Indian Journ al of Pu re & Applied Ph ysics Vol. 40, November 2002 . pp. 80 1-8 15 )

Double relaxation I phenomena of ~i-substituted benzenes and anilines , in non-polar aprotic solvents under !tigh frequency electric field

. _ K~O~ tt~, !- \Ka.rmaka~-: (Mrs) iL;Out\ ,Y, S (s it )&LS ;"charyya\ _ I .

De~~rtmen t oflphy~iCS, Raiganj Co lI~ge (University Co llege{ PO Raiganj Dist. Uttar Dinajpur 733 134 ,... ........ ,.

Ie -mail: koushi kdutt ajsm@red iffmail.com]

Received I October 200 I; rev ised 12 February 2002: accepted 15 Apri l 2002 I

The derived linear equ ation (Xuij - XiOIXi( = m('1 +11) X{ IXi( - m2' 1' 2 for d i ff~ren t weight fractions ~I'j of di-substi tuted

benzenes and an ilines (j) in apro tic and non-po lar so lvenCi/U) C(,H(, and CCI4 under 9.945 GHz electrIC lield are obtained fro m the available measured dielectric relat ive permitti vi ti es at 35 °C. The dou Ie relaxation times ' I and '1 of the fl ex ible part and the whole molecu le are estimated from the slope and in tercept of the above e, uati onJ Xi/ and Xi/' arelthe real and imaginary parts of the hi gh frequency complex orientati onal dielectri c suscept ibi lity Xij' and Xui jl!.S the low frequency dielectri c susceptibili ty, whi ch is rea l. They arc. however. related with the measured relat ive permitti vities. Values of ' j are

_ calcul ated from the ra ti o of the ind ividual slopes of the var i a t ion~o f xi/' and X/ with W j at H 'j~O,!~~uming single Debye­li ke d ispers i o l~and. compared with Murt hy el al. [In dian J Ph.".I'. 63 B (1989) 49 1] and Gopalakr ishna [Trons Faroda." Soc, 53 ( 1957) 767J.!'le weighted contribu!i? ns CI and C2 towards dielectri c relaxations for 'I and ' 2 ca~. however,rbe obtained ­from Frohli ch' s theo reti cal fo rmul ations,e0f Xi(IXuij and Xi/,/Xuij and compared with those fro m the experimental y measured values of (X/IXuij )"j->O and (Xi('IXuij),,·j .... o.· The latter measured values are employed to get symmetric dist ribution parameter y to yield symmetric relaxati on time ' " 'The curve of ( 1/<1» log(cos <1» agai nst <I> in degrees together wi th the values of (Xi(IX"ij) ,,, .... O and (Xil"IX"ij )"j .... o experimentall y obtained. gives the asymmetri c dist ri but ion parameter 8 to get the characteris ti c relaxati qn time ' " . All these find in gs ultimately establish the diffe rent types of relaxation behaviour fo r such co mplex molecules: The dipole moments PI and P:> fo r the Il exible part and the whole molecul e are ascertained fro m 'I and 12\and the linear co~fficient s ~I of Xi( versus Wj and ~2 of (Jii versus Wi curves respecti vely. where (Jij is the hf conductivity.

( The values of J.l are finall y compared with the reported J.l 's and J.l lhe,,' S derived fro m avail able bond angles and bond , ,-moments of the substitu ted po lar groups of di-substi tuted anilinesJ o concl ude th at a part of the molecule is rotating while

the whole molecular rotation occurs for di -substituted benzenes! Tfle sli ght di sagreement between measu red values of J.l and Plhe" ca " howevcr:-be interpreted by the inductivc. mesomeri c~ and electromeric effects of the polar groups of the parent molecules. ' ~

1 Introduction

The die lec tric re laxation phenomena of nonspheri ca l and rig id polar liquid molecule in di fferent non-polar solvents at a given temperature, under a high frequency (hf) e lectri c fi e ld attracted the attenti on of a large number of workers l.

2• The

dipole moment f..I. from the relaxati on time 1 of the polar liquid molecule is of much importance'u to determine the shape, size, structure and molecul ar assoc iati on of a polar mo lecule. The rea l c;;' and imaginary C'I" parts of complex relati ve permitti vity Ci j' , static and inf inite frequency re lative

permi ttivities C"ij and C~ ij of a polar liquid molecule U) in a non-polar solvent (i) at a fixed ex perimental temperature under a single frequency e lec tric fie ld of GHz range are used to obtain the double re laxation times 12 and 11 due to rotation of the

whole molecule as we ll as the flex ible part attached to the parent molecule' .

Khameshara & Si sodi a\ Gupta et ae and Arrawati a et aP measured the re lat ive permitti vities of some di-substituted benzenes and anilines in aprotic non-polar solvents Cr,Hr, and CCI 4 under 9.945 GHz e lectric fi e ld at 35 °C to predict the conformati on of the molecules in terms of the re laxation time 1, based on the single frequency concentrati on variation method of Gopalakri shna~

and the dipole moment, f..I. by Higas i' s method III. The compounds are very interesting fo r the di fferent functi onal groups like -NH2' -CH3, -N02, - C I, etc. attached to the parent molecules. The samples were of purest quality and supplied by Mis Fluka and Mis E Merck, respecti ve ly. The solvents Cr,H(, and CCI .! of Mis BDH were used after double di stillation and

H02 INDI AN J PURE & APPL PHYS, VOL 40, NOVEMBER 2002

suitabl y dried over NaCI and CaCI2. £uii at 35 °C was measured by heterodyne beat method at 300 kHz

£~ ii=n O/ ' where the refracti ve index nOij was measured by Abbe ' s refractometer. The we ight fracti on WI of the respecti ve so lute, which is defined by the weight of the so lute per unit weight of the soluti on was taken up to four dec ima l pl aces, as the

accuracy in the measurement was 0.001 2 %. £/ and £ij" within I % and 5 % accurac ies were carried out by using the vo ltage standing wave rati o in slotted line and sho rt-c ircuiting plunger, based on the method of Hes ton et 0/. 11 . The poss ibl e ex istence of

11 and 12 of the compounds was, however, detected fro m the re lat ive permitti vity measurements I", under

9 .945 GHz e lectric fie ld at 35 °C.

