan, Support vectormachines-based quantitative structure–property relationship for the predic-tion of heat capacity, J. Chem. Inf. Comput. Sci. 44 (2004) 1267–1274.

10] O.N. Kadkin, Ho Kim, E. So, Y. Kim, M.-G. Choi, Synthesis and liquid crystal prop-erties of copper(II) and palladium(II) chelates with new ferrocene-containingenaminoketones, Polyhedron 28 (2009) 1301–1307.

11] O.N. Kadkin, H. Han, Y.G. Galyametdinov, Synthesis, Computational model-ing and liquid crystalline properties of some [3]ferrocenophane-containingSchiff’s bases and �-aminovinylketone: molecular geometry–phase behaviourrelationship, J. Organomet. Chem. 692 (2007) 5571–5582.

12] S. Vyazovkin, I. Dranca, X. Fan, R. Advincula, Kinetics of the thermal and thermo-oxidative degradation of a polystyrene–clay nanocomposite, Macromol. RapidCommun. 25 (2004) 498–503.

13] R.G. Gamper, P.T. Funke, A.A. Volpe, Synthesis and thermal degradation of someferrocene-containing polyazines and poly-schiff bases, J. Polym. Sci. Pol. Chem.9 (1971) 2137–2146.

14] X. Fengjuan, S. Minmei, P. Lei, L. Yunjun, Z. Junchai, Ferrocene end-cap hyper-

branched poly (amine-ester): structure and catalytic performance for thermaldecomposition of ammonium perchlorate, J. Inorg. Organomet. Polym. 21(2011) 175–181.

15] W. He, F. Deng, Y.Y. Jiang, D. Wu, H.L. Fan, X.G. Jian, Novel organometallicaromatic polyester based on ferrocene, Chin. Chem. Lett. 21 (2010) 748–752.

[

[

Acta 521 (2011) 26– 36

16] C.N. Myer, C.W. Allen, Copolymerization of chlorocyclotriphosphazene deriva-tives containing the methacycloylbutenedioxy and n-(ferrocenylmethyl)-n-methylamino substituents with methylmethacrylate, J. Inorg. Organomet.Polym. 17 (2007) 143–148.

17] A.C. de Souza, A.T.N. Pires, V. Soldi, Thermal stability of ferrocene deriva-tives and ferrocene-containing polyamides, J. Therm. Anal. Calorim. 70 (2002)405–414.

18] G. Fayet, P. Rotureau, L. Joubert, C. Adamo, QSPR modeling of thermal stabilityof nitroaromatic compounds: DFT vs. AM1 calculated descriptors, J. Mol. Model.16 (2010) 805–812.

19] G. Fayet, P. Rotureau, L. Joubert, C. Adamo, On the prediction of thermal stabilityof nitroaromatic compounds using quantum chemical calculations, J. Hazard.Mater. 171 (2009) 845–850.

20] Z. Xiong, J. Zhang, Neural network model-based on-line re-optimization controlof fed-batch using a modified iterative dynamic programming algorithm, Chem.Eng. Proc. 44 (2005) 477–484.

21] K. Deb, An introduction to genetic algorithms, in: Sadhana-Academy Proceed-ings in Engineering Sciences, vol. 24, 1999, pp. 293–315.

22] K. Deb, Multiobjective Optimization Using Evolutionary Algorithms, Wiley,Chichester, UK, 2001.

23] X.F. Yan, D.Z. Chen, S.X. Hu, Chaos-genetic algorithms for optimizing the operat-ing conditions based RBF-PLS model, Comp. Chem. Eng. 27 (2003) 1393–1404.

24] S. Curteanu, M. Cazacu, Neural networks and genetic algorithms used formodeling and optimization of the siloxane–siloxane copolymers synthesis, J.Macromol. Sci. A 40 (2007) 123–126.

25] N. García-Pedrajas, D. Ortiz-Boyer, C. Hervás-Martinez, An alternative approachfor neural network evolution with a genetic algorithm: crossover by combina-torial optimization, Neural Netw. 19 (2006) 514–528.

26] S. Curteanu, F. Leon, Hybrid neural network models applied to a free radicalpolymerization process, Polym. Plast. Technol. Eng. 45 (2006) 1013–1023.

27] S. Curteanu, F. Leon, Optimization strategy based on genetic algorithms andneural networks applied to a polymerization process, Int. J. Quantum Chem.108 (2008) 617–630.

28] F.A. Caliman, S. Curteanu, C. Betianu, M. Gavrilescu, I. Poulios, Neural networksand genetic algorithms optimization of the photocatalytic degradation of AlcianBlue 8GX, J. Adv. Oxid. Technol. 11 (2008) 316–326.

29] C.G. Piuleac, S. Curteanu, M. Cazacu, Optimization by NN - GA technique ofthe metal complexing process. Potential application in wastewater treatment,Environ. Eng. Manage. J. 9 (2010) 239–247.

30] D. Apreutesei, G. Lisa, H. Akutsu, N. Hurduc, S. Nakatsuji, D. Scutaru,Thermotropic properties of ferrocene derivatives bearing a cholesterylunit: structure–properties correlations, Appl. Organometal. Chem. 19 (2005)1022–1037.

31] D. Apreutesei, G. Mehl, D. Scutaru, Ferrocene-containing liquid crystals bearinga cholesteryl unit, Liq. Cryst. 34 (2007) 819–831.

32] I. Carlescu, A.M. Scutaru, D. Apreutesei, V. Alupei, D. Scutaru, The liq-uid crystalline properties of some ferrocene-containing Schiff bases, Appl.Organometal. Chem. 21 (2007) 661–669.

33] I. Carlescu, A.M. Scutaru, D. Apreutesei, V. Alupei, D. Scutaru, The liquid crys-talline behaviour of ferrocene derivatives containing azo and imine linkinggroups, Liq. Cryst. 34 (2007) 775–785.

34] R.M. Aioanei, I. Carlescu, D. Scutaru, Ferrocene-Containing Liquid Crystals,Buletinul Institutului Politehnic Iasi, Buletinul Institutului Politehnic Iasi, TomLV (LIX), 2009, pp. 181–190.

35] G. Lisa, D. Apreutesei Wilson, D. Scutaru, N. Tudorachi, N. Hurduc, Investigationof thermal degradation of some ferrocene liquid crystals, Thermochim. Acta507–508 (2010) 49–59.

36] D. Apreutesei, G. Lisa, N. Hurduc, D. Scutaru, Investigations on the thermalbehavior of some ferrocene derivatives with liquid crystalline properties, Sci.Study Res. VI (2005) 165–172.

37] D. Apreutesei, G. Lisa, N. Hurduc, D. Scutaru, Thermal behavior of somecholesteric esters, J. Therm. Anal. Calorim. 83 (2006) 335–340.

38] D. Apreutesei, G. Lisa, D. Scutaru, N. Hurduc, Investigations on thermal stabilityof some ferrocene liquid crystals bearing azo, ferrocenyl and cholesteryl units,

J. Optoelectron. Adv. Mater. 8 (2006) 738–741.

39] I. Carlescu, G. Lisa, D. Scutaru, Thermal stability of some ferrocene containingschiff bases, J. Therm. Anal. Calorim. 91 (2008) 535–540.

40] R. Todeschini, V. Consonni, in: R. Mannhold, H. Kubinyi, H. Timmerman (Eds.),Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, New York, 2000.