Research Article Electron Charge Density Distribution from X-Ray …downloads.hindawi.com/archive/2013/326457.pdf · 2019. 7. 31. · tronic charge density study of the -methoxybenzenecarbo-thioamide

Hindawi Publishing CorporationJournal of CrystallographyVolume 2013 Article ID 326457 7 pageshttpdxdoiorg1011552013326457

Research ArticleElectron Charge Density Distribution from X-Ray DiffractionStudy of the 4-Methoxybenzenecarbothioamide Compound

Mokhtaria Drissi Abdelkader Chouaih Youcef Megrouss and Fodil Hamzaoui

Laboratoire de Technologie et Proprietes du Solide (LTPS) Faculte des Sciences et de la TechnologieUniversite Abdelhamid Ibn Badis de Mostaganem 27000 Mostaganem Algeria

Correspondence should be addressed to Abdelkader Chouaih achouaihgmailcom

Received 31 March 2013 Accepted 1 July 2013

Academic Editors N Ishii and E Suresh

Copyright copy 2013 Mokhtaria Drissi et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The molecular electron charge density distribution of the title compound is described accurately using the multipolar model ofHansen and Coppens The net atomic charge and the in-crystal molecular dipole moment have been determined in order tounderstand the nature of inter- and intramolecular charge transfer The study reveals the nature of intermolecular interactionsincluding charge transfer and hydrogen bonds in the title compound In this crystal the molecules form dimers via NndashHsdot sdot sdot Sintermolecular hydrogen bondsThe dimers are further linked byCndashHsdot sdot sdotOhydrogen bonds into chains along the 119888 crystallographicaxis This study has also allowed us to determine the electrostatic potential and therefore locate the electropositive part and theelectronegative part in molecular scale of the title compound

1 Introduction

The chemistry of thioamides and their derivatives continuesto be of particular interest due to their interesting structuralfeatures and also due to their biological importance Hetero-cyclic compounds of these types exhibit a wide spectrum ofbiological activity and have extensive practical applications[1ndash3] In addition thioamides are important ligands in thefield of coordination chemistry [4] Due to these positivetraits thioamides have been under study for a long time butmuch of their basic chemistry remains unexplored

The heterocyclic 4-methoxybenzenecarbothioamide com-pound of chemical formula C

8H9NOS crystallizes in the

P212121space group with eight molecules in the unit cell

The general features of the structure have been describedpreviously [5] It contains two independent molecules withthe methoxy groups oriented in opposite conformationsThe mean planes of the carbothioamide groups are tilted by788(15) and 1116∘(9) from the mean planes of the benzenerings

In this work the crystallographic data were taken fromanother article [5] and used for the current study The struc-ture has been redetermined using the same X-ray diffractiondata

So this work focuses on the thermal analysis and elec-tronic charge density study of the 4-methoxybenzenecarbo-thioamide molecule The scope of this study is to modelaspherical features of the atomic electron density arisingfrom chemical bonding at low temperature of the moleculeby transferring the electron density multipole parametersobtained from accurate X-ray diffraction experiments andcalculate the molecular dipole moment In order to under-stand the nature of inter- and intramolecular charge transferthe electrostatic potential distribution of the molecule incrystal has been analyzed

2 Materials and Methods

21 High-Order Spherical Atom Refinement A high-orderspherical atom refinement (HO) on the non-H atoms is per-formed to get least-biased positional and thermal parametersHence due to the properties of the Fourier transform thisHO procedure refines the positional and anisotropic thermalmotion parameters only on core electrons Because valenceelectron scattering factors diffuse only at low resolution HOrefinement gives precise positions and displacements of thecore electrons only

2 Journal of Crystallography

In order to extract the aspherical features of the electrondensity the following strategy was designed First a full-anisotropic spherical atom refinement using starting param-eters from a Shelxl [6] refinement is performed Then themultipole refinement which has been developed by Hansenand Coppens [7] is selected to perform the electron densityanalysis using the MoPro package software [8]

In parallel the net atomic charge on the different atomsof the title compound and the molecular dipole momentwere also estimated by theoretical calculations Theoreticalcalculations were performed with the Gaussian package [9]at the HF6-31Glowast level of theory and semiempirical methods

A higher-order refinement of X-ray data becomes essen-tial to obtain accurate core positions and the associatedthermal parameters of the different atoms of the molecule