Now-a-days, the usua l practiceI' is to study the die lectric re laxati on phenomena in terms of

die lectric orientat ional susceptibilities Xi j' Xij'S are linked with the orientationa l po larization of a po lar

mo lecul e . So it is bette r to work with X;;' s rather than £;;' s or conducti vity a;;' s as the latter are in volved with a ll the po lari zati on processes and the transport of bound molecul ar charges , respecti ve l y l~ .

The real Xi;'(= £/-£~ ij) and imaginary x t(=£,n parts of the complex die lectric orientationa l susceptibility

Xi/ ( = £ij'- Lij) and the low frequency susceptibility

X .. (= £ .. -£ '11) which is real of the di-substituted 11 11 11 11 cc

benzenes and anilines in C"H" and CCI~ of Table I are used to obtain the ir confo rmational structures in terms of mo lecul ar and intra-molecular dipo le

moments J..l2 and J..l1 involved with the estimated 12 and 11, Di-substi tuted benzenes and an ilines are thought to absorb e lec tric energy much more strongly, in nearl y 10 GHz e lectric fi e ld yie lding considerable va lues of 11 and 12, T he II po lar-non­po lar liquid mi xtures under investigation are found to show the double re laxation phenomena. Most of the po lar mo lecules are isomers of aniline and benzene . Some of the po lar solutes are di sso lved in Cr,H(" while a few in CCI4 to observe the solvent effect too . M oreover, a fe w of the po lar molecules are para-compounds, in which a peculi ar feature of re laxati on phenomena is expected ". A strong conc lus ion of double re laxati on phenomena of polar mo lecule in a non-po lar solvent , based on the single frequency measurement of re laxation parameters

can be made onl y if, the accurate value of Xuij (± I %) in volved with £uij and £~ ij is ava ilable . The use of no/

for £~ il often introduces"'x an additional e rror in the

ca lcul ati on, since £~ i j is approx imate ly equa l to 1-1 .5 times of IlOi/.

Bergmann et 01. I", however, devised a graphical

method to obtain 11 and 12 fo r a pure polar liqui d . The respecti ve weighted contribu tions ('I and ('2 towards die lec tric re laxati ons were estimated in te rms of 11 and 12, Bhattacharyya et 01.17 subsequently attempted to s implify the procedure of Bergmann et at. I" to get the same for a pure po lar

mo lecule with £', £", £u and £~ . measured at two di fferent frequenc ies in G Hz range. T he graphical ana lys is ad vanced by Hi gas i et 01. IX on po lar-non­polar liquid mi xture was a lso a crude one.

Thus, the obj ect of the present paper is to detect

11 and 12 and hence, to measure J..l1 and J..l2 using va lues of Xij based on the sing le frequency measurement technique I2.IY• The aspect of molecular orientati onal polarizati on is, however, achi eved by

introducing Xij because £~ i j which includes fas t po lari zation, frequentl y appears as a subtracted te rm in Bergmann equati ons. Thus, to avo id the clumsiness of a lgebra and to exc lude the fas t polari zation process, Bergmann equati ons l

(, are

simplified by the establi shed symbo ls of X/ , xt and Xuij of Table I in SI units:

xD .. . ( I ) X llij

and

... (2)

assuming two broad Debye-type dispe rsions fo r which the sum of C I and C2 is uni ty.

Eqs ( I) and (2) are now solved to get:

.. . (3 )

The vari ables (Xui j-X/)lX;;' and Xi/'iX;;' are plotted aga inst each other for different values of Wj of the po lar liquid under a single angular frequency w (=2rrf) of the e lectric fi e ld to get a stra ight line wi th inte rcept _W21112 and s lope w(11+12), as shown in Fig . I . The intercept and slope of Eq . (3) are obtained by linear regress ion ana lys is made with the

measured values of Xii of solutes in CC I4 and CoH" to get 12 and 11 as found in the 6th and 7th co lumns of

DUTTA cl al. :DOUBLE RELAXATION PHENOMENA

Table I - The real Xii' and imagi nary xii", parts of the complex dielectric orientational susceptibility Xij* and stati c dielectric susceptibility X"ij which is real for various weight fraction Wj of different di-substituted benzenes and ani lines at 35°C under 9.945 GH z electric field

Weight fraction Xii' Xii" X"ij It'-J

(I) o-ch loronitroben zene in C" H(,

0.0109 0. 117 0.066 0. 167 0.0173 0.169 0.100 0.254 0.0217 0.197 0.126 0.305 0.02S0 0.253 0.165 0.376 0.0330 0.284 0.192 0.461

(III ) 4-chloro 3-nitro toluene in C"H"

0.0072 0.075 0.046 0.132 0.0144 0.098 0.088 0.241 0.0224 0.150 0.133 0.310 0.0323 0.200 0179 0.464 0.0453 0.271 0.252 0.630

(V) o-nitrobenzotrifluoride in C"H(,

0.0085 0.094 0.058 0.154 0.0167 0.166 0.108 0.257 0.0244 0.226 0.159 0.384 0.0335 0.297 0.205 0.495 0.0402 0.353 0.255 0.604

(V II ) 2-chloro 6-methyl aniline in C" Hr,

0.0184 0.072 0.017 0.075 0.Q305 0.096 0.026 0.097 0.0417 O. I 17 0.040 0138 0.0573 0 .1 63 0.058 0.191 0.0636 0.183 0.065 0.2 14

(IX) 3-chloro 4-methyl aniline in C"H"

0.0214 0.088 0.032 0.099 0.0374 0 .1 23 0.060 0.167 0.0403 0.133 0.066 O.IS5 0.054S 0. 166 0.091 0.244

(XI) 5-chloro 2- met hyl aniline in C(JIr,

0.0194 0.094 0.050 0.123 0.0249 0.1 10 0.064 0 .1 53 0.0307 0.129 0.081 0 .1 91 0.0480 0. 182 0.129 0.292 0.0569 0.206 0.150 0.362

Table 2. The variables of Eg . (3) are extracted from Table I, where all the data are collected together, system-wise, up to three decimal places in close agreement with the expected l 2

1 2 and 1[ of Table 2.

Both 1 2 and 11 were found to deviate significantly, when the data of Table I were taken up to two decimal places with the claimed accuracy of measurement. The values of correlation coefficient

Weight fract ion wi Xii' xii" X"ij

(II) 4-chloro 3-nitro benzotrifluoride inCCI~

0.0050 0.122 0.019 0.155 0.0101 0.145 0.037 0.IS5 0.0147 0.150 0.054 0.233 0.0193 0.167 0.068 0.266 0.0231 0 .1 79 0.075 0.302

(IV) 4-chloro 3-nitro toluene in CCl4

0.0041 0.145 0.039 0.20S 0.0087 0.173 0.071 0.315 0.0128 0 .1 90 0.101 0.419 0.0162 0.2 18 0.138 O.4R2 0.0203 0.241 0.165 0.586

(V I) m-nitrobenzotrifluoride in C(,Hr,

0.0096 0.082 0.032 0.094 0.0173 0.103 0.060 0.157 0.0245 0.129 0.082 0 .202 0.0326 0.1 57 0.106 0.265 0.0380 0.187 0. 128 0.323

(V III ) 3-chloro 2-methyl ani line in Cr, Hr,

0 .OOS3 0.059 0.018 0.065 0.0207 0.099 0.043 0.128 0.0270 0.128 0.055 0.166 0.0363 0.165 0.073 0.221 0.0421 0.193 0.OS6 0255

(X) 4-chloro 2-methyl aniline in C"Hr,

0.0196 0.124 0.063 O. 151 0.0300 0.157 0.090 0.2 19 0.0417 0.199 0.121 0.304 0.0481 0.216 0.138 0.354

(r) and the % error were worked out to place them in Table 2, only to see how far the variables of Eg. (3) are collinear to each other.

The relaxation times 1'S due to Oebye model are

measured from the slope of Xi/' versus X/ curves of Fig. 2 and the ratio of the individual s lopes of X/' versus Wj and X;( versus W i curves at wi~O of Figs 3

804 INDIAN J PURE & APPL PHYS , VOL 40, NOVEMBER 2002

and 4, respective ly. Va lues of 1 from both the methods are entered in the 8th and 9th columns of

Tabl e 2 onl y to see how far they agree with 11 and 1 2

due to doubl e re laxat ion method of Eq . (3) .

:=-~ -. -~

(5

~ --

1.5 ~------------------~----~~

1.2

0.9

0.6

0.3

0.0 0.0 0.2 0.4

"/ ' x.. X I) I)

0.6 0.8 1.0

Fig. I - Linear variation of (Xoij - Xi()lXi( wi th Xi,"/X,( for different values of Wi for : I. o-chloronitrobenzene in Cr,H(, (- 0 - ); II. 4-chloro 3-n itrobenzotrilluoride in CCI~ (-6 - ); III. 4-ch loro 3-ni trotoluene in C(,Hr, (-0-); IV . 4-chloro 3-nitrotoluene in CCI ~ (-e -) ; V . o-nitrobenzotritluoride in Cr,Hr, (-A -); VI. m-nitrobenzotriflu oride in C(,H(, (- . -) ; V II . 2-chloro 6-methyl ani l ine in C(, H(, (- T -): VIII . 3-chloro 2-methyl aniline in C(,H(, (- * -): IX. 3-chloro 4-methyl aniline in C(,Hr, (-0-) : X. 4-chloro 2-methyl anil ine in C(,Hr, (-\7- ) and XI. 5-ch loro 2-methyl aniline in Cr,H(, (-181 -) at 35 °C under 9.945 GHz electric field

The theoret ical va lues of C I and c~ towards

die lectri c di spersions for 1 1 and 1 2 of different di­substituted benzenes and anilines in C,Hr, and CCI~ were calcu lated from Frohlich 's20 theore tical

formulation s o f X;/IXoii and X;;"IXoii ' The ex perimenta l va lues of C I and C2, on the othe r hand , were fou nd

out from (X/ IX",)wi-->O and (Xi/'IXoii)"'i -->o by graphical

variati ons of X;/IXoii and X/'IXoij with va lues of Wi of Figs 5 and 6, in order to place the m in Table 3 for

comparison. The pl ots of X/IXoij and Xii"IXoij agai nst I'Vj of the polar liq uids in Figs 5 and 6 are the leas t square fitted curves WIth the experimenta l points placed upon them . With the va lues of rhe inte rcepts presented in Table 3 fro m Figs 5 and 6 and the

graphi cal plot of ( 1/<jl) log(cos <jl) aga in st <jl in degrees gi ven e lsewhere\ the sy mmetric and

asy mmetric distributi on parameters y and 8 re lated

to sy mmetric and characterist ic re laxati on times 1 ,

and 1" of the molecul es were de termined . They are seen in Table 3. The object of such determination s

of y, 8, 1, and 1;" is to conclude the mo lec ul a r no n­ri gidity and di stributi on of re laxation behav iour as well.

0.30 ~---------r-r---"

:0 :;:; 0.24 a. w U en :::J en U 0.18

'L: -U ~ .!E ""0 o 0.12 t <1l a. ~ ~ 0.06 Cl <1l E

o. 00 L....£..44....-----J"-L...~---I._-'--_.L_-'--___.J

0.0 0.1 0.2 0.3 0.4

Real part of dielectric susceptibility Xij '

Fig. 2 - Linear variati on of Xi{ with X/ for di fferent values of Wi for: I. o-ch loronit robenzene in (, Hr, (-0 -) ; I I. 4-chloro 3-nitrobenzotrifluoride in CCI ~ (- 6-); II I. 4-chloro 3-nitroto luene in Cr,Hr, (-0-); IV. 4-chloro 3-nitrotoluene in CCI~ (- e -): V. o-nitrobenzotritluoride in C(,Hr, (-A -): VI. m­nitrobenzotritluoride in C(,H(, (-. -): V II. 2-cll loro (i-methyl aniline in C(,H(, (- T -) ; V III. 3-chloro 2-methyl an iline in C" H(, (-* -); IX. 3-chloro 4-methyl an ili ne in C(,H" (-0-); X. 4-ch loro 2-methyl aniline in Cr,H(, (-\7 --) and XI. 5-chloro 2-meth yl ani line in C(,H(, (-181 -) at 35 °C under 9.945 GHz electric field