The X-ray scattering factors for S C N and O atomscome from the international tables for X-ray crystallography[10] while for H atom the bonded H-atom scattering curveof Stewart et al (1965) was used [11] The H atoms werefound by difference Fourier synthesis and their coordinateswere adjusted by extending along the CndashH and NndashH bonddirections to bond lengths of 1105 A and 1020 A respectivelyAny position error of the hydrogen atom will bring abouterrors strongly correlated with the dipolar population ofhydrogen Refinement details are displayed in Table 1

22 Charge Density Multipole Model The Hansen-Coppensmultipole formalism as implemented in the Mopro least-squares program for multipole refinement was used for bothobserved and theoretical structure factor fitting It describesthe crystal electron density as a superposition of asphericalpseudo-atoms each modeled on a multipole expansion

120588atom ( 119903) = 120588

119888( 119903) + 119875

119881119870

10158403120588V (1198961015840119903)

+

119897maxsum

119897

+1

sum

119898=minus1

119870

10158401015840119877

119897(119870

10158401015840119903) 119875

119897119898119884

119897119898(

119903

119903

)

(1)

Here120588119888and120588V are spherically averagedHartree-Fock core and

valence densities with 120588V being normalized to one electronThe Slater-type radial functions 119877

119897( 119903) = 119873

119897sdot 119903

119899119897

119897exp(minus1198961015840120585

119897119903)

modulate the spherical harmonic angular functions 119884119897119898plusmn

and119873

1is a normalization factorThe values for parameters 119899 = 119899

1

and 120585 were chosen according to rules provided by Coppens(1997) [12]

In practice two charge density variables the populationparameter and a kappa parameter which allows expansionand contraction of the valence shell are added to the conven-tional parameters of structure analysis [13] The populationparameters119875V and119875119897119898 are floated along with 120581

1015840 and 12058110158401015840 duringthe refinement

The sum over 119898 in (1) includes plusmn119897 so that for each one2119897 +1 functions are includedThe aspheric charge density wasdescribed at the octupole level (119897 = 3) for the atoms C N andO and the hexadecapole for the atoms S (119897 = 4) and at thedipole levels (119897 = 1 or 2) for hydrogen atoms not involved andinvolved in strong H bonds respectively Charge densities ofall hydrogen were considered to have cylindrical symmetryalong the corresponding hydrogen-heavy atom bond

Table 1 Refinement details

N R 119908119877

Spherical refinement 13 00274 003997Multipole refinement 68 002358 003165Wavelength 120582 (A) 071073Completeness () 994Resolution Sin120579120582 (Aminus1) 08N is the number of refined parameters 119877 = sum |119865119900| minus |119865119888|sum |119865119900| 119908119877 =[sum119908(|119865119900| minus |119865119888|)

2sum119908|119865119900|

2]12

C1

S1

H1A

H1BN1

C3

C2

C7

C4

C5

C6

C8

O1

H3H4

H7H6

H8AH8B

H8Cy

z

x

z

x

x

x

x x

xx

x

x

xy

xx

x

x xx

y

x

z

z

z

y

y

y

y

y

y

y

yy

y

x

x

y

y

Figure 1 Labeling of the atoms and definition of local orthogonalreference axes for the atom-centered multipolar functions

Table 2 Matrix for differences in MSDAs (mean square displace-ments of atoms) (values listed are 104 MSDAs for column atomminus that for row atom values correspond to chemical bonds)

Molecule A C5 C1 C8 C2 C7 C4S1 36C3 minus21 minus19N1 minus4C6 18C4 7C7 1C2 16Molecule B C14 C13 C9 C15 C12S2 42N2 31C11 minus3C12 7C10 28 35C15 1

The quality of a refined model can be monitored basedon the residuals and the goodness of fit apart from closelyinspecting the deformation density maps This model pro-vides the advantage of using constraints based on assumedlocal symmetry on the atomic sites to limit the number of

Journal of Crystallography 3

Table 3 Rigid-body motion parameters

119871 (rad2) 119879 (A2) 119878 (rad A)

(

000415 000036 minus000003

000011 minus000009

000029

) (

002595 000051 000165

005841 minus000143

003275

) (

minus000001 minus000055 minus000002

minus000011 minus000010 000050

minus000016 minus000011 000009

)