DUTTA ef (l 1. :DOUBLE RELAXATION PHENOMENA 805

Tab le 2 - The relaxati on times ,~ and ' I from the slope and intercept o f straight line Eq. (3) , co rre lati on coefli cient s )"s and % of error in reg ression technique, measured ' i fro m the slope of xt versus Xi(of Eq. ( 15) and the ratio o f the ind ividual slopes of X/' versus IVi and Xi( versus IVi at wi-'O of Eq. ( 16). reported , . symmetri c and charac teristic relaxation times " and ' cs for different disubst ituted benzenes and ani lines at 35 °C under 9.945 GH z elect ri c fi eld

Sys tem Eq. (3) Corrl . % with S.No. Coel'!' o f

Siopellntercept ()') Error

(I ) o-chl oro ni tro-

benzene in Cr,Hr, 1.3 10 0.301 0.82 9.88

(II ) 4-chl oro 3-nitroben-zotritluoride in CCI ~ 1.666 0.059 0.95 2.94

(II! ) 4-chloro 3-nitro-to luene in Cr,!-l r, 1.865 0.389 0 .88 6.80

(IV) 4-ehloro 3-nitro-toluene in CCI ~ 2.283 0. 134 0 .98 1.19

(V ) 0 - nit robenzo-trifluoride in Cr,Hr, 1.063 0 .067 0.70 15.38

(VI ) m-nitrobenzotri -flu oride in Cr,Hr, 1.898 0.597 0.99 0.60

(V I! ) 2-chloro 6-meth yl aniline in Cr, Hr, 1.37 1 0.3 13 0 .93 4 .08

(VI!I) 3-chloro 2-me-thyl aniline in Cr, Hr, 1.596 0.386 0 .99 0.60

( IX ) 3-chl oro 4- meth yl aniline in Cr, Hr, 1. 89 1 0.561 0.99 0.67

(X ) 4-chl oro 2- methyl an iline in Cr, Hr, 3.2 17 1.428 0.99 0.67

(XI) 5-ch loro 2- methyl anil ine in C(, Hr, 2.075 0.811 0.97 1.78

The dipole moments /J.2 and /J. I were then measured in terms of dimensionless parameters (b) invo lved with measured values of '( of Table 2 and

coeffi c ients ~ I and ~ 2 presented in Table 4 of the variations of hf X/ and tota l hf conductivity O'ii with va lues of Wi of Figs 4 and 7, respectively . The

measured values of /J. are presented in Table 4 in orde r to compare wi th theoretical dipole moment

/-l lhc" derived from available bond angles and bond moments of the substituent polar groups attached to the parent molecules as sketched in F ig. 8. The structural aspect of some interesting polar molecules presented tn Fig. 8 exhibits the prominent mesomeric , induct ive and e lectromeric effects of the substituted polar groups. All these effects are taken

into account by the ratio /J.CXp//J.lhcm in agreement with the measured valuesr,x of /J. presented in Table 4 .

Estimated Measured ' i in ps Rept. " Ln

'2 and 'I from ,in in ps in ps in ps ps

Eq . ( 15) Eq.( 16)

16.2 1 4.76 12.08 10. 13 13.5 7.87 17.08

26.08 0.58 16.43 22 .66 2 1.1 0.00

26.02 3.83 16. 13 19.89 20.9 10.76 39.65

35 .57 0.96 21.47 22.6 1 35.0 1.47 38.84

15.93 1.08 12 .09 11.08 13.7 10 .89 28.83

24.0 1 6.37 14 .33 36.57 19.7 6 .20

17.3 I 4.63 7.05 14.55 7.8 4.08

20.79 4.76 7.98 11 .49 9 .9 4.57

24.37 5.90 12.07 13.65 13.6 7.28

42.97 8.5 1 12.80 11 .04 18.5 7.59

24.85 8.36 14.34 14.35 16.6 5.60 4.52

2 Formulations of Cl and C2 for '(I and '(2

Eqs ( I) and (2) are now so lved to get CI and ('2,

where :

. .. (4)

... (5)

where a l = 0)1 1 and a 2 = (O't2 provided ~ > a l . The molecules under cons iderat ion are of complex type and onl y little data are ava ilabl e under sing le frequency measurement in the low concentrat ion

region . A continuous di stributi on of '( with two

discrete va lues of '(I and '(2 cou ld, therefore, be ex pected. Thus, from Frohlich' s equations20 based

806 INDIAN J PURE & APPL PHYS, VOL 40, NOVEMBER 2002

on di stributi on of 1: between the two ex treme va lues

of 1:1 and 1:2, one gets:

. . . (6)

X~ I r _ I ( ) - I ( ) ] - -- =- Llan WT 2 - Ian WT 1 X liii A

... (7)

where the Frohlich paramete r A is g iven by A = In

(1:/ 1: 1) , The theore tical va lues of X;/IX";I and X/'IX";I of Eqs (6) and (7) were used to get theoreti ca l C 1 and C2 from Eqs (4) and (5) in order to compare them with the ex perimenta l va lues of C 1 and C 2 from the

graphica l pl o ts of X' I'IX"IJ and X/,IX";I at WI~O, as seen in Figs 5 and 6, respec ti ve ly. Both the theoreti ca l and experimenta l va lues of CI and C2 are presented in Table 3 fo r compari son.

~;.:z 0.30 ,.--------------.--,

>­::: :0 +=' 0.. (l) () C/) ::J C/)

() ·c .-() (l)

~ "0

0.24

0.18

'0 0.12

t co 0..