Table 4Net charges (q) in the different atoms of the title compound

Atoms qExperimental Ab initio Semiempirical

S1 minus0332 minus0250 minus0223O1 minus0124 minus0243 minus0207N1 minus0004 minus0026 minus0035C6 0026 minus0038 minus0166C3 minus0020 minus0079 minus0077C5 0022 0025 minus0146C2 0084 minus0098 0102C1 minus0002 minus0026 minus0212C8 0138 minus0037 minus0078C7 minus0019 minus0053 0077C4 0026 0134 minus0036H1A 0017 0207 0221H1B 0017 0213 0243H3 0019 0070 0135H4 0047 0060 0133H6 0053 0076 0163H7 0019 0063 0144H8A 0104 0075 0109H8B 0104 0066 0077H8C 0104 0062 0075

least-squares variables Figure 1 gives the local site symmetryof the different atoms of the molecule

3 Results and Discussion

31 Structural and Thermal Vibration Analysis The maincharacteristic of this structure is that the eight molecules inthe unit cell are engaged in seven chains formed by infinitechains of hydrogen-bonded coplanarmoleculesThedifferentchains link translationally equivalent molecules along the 119888crystallographic axis through CndashS and NndashH bonds

The rigid bond test indicated that the differences betweenthe mean square displacements amplitudes (MSDAs) alonginteratomic directions have magnitudes Δ le 10 times 10

minus4 A2

for nearly all the bonded pairs of the non-H atoms [14] Incontrast along intramolecular interatomic directions someΔvalues were considerably larger indicating that the moleculeis not entirely rigid and that low-frequency soft modesof internal molecular vibration contribute significant1y tothe observed mean square displacements [15] The thermalmotion analysis of the title compound has been performed

S1

C1C2

C3

C4

C5

C6C7

N1

C8

O1

H6 H7

H3H4

H1A

H1BH8A

H8B

H8C

Figure 2 ORTEPIII diagram of the title compound Thermalellipsoids are shown for the 30 probability level

using the THMA11 program [16] Selected results are pre-sented in Table 2

The rigid-body motion is described by three tensors 119879119871 and 119878 taking into account translation liberation and thecorrelation between translation and liberation of the rigidgroup respectively These tensors are obtained by a least-squares fit refinement using the observed atomic thermalmotion parameters obtained by the refinement

In terms of rigid-body 119879119871119878 the calculated anisotropicthermal parameters are given in the Trueblood notation assuch

119880

119894119895= 119879

119894119895+ 119866

119894119895119896119897119871

119896119897+ 119867

119894119895119896119897119878

119896119897+ 119863

2Ω

2119899

119894119899

119895 (2)

where 119866 and 119867 are geometrical parameters The analysis ofthe non-H atoms in terms of rigid-body motion yields the 119879119871 and 119878 tensor values summarized in Table 3 The ellipsoidsof the different atoms representing their thermal motiondescribed before are shown with an ORTEPIII diagram [17]in Figure 2

32 Electron Density Maps The aspherical atom model usedinmultipole refinement gives structure factor phases closer tothe true phases for crystals than the spherical or independentatom model does This enables the mapping of the electrondensity by the Fourier synthesis in various ways using theWinGX program [18] to represent the experimental densitydeformation and the VMoPro program implemented in theMoPro package to observe the dynamic density deformationof the molecule

The residual map using a spherical atom model is shownin Figure 3 from which we can notice the absence of thedensity on the atomic sites and the appearance of all the bonddensity peaks This map confirms the high quality of the data

4 Journal of Crystallography

Table 5 Components of the dipolar moment of the charge distribution from the point charge models (AM1 and B3LYP6-31Glowast) andcomparison with the components derived from experimental electron density (multipolar refinement)

Methods Models 120583

119909120583

119910120583

119911120583 (Debye)

X-Ray experiment Multipolar refinement minus21064 15995 15281 30546Semiempirical AM1 minus12175 13216 13220 22308Ab initio B3LYP6-31Glowast minus24646 22520 18834 38332

C1C2

C3C4

C5

C6 C7

S1

N1

H1AH7H6

H4 H3

O1

Figure 3 Experimental density map from high-order refinementContour map is 006 esdotAminus3

sets and the efficiency of the formalism used for the dataprocessing as proposed by Blessing [19]