~ co 0.06 c Ol co E

0.00 0.02 0.04 0.05

Weight fraction Wj

Fig. 3 - Variation of X.;" agai nst Wi of solutcs at 3S °C under 9.945 GHz electri c fi eld for: I. o-chloron itrobenzcnc in C"H" (-0-): II. 4-chloro 3-nitrobcnzotrifl uoridc in CCI.j (-6-); III. 4-chloro 3-ni trotoluenc in C"H(, (- 0 - ); IV. 4-chluro 3-nitroto luenc in CCl 4 (-e -); V. o-nitrobcnzotri fl uori dc in C(,H" (- A -); VI. m-nitrobenzotrifluori de in Cf,Hf, (-.- ); VII. 2-chloro 6- lllethyl ani l ine in C(,H" (- T - ); V III . 3-chloro 2-methyl ani linc in C"H" (- * -) ; IX . 3-chloro 4- lllcthyl anil inc in Cf,Hf, (- <8>-); X . 4-chloro 2-lllcthyl ani l inc in Cf,H(, (-V-) and X I. 5-chloro 2-mcth yl ani l inc in C(,l-I (, (- (gJ - ) at 35 °C undcr 9.945 GHz electri c fi cld

0.4 r------..,.------.---.

:=-~

>. ~

.0 -Q. Q.) U Cf) :J Cf)

u ·c -u Q.)

Q.) ,-"0 '+-0 t ro Q.

ro Q.)

0:::

0.3

0.2

0.1

0.0 0.00 0.02 0.04

Weight fraction w J

0.06

Fig. 4 - Vari ation of X;/ against lI 'i of soluh;s at 35 °C under 9.945 GHz elcc tri c field for: I. o-chloronitrpbcnzcnc in C(, H(, (-0-); II. 4-chloro 3-n it robenzotri fl uoridc in CCI.j (- 6- ): III. 4-chloro 3-nit ro tolucnc in C" I-I (, (- 0-) ; IV. 4-chloro 3-ni tro tolucne in CCI.j (-e -) ; v . o-n it robenzotri rluoride in C(,I-I (, (- A - ); V I. m-ni trobcnzotrilluori de in C(, H" (-. -) ; V II. 2-chloro 6-methyl ani l ine in C"H(, (- T -); V III. 3-ch loro 2-mcthyl ani l inc in C"H" (- * - ): IX. 3-chloro 4-meth yl aniline in C(, H(, (-<8>-) ; X. 4-chloro 2-meth yl anilinc in Cf,H" (- V - ) and X I. 5-ehloro 2-methyl ani l ine in Cr.H" (- (gJ - ) :1 t 35 °C under 9.945 GHz electric fi eld

3 Distribution Parameters Related to Symmetric and Characteristic Relaxation

The mo lecul es are expected to show e ithe r symmetrical c ircul ar arc or a skewed arc in additi on

to othe r modei s1l when the va lues o f X/'IX,,;i are

pl otted aga inst X/IX";i at wi~O fo r varI OUS frequencies of the e lec tri c fie ld to y ield

Xi;

Xoi;

Xi;

Xoii

I ( . ) I- y + .IWTs

Ii ( 1+ jWTn)

. . . (8)

.. . (9)

DUTTA ef al .: DOUBLE RELAXATION PHENOMENA S07

Table 3 - Frohlich's parameter A, theoretical and cxperi mental values of Xi/IXoij and Xi('IX"i j or Frohli ch cquat ions (6) and (7) and rro m tilting cquati ons of Figs 5 and 6 at lI 'j-'O, respecti vely, theoreti cal and experimental relative contributions (;1 and c, towards dielectri c dispersion due to 1 1 and l~ symmetri c and asymmetri c distribution parameters y and 8 for po lar-non-po lar liquid mixtures of di -substituted benzenes and anil ines at 35 °C under 9.945 GHz elect ric fi eld

System A= Ln Theoreti cal Theoretical Exptl. valucs or Exptl. va lues or Estimated

wi th SI.No. (l ill) values or values of x';!X"ij & X"i/X"ij CI & c, va lues or

Xi;'/X"ij & C I and C2 at Wj->O or y and 8 X,('IX"ij rrom Figs 5 & 6 Eqs (6) & (7)

(I )o-chl oronit ro-1.225 0.746 0.4 10 0.526 0.533 0.733 0.349 0.599 0.37 1 0. 13 0.010

benzene in C(J Ir,

(II ) 4-chloro 3-ni tro-benzotrifluoride in 3.806 0.830 0.259 0.687 0.525 0.890 0.027 0.894 -0.0 12 0.82

CCI-l

(III ) 4-ehl oro 3n it ro-1.9 16 0.677 0.409 0.527 0.649 0.600 0.309 0.508 0.435 0.28 0.007

toluene in C(J I(,

(IV) 4-chloro 3-n i tro-3.6 12 0.754 0.30 1 0.638 0.703 0.863 0. 144 0.823 0,253 0.38 0.002

toluene in CCI -l

(V ) o-nit robenzo-2.69 1 0.873 0.266 0.653 0.444 0 6 16 0.347 0.288 0.655 0.2 1 0.008

trifluoride in C(,H(,

(V I) m- nitrobenzo-1.327 0.6 11 0.455 0.485 0.625 1. 134 0.26 1 1.5 14 -0.56 1 -0.45

tritluoridc in Cr,Hr,

(V II ) 2-chloro 6-me-1.3 19 0.737 0.4 12 0.527 0.544 I.Cl78 0. 14 1 1.402 -0.468 -0.40

thyl ani line in Cr,H(,

(V III ) 3-chl oro 2-methyl ani l inc in 1.474 0.693 0.424 0.5 18 0.585 1.023 0.232 1. 192 -0.194 -0.20 Cr,H(,

(IX ) 3-chlonl 4- me-1.4 18 0.622 0.449 0.490 0.632 1.244 0.254 1.6 14 -0.588 -0.62

th yl ani l ine in C(i Hr,

(X) 4-chloro 2-mc-1.6 19 0.427 0.448 0.41 6 0.842 1.062 0.4 19 1.449 -0.556 -0.3 3

thyl aniline in C(,H(,

(X I) 5-chloro 2-me-1.089 0.547 0.475 0.462 0.627 0.907 0. 312 1.354 -0.5 36 -0.03 0.021

thyl anilinc in C(,H(,

Here, y and 8 are the symmetric and asymmetric di stributi on parameters related to symmetric and characteri stic relaxati on times 1:, and 1:m

respecti vely. Separating the real and imaginary parts of Eq. (8) one gets:

Figs 5 and 6 in the limit Wj=O. Again 8 and 1:" can be had from Eq. (9) as:

[[ '] ' / #] 2 - I I Xi; Xi; Xoi; Xi; y=- tan - - '- ~ ' - - -

7r Xiii; Xi; / Xoi; Xoi; . .. ( 10)

and

.. . ( II )

where X/ IX"ij and X/,/X"ij are obtained from intercepts of each variable with values of WI of

(xu / Xoi; )"i ->O \an (1/>8 ) = r, ) ' ... ( 12)

IX ij / Xiii; IV; ->O

.. . ( 13)

Since, </> cannot be evaluated direc tl y. a theoretical curve of ( II</» log(cos </» with ¢ tn

degrees was drawn as shown elsewhere-l , from which:

I 10g l(X:; / Xoi; )/ cos(1/>8) J - log(cosi/» = -:....::.:..:.:.!..!....:.:.::.:!....:.!..--~ I/> 1/>8

.. . ( 14)

808 INDIAN J PURE & APPL PHYS , VOL 40, NOVEMB ER 2002

was found out. The known va lues of ( 1/<1» log(cos <1»

was the n used to obta in <1>. With known <1> and 8, 1<,

we re obtained from Eq s ( 12) and ( 13) fo r each

mo lecul e . The es timated y and 8 are presented in

co lumns II and 12 of Table 3 . Va lues OfT, and 1 <.,

a re e nte red in co lumns I I and 12 of T a ble 2 to conc lude symmetric re laxati on be haviour for di­substituted ani lines and asymme tric re laxation be hav iour for di-substituted be nzenes, respective ly .

1.2

1.0

:g ~

0.8 --.;t"

0.6

III

0.4 0 .00 0.02 0.04 0 .06

Weight fraction ~

Fig. 5 - Pl ot of Xi(/X"ii with Wi of so lules at 35 °C under 9.945 GHz eleclri c field for: I. o-chloronilrobcnzenc in C"H" (-0-); II. 4-chloro 3-nilrobenzolrilluori de in CCI.j (-6-): III. 4-chloro 3-nil rololuene in C(,Hr, (-0-); IV . 4-chloro 3-nilrotoluene in CCI.j (- e - ); v . o-n il robenzolri tl uoridc in C(,H(, (-~-); VI. Ill ­

nil robenzolri lluoridc in Cr,H" (-. -); VII. 2-chloro 6- lllelhyl ~lIli l i n c in C(,H(, (- T -); V III. 3-chl oro 2- 111elhyl anili nc in C(,H" (-* -) ; IX . 3-chloro 4-mclhyl aniline in C"H" (-@-); X. 4-chloro 2-melhyl anilinc in Cr,H(, (-\7-) and XI. .'i-chiaro 2-mClhyl anil ine in Cr,Hr, (-18l -) al 35 °C under 9.945 GHz elecl ric fi eld

4 Theoretical Formulation for Dipole Moments

112 and III

The De bye equation22 fo r a po lar-nonpo lar liquid

mi xture unde r hf e lectric f ie ld in terms of X/s is writte n as:

... ( 15)

(dx~ jdw ) ~ IJ .I \Vi~O . = mT

(dX:jclw ) 1/ .I 11:/ --;0

. . . ( 16)

1 'S of the po lar liquids could, however, be es timated from Eqs ( 15) a nd ( 16) as seen in 8th and 9th

columns of T able 2 . Again , the imag ina ry part xt of

the complex hf susce ptibility Xii' as a fun c ti on o f Wi

of a solute can be written asD -2.j:

0.5

0 __ _

0.3 :5 ~

-.... ~

~ 0.2

0.1

0.0 0.00 0.02 0.04 0.06

Weight fraction W, J

Fig. 6 - Plot OfXi,"/X"ii wilh lI 'i of SolUICS al 3.'i 0(' undcr 9.945 GHz electri c ficld for: I. o-ch loronitrobenzene ill C" H" (-0-) :

II . 4-chloro 3-nit robenzotrifllloridc in CCI.j (-6 - ) ; III. 4-c l1l oro 3--nilrololuene in Cr,H(, (-0-); IV. 4-ch lnro 3- llilrolo llicne in CCI4 (-e -); V . o-n ilrobenzotrilluoride in C"H" ( -~-) ; V I. Ill­

nil robcnzol ri ll uaride in C(,H" (- . -) ; V II . 2-ch loro (i- mclhyl aniline in Cr,H" (- T -); V III. 3-ch loro 2-mclhyl an il ine in C"H(, (- * -); IX . 3-chloro 4- lllclhyl ani l ine in C ,H(, ( - @-) ; X. 4-chiaro 2-Il!elhyl an i li nc in Cr, H" (- \7-) and XI. 5-chlom 2-mclhyl anil ine in C"H(, (-18l -) at 35 °C under ').945 GHz electri c fi eld

2 H NPi; Ji ; mT ( \1

Xij = - ) ) \Ei; + 2) w; 27E"knTM J I +m-c

whic h on differenti a ti on w ith respect to 11'; and at

w;---jO yi e lds:

( dX;; J ' cl w . l J w 1 --;0

... ( 17)

DUTTA ef ({I.:DOUBLE RELAXATION PHENOMENA 809

Tab le 4 - Siopc ~, of x ii versus Wj and ~~ of (Jij versus Wj cu rves , measured dipole moments ~j from susceptibi l i ty measurement tcchniquc and hI' conductivit y mcthod from Eqs ( 19) and (26), respecti vely, reported dipole moment. thcoretical dipole moment ~ ' h,'" from availablc bond angles and bond moments cx presscd in Coulomh-metrc (C-m) and thc valucs o f ~Lx,,,l~ , , ,,, ,, for di fferent disubstitutcd benzenes and anilines at 35 °C undcr 9,945 Gl-lz electri c lield

System wi th SL No, & Siopc of Dipole moments ~j ( x 10 - .111 ) in em MoLwt. X;(-Wj & (Jij - Wj ~LXr/

curves From From P tlll'\ )