The final electron density deformation was calculatedusing the following equation

Δ120588dyn ( 119903)

=

1

119881

sum

119867

[

1003816

1003816

1003816

1003816

1003816

119865mul (

119867)

1003816

1003816

1003816

1003816

1003816

119890

119894120593mul()minus

1003816

1003816

1003816

1003816

1003816

119865sph (

119867)

1003816

1003816

1003816

1003816

1003816

119890

119894120593sph()] 119890

minus1198942120587sdot 119903

(3)

This map is obtained from the calculated multipole structurefactors119865mul(119867) where119865sph(119867) is computedwith atomic posi-tions and thermal parameters obtained from the multipolerefinement Figure 4 shows this electron density deformationon the different atoms in the benzene ring section of the titlecompoundwhere one can easily observe the obvious increaseof the density and the good localization peaks in themiddle ofcovalent bonds of the cycle of the molecule In Figure 5 thedensity map contains two independent molecules A and BThe density maps are given in the two representations of themethoxy groups Figure 6(a) shows the density deformationat the plane 119910119911 and Figure 6(b) the deformation in the plane119909119910

A residual density map in the molecular plane obtainedin the final cycle of multipole refinement (see Figure 7)shows the adequacy of the multipolar model to describe theelectron experimental density of the molecule The quasi-totality absence of the density peaks again confirms the high

quality of the recorded data and the precision of the usedequipment

33 Hydrogen Bond Hydrogen bonds can be classified onthe basis of charge density The crystal structure of the titlecompound rests on chains of molecule joined by hydrogenbonds The almost linear hydrogen bonding links by transla-tion of equivalent molecules along the 119888 crystallographic axisin the unit cell In this crystal the molecules form dimersvia intermolecular NndashHsdot sdot sdot S intermolecular hydrogen bondsThe dimers are further linked by CndashHsdot sdot sdotO hydrogen bondsinto chains along the 119888-axis

Figure 8 shows the electron density in the plane ofthe hydrogen bonds formed by the atoms (N2 H2B andS1) existing in the molecule The electron density in theintermolecular hydrogen bonds is deficient in charge betweenthe donor and acceptor of the molecule

34 Net Atomic Charges Knowledge of the charge densityfunction can lead to some important properties of themolecule such as the net charges on the different atomsthe molecular dipole moment and the electrostatic potentialaround the molecule The valence population coefficients 119875119894Vwere used to estimate the partial charges on the differentatoms according to the following equation

119902

119894= 119899

119894minus 119875

119894

V (4)

where 119899119894is the total number of electrons of atoms 119894 The

population coefficients are presented in Table 4 The refinedatomic charges are generally of the sign expected fromchemical knowledgeH atoms are positively charged whereasO S and N atoms are negatively charged The net atomiccharges obtained by the X-ray experimental method usingthe multipolar model are compared to those derived fromthe theoretical calculations Semiempirical calculations werecarried out using the AM1 (Austinrsquos method) and ab initiocalculations were carried out at the HF6-31Glowast levels oftheory using the Gaussian package The results obtained byboth theory and experiment methods are summarized inTable 4 The experimental results and those derived fromthe semiempirical and ab initio calculations are in goodagreement concerning the signs of the net charges of the Hatoms and those of the N S and O atoms

Journal of Crystallography 5

Molecule A

H1B

H1AN1

C2

C1S1

H3

H7

H6

H4

C7

C6C4

C3

C5

O1H8C

H8A

C8

H8B

(a)

Molecule B

H2B

H2A

S2

C9 N2

C10C15

C14

C13C12

C11H11

H12

H14

H15

O2C16

H16B

H16A

H16C

(b)

Figure 4 Dynamic density maps of the two molecules A and B with the methoxy groups oriented in opposite conformations of the titlecompound Contour map is 005 esdotAminus3

H2B

H2AS2C9

C10 C11C15

N2H2B

H1B

H1AN1

C2

C1S1

H3

H11

H15

H7

H6H4

C7

C6C4

C3

C5

O1H8C

H8A

C8

Figure 5 Dynamic density map in the plane (S1 C1 and N1)contains two independent molecules A and B Contour map is005 esdotAminus3

35 Molecular Dipole Moment The molecular dipolemoment was first estimated using the population coefficientsof the multipolar density model from the following equation