Eq, ( 19) Eq, (26) ~i' ~i' ~( ~Iheo

~ , ~ ~ ~ 2 PI P2 ~ 1

(I)o-chloronitro bcnzcne in C(, I-I (, 8.326 4.706 16,93 12,4 1 17, II 12,54 14,90 14,07 14,50 17.60 0,96 M j=O. 1 57S kg

(II )4-chloro3-nitrobcn-zotri lluoridc in CCI.j 3, 358 1,875 1],02 6,8 1 13,08 6, 84 9,76 11 ,80 10,57 12.60 1.03 Mj=0,2255 kg

(1I1 )4-chlo('() 3-nit ro-toluenc in c" I-I (, 4,490 2,570 17,39 9,37 17,69 9,53 12,94 14,54 14,97 I S,60 0,93 M i=0 17 15 kg

(IV )4-chloro 3-nitro-toluene in CCI.j 4,854 3,00 1 17,40 7. 15 11U9 7,56 11.95 12,36 15 ,60 I S,50 0,94 M j=0,1715 kg

(V)o-nitrohcnzo-trilluoridc in c" I-I (, 8,598 4,662 18.7X 13,34 18,59 13,20 16,68 16, 18 16,54 20,60 0.9 1 M ,=0 19 10 kg

(V I )m-nitrohenzo-trilluoridc in C(, I-I (, 1,426 0.702 9,77 5Xj 9,22 5,50 7,27 13.52 12.24 12,47 () 78 M j=0.19 10 kg

(V II )2-ch loro 6-methyl-anilinc in C(,Hr, 0.728 0,560 4,9 1 3,47 5,79 4,09 3,64 4,50 7,73 6, 16 0,56 M ,=O, 1415 kg

(V II1)3-chloro 2-me-thylaniline in C ,I-l r, 2,674 1.693 10,47 6,66 11.20 7,13 7, 14 7,86 I (),07 lU7 081 M j=0, 14 I S kg

(I X )3 -ch loro4-methyl aniline in C(, I-l (, 2, 128 1.269 10,38 6,07 10,78 6,30 7,14 7.49 8,70 7,33 0,83 M ,=01415 kg

( X)4-ch loro2-meth yl anilinc in Cr, I-l (, 3,650 2,063 21.38 8,45 2 1.6 1 8,54 9,56 9,07 10,94 10.20 0, 83 M j=01415 kg

(X I )5 -chloro2-mcth yl aniline in C(,I-l (, 3.481 2, 196 13.46 8,22 14,37 8,78 9,79 9,79 10.34 9,44 0.87 M j=01 4 15 kg

Pi' = dipolc moment by usi ng '( from the direct slope of Eq, ( I S) ; p( = reported dipole moment Pi' = dipolc moment by using '( from the rati o of indi vidual slopes of Eq, ( 16) ~Iheo = theoret ica l dipolc moment from the available bond angles and bond moments

where the d ensity of the so lution P,j becomes Pi = of free space = 8,854 x 10-12 Em-I, All are expressec

density of so l vent, (£i;+2)2 b ecom es (£i+2)2 at Wj~O, in SI units,

k B=Bo l tzmann constant, N= Avogadro ' s number, £i= Compari ng Eqs ( 16) and ( 17) one gets:

re lative permittivity of so l vent and £,,= permittivity

8 10 INDIAN J PURE & APPL PHYS, VOL 40, NOVEMB ER 2002

( dX' ] '/

dw . I w - )0

j

?

_ _ N_P_il......:.' i_- _ . . _--;;1 ~( . 2)" = {3. ?? E, + 1

27E" k n TM j ( I + Un -)

... ( 18)

where ~ I is the slope of Xi/ versus Wi curves of Fig.4 at lVi-,)O. Here, no approx imation in determin ati on

of l-1i is made, like the conducti vity measurement technique.j given below. After simplifi cati on, the hI'

dipole moment 1-1, is given by:

. . . ( 19)

where dimensionless parameter b is given by :

"';"

E "';"

a c b=' » ....... . ::;

....... () ::J "0 c 0 () -~ co ....... 0 f-

1.44 ,------7"":""7-----,

1.40

1.36

1.32

1.28

1.24

1.20 0.00 0.02 0.04

Weight fraction w J

0.06

Fig. 7 - V ariati on of (Jii agaim t I \ 'j of solu tes at 35 DC under 9.945 GHz electric field for: I. o-chloroni trobenzene in Cr, Hr, (-0 -); II. 4-chloro 3-nit robenzotrilluori de in CCI.j (-6-); III.

4-chloro 3-ni tro toluene in C(,H(. (-D-); IV . 4-chloro 3-nitrotoluene in CCI.j (-e -); v . o-nitrobenzotri lluoride in CI\Hr, (-A -) : VI. m-nit ronenzotri tlu oride in Cr,H(, (-. - ): V II. 2-chlon> 6-methyl anil ine in C(,H(. ( - l' -) : V III. 3-chl ol"(> 2-methyl ani line in C(,H(, (- * -); IX. 3-chloro 4-mcthyl anil ine in Cr, Hr, (-(8)-) ; X. 4-chloro 2-methyl aniline in Cr,Hr, (-V'- ) and XI. 5-cil loi'll 2-methyl aniline in C"H" (-119 -) at 35 DC under 9.945 GHz electri c li elcl

5 Dipole Moments 1-12 and ~l t from hf Conductivity

The complex hI' conducti vity a ii' of polar-non­polar liquid mixture in a GHz electric fi eld is gi ven bi ':

.. . (2 1)

where a /(=CD£,,£i;") and ai('(=CD£"E;;') are the real and imaginary parts of the complex conduct i vity a ii' in Q -\ m i. The magnitude of the total hf conducti vity IS:

... (22)

A lthough Ei(» Eii" , but in the high frequency

region, E/ = E'I'" E,/' is responsible for absorpti on of electric energy and offers res istance to polari zation .