120583 = sum

119894

119902

119894119903

119894+sum

119894

4119899 + 3

3119896

10158401015840

119894

(119875

119909119894119894 + 119875

119910119894119895 + 119875

119911119894119896) (5)

where 119903119894is the atomic position and 119899 is the number of elec-

trons in the molecule 119875119894are the dipolar electron populations

Dipole moment orientation in the molecule is shown inFigure 9The resulting molecular dipole moment direction is

in accordance with the evaluation of the positive sign of thenet charges on the H atoms and the negative sign of the netcharges on the O S and N atoms

In a parallel study the net charges on the different atomsand the molecular dipole moment were also estimated byab initio (B3LYP6-31Glowast) and semiempirical (AM1) calcu-lations In this procedure the treatment is confined to thevalence-shell electrons The results of these calculations arepresented in Table 5

From the results we can see a good agreement betweenthe value obtained with X-ray diffraction (30546D) and theother values obtained by theoretical calculation (AM1 gives22308D and DFT gives 38332D)

Analysis of obtained dipole moments shows that the sizeand direction of the dipole moment vector dependmainly onthe position of substituents Furthermore the orientation ofthe dipole moment vector is toward the sulfur atom

36 Electrostatic Potential The distribution of positive andnegative charges in a crystal fully defines physical propertieslike the electrostatic potential and its derivatives The elec-trostatic potential is important in the study of intermolecularinteractions of molecular systems

For a continuous charge distribution study the potentialis obtained by integration over the space containing thedistribution At a point defined by 1199031015840 the potential in givenby

120601 (119903

1015840) = int

120588total(119903)1003816

1003816

1003816

1003816

119903 minus 119903

101584010038161003816

1003816

1003816

119889119903 (6)

In which 120588total represents both the nuclear and the electroniccharge where the integration is over the molecular volume

6 Journal of Crystallography

H8A

H8B

C8

H8C

(a)

H16C

H16B

H16A

C16

(b)

Figure 6 Dynamic density map of the methoxy groups (a) deformation in the plane 119909119910 of the molecule A (b) deformation in the plane 119909119910of the molecule B Contour map is 005 esdotAminus3

S1

C1C2

C3C4

C5

C6C7N1

C8

O1

H6H7

H3H4

H1A

H1B

H8A

Figure 7 Residual density map 120588res = 120588

0minus 120588mult Contour map is

005 esdotAminus3

and 119903 represents the atomic position relative to commonorigin

The integration includes the atoms of only one moleculeand therefore does not include directly the effects of chargedistribution of the neighboring molecules

Figure 10 shows the electrostatic potential distributionin the plane of the base ring The extension of the positiveelectrostatic potential around the carbothioamide and CndashH groups and the regions of negative electrostatic potentialaround the nitro and hydroxyl groups confirm the nature ofthe intramolecular charge transfer as found by the orientationof the molecular dipole moment

The obtained point charges corresponding to S atom areminus0332 minus0250 and minus0223 e from experimental ab initioand semiempirical methods respectively But the region veryclose to S appears positive This is because of the fact thatS atom of the title compound is surrounded by the most

H2A

S2

N2

H2B

H1B

N1

C9

C1

S1

H15

Figure 8 Deformation density map in the plane of the hydrogenbond formed by the atoms (N2 H2B and S1) Contour map is005 esdotAminus3

electropositive hydrogen atoms (H1A = 0017 H1B = 0017 H3= 0019 and H7 = 0019 e)

4 Conclusion

This study has obtained good accurate results on the structurewhich gives high-quality descriptive model for the electroncharge density distribution from X-ray diffraction experi-ment It also shows that electron density can yield electronicproprieties such as dipole moment Its determination lets uslocate the region of the donor and the acceptor groups andalso the direction of charge transfer within the moleculeThe deformation of the electrostatic potential of the titlecompound shows that the electronegative potential is locatedon the side of methoxy group and electropositive potential ison the side of carbothioamide group

In the multipole refinement all nonhydrogen atoms wererefined anisotropically and subject to a rigid-bond constraintH atoms anisotropic parameters are obtained from 119879119871119878

Journal of Crystallography 7

z

x

y

minusrarr120583Aminusminusrarr120583Mminusrarr120583S

Figure 9 Orientation of the molecular dipole moment of the titlecompound the origin is at the center of mass of the molecule 120583

119872

molecular dipole moment from themultipolar model 120583119878 molecular

dipole moment from the semiempirical calculation 120583119860 molecular

dipole moment from the ab initio calculation

S1

C1

C2

C3C4

C5

C6 C7

N1

C8

O1

H6

H7

H3

H4

H1AH1B

H8A

H8BH8C

Figure 10 The electrostatic potential maps around the moleculeThe section is in the plane of the benzene ring

analysis The final 119877 factor (22) attests to the quality of thedata

To study the effect of electron charge transfer in biologicalactivity more we should perform vibrational analysis usingFT-Raman and FTIR spectroscopic techniques

References

[1] H Quiniou and O Guillton ldquo13-Thiazinesrdquo in Advances inHeterocyclic Chemistry A R Katritzky Ed vol 50 pp 85ndash156Elsevier San Diego Calif USA 1990

[2] S P Singh S S Parmar K Raman and V I StenbergldquoChemistry and biological activity of thiazolidinonesrdquoChemicalReviews vol 81 no 2 pp 175ndash203 1981

[3] M D Mashkovskii ldquoDrugsrdquo Torsing vol 2 p 244 1998(Russian)

[4] S T Lebana R Sultana and G Hendal ldquoHeterocyclicthioamides of copper(I) synthesis and crystal structures of cop-per complexeswith 13-imidazoline-2-thiones in the presence oftriphenyl phosphinerdquo Polyhedron vol 27 no 3 pp 1008ndash10162008

[5] S Ali S Hameed A Luqman T Akhtar and M Parvez ldquo4-Methoxybenzenecarbothioamiderdquo Acta Crystallographica Sec-tion E vol 66 no 6 p o1272 2010

[6] G M Sheldrick SHELXL97 Program for Crystal StructureDetermination University of Gttingen Gottingen Germany1997

[7] N K Hansen and P Coppens ldquoTesting aspherical atom refine-ments on small-molecule data setsrdquo Acta Crystallographica Avol 34 pp 909ndash921 1978

[8] C Jelsch B Guillot A Lagoutte and C Lecomte ldquoAdvancesin protein and small-molecule charge-density refinementmeth-ods using MoPrordquo Journal of Applied Crystallography vol 38no 1 pp 38ndash54 2005

[9] M J Frisch G W Trucks H B Schlegel et al GAUSSIAN-03Revision E01 Gaussian Wallingford UK 2004

[10] E Prince and A J C Wilson International Tables for X-RayCrystallography vol C Kluwer Academic Boston Mass USA2nd edition 1999

[11] R F Stewart E R Davidson andW T Simpson ldquoCoherent X-ray scattering for the hydrogen atom in the hydrogenmoleculerdquoThe Journal of Chemical Physics vol 42 no 9 pp 3175ndash31871965

[12] P Coppens X-Ray Charge Densities and Chemical BondingOxford New York NY USA 1997

[13] M A Spackman ldquo5 Charge densities from X-ray diffractiondatardquo Annual Reports on the Progress of Chemistry C vol 94pp 177ndash207 1998

[14] F L Hirshfeld ldquoCan X-ray data distinguish bonding effectsfrom vibrational smearingrdquo Acta Crystallographica A vol 32pp 239ndash244 1976

[15] R E Rosenfield K N Trueblood and J D Dunitz ldquoA test forrigid-body vibrations based on a generalization of Hirshfeldrsquosldquorigid-bondrdquo postulaterdquo Acta Crystallographica A vol 34 pp828ndash829 1978

[16] K N Trueblood THMA11 Program Department of chemistryand biochemistry University of California Los Angeles CalifUSA 1990

[17] L J Farrugia ldquoORTEP-3 for windowsmdasha version of ORTEP-III with a graphical user interface (GUI)rdquo Journal of AppliedCrystallography vol 30 no 5 p 565 1997

[18] L J Farrugia ldquoWinGX suite for small-molecule single-crystalcrystallographyrdquo Journal of Applied Crystallography vol 32 no4 pp 837ndash838 1999

[19] R H Blessing ldquoOutlier treatment in data mergingrdquo Journal ofApplied Crystallography vol 30 no 4 pp 421ndash426 1997

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