Hence, a/' is rel ated to a/ by the relati on2l,:

" 1 , (J i,' = (J~ii + - O'i '

. . CVT .I

1 , (J ii = (J~ii +-(Jii

CV T . ... (23)

Here, the approximati on a ii"= a ii is made. Di f ferentiati on of Eq. (23) w ith respect to Wi at wi-,)O y ields:

( d(J~] (d(J ] __ 1.1 =CVT __ 1.1

dw · dw . / II ' -->0 .I 11 ' ->0

j j

... (24)

where ~ 2 is the slope of a ii versus Wi curves of Fig. 7 at infinite dilution wi-,)O and placed in Table 4. The

real part of hf conductivity a/ at T K (Ref. 23) is given by :

. .. (25)

Comparing Eqs (24) and (25) one gets the dipole

moment l-1i from:

... (26)

DUTTA el a{:DOUBLE RELAXATION PHENOMENA 8 11

I. o-chloronitrobenzene in C6H6

CH3

&-,_____ <;=1 , 0- ..... ,: -""'---- ... : &- CI---=-. ; &+ &- ~ \ ,,0--= C -- CI ' ',_ u-CI-::-_-I...- ______ •

-----

-- '

IV. 4-chloro 3-nitro toluene in CCl4

VIT. 2-chloro 6-methyl aniline in C6H6

~ C F3

UCF3 -r ~ (1)

~ C I

N02

CI N02

If. 4-chloro 3-nitrobenzotrifluoride in CCl4

V. o-nitrobenzotrifluoride in C6H6

CI C H3'-...

CH3

IX. 3-chloro 4-methyl aniline in C6H6

Fig. R - Conformat ional structu res o f so lutes from bond angles and b()nd moment s in mu lt ip le I Q' o C-m

All the measured dipole moments fl i from the susceptibility measurement technique of Eq. ( 19) and hf conducti vity method of Eq . (26) are entered in the 4th to 7th columns of Table 4, respecti ve ly.

Results and Discussion

The double relaxation times 11 and 1 2 for the polar liquid molecules in different so lvents are found out from the slope and intercept of Eq. (3) , as

INDI AN J PURE & APPL PHYS, VOL 40, NOVEM BER 2002

shown in Fig. I, in terms of the orientati onal suscepti bility parameters X'I of Table I. The Xii va lues are, however, derived from the relati ve permittiviti es("x £ii for different weight fracti ons IVi of the polar liquids. The va ri ables of Eq. (3) i.e (X"ii ­X/)/X/ and X/'/X/ are plotted aga inst each other fo r diffe rent va lues of Wi of solutes under 9.945 GHz electri c fi eld at 35 °C to get linear equ ation by regress ion analys is. From Fig. I, it is revea led that, the fitt ing is good fo r some cases, but poor in other cases. It appears th at the linear fit fo r II (-.6-), 1II (-0-) and IV (-e-) in Figs I and 2 often passes th rough two among five data poin ts, others being off from the fit. Nevertheless, the regress ion analys is was made on the bas is of Eq. (3). However, the accuracy of Fig. I is tes ted by the correlation coeffi cients ( r ), which were fo und to be close to unity, indicating th at the va ri ables are almost co ll inea r.

The % errors in terms of r-va lues in getting the intercepts and slopes were worked out to find the accurac ies of 'I I and 'I" respective ly. In order to locate the double relaxati on phenomena of the polar liquid molecules in non-polar aproti c so lvents under in ves ti ga ti on, accurate measurement of X"'I in vo lved with £"il and £~ 'i is necessary . The refrac ti ve index II D'I measured by Abbe's refractometer often yields £~ ' i = II llil' , although Cole Co le27 and Cole Davidson"x

plots usuall y give £-ii == 1.0-1.5 times of IlD{ Thi s often introduces an additi onal error In the ca lcul at ions. Nevertheless , the accurac ies of X/', X/ and X"'i are of 5 % and I %, respecti ve ly deri ved fro m measured("x relati ve permitti viti es £/', £il" £"ii and £~ il ' The estimated 1 , and 'I I are pl aced in Table 2, in order to compare them with those of Murthy ef al.1(' of Eq. ( 15) and by the rati o of the individual slopes of the vari ati ons of xt and Xii' with IVI in the limit 11'1=0 of Eq.( 16). The latter method seems to be better to ca lcul ate 'I, since it eliminates polar-polar interac ti on almost completely. The linear plot of xt against Xii' of Fig. 2 fo r different WI of so lute has intercepts, although it was ex pected fro m Eq. ( IS) that, they shou Id pass through the ori gin . Nevertheless, values of 1: are fo und to be in close agreement with those calcul ated from the rati o of the individual slopes of the va ri ati ons of X,,"and xu' with Wi at wi~O of Eq. ( 16), as shown in Figs 3 and 4. The ex perimental points as shown in Figs 3 and 4 with the fit are presented

(Table 2) to back up the results of Eq. ( 16) due to Debye model. Values of xt increase monotonicall y with Wi and have a tendency to meet rhe ori gin fo r all the curves. This type of behav iour indicates that, under an electri c field of 9.945 GHz, X'I" tends to pass through the ori gin at WI~O ,

It is evident fro m Tab le 2 thaI, a ll the di­substituted benzenes ex hibit the who le molecul ar rotati on, whil e the di -substituted anif ines show the rotati on of the flex ibl e parts under I () GH z electric field when 'II 'S and L:"s are compared with the reported data. Thi s ind icates the fl ex ible parts are more ri gid in the di-substituted benzenes rather than the di -substitu ted anil ines. The assu mptions of symmetri c and asymmetric relaxation behaviour from Eqs (8) and (9) fo r such non-ri gid polar molecul es yield T, and 'To from Eqs ( II ) and ( 13) to place them in the las t two co lumns of Table 2. It revea ls that the symmetric and asymmetric relaxati on processes are more probable si nce, 'I, and 'Ie' are almost in agreement with the reported 'I va lues in a solution. The characte ri stic re laxati on times 'Ie, are sometimes very hi gh th rough asymmetric distributi on parameter 0 and often cou ld not be determined fo r most of the molec ul es.

The di-substi tuted benzenes showed Ll' S in agreement with the reported L's and 'I" except o-nit robenzotrifluoride in C"H(" which agrees with 'I, onl y. But, 4-chl oro 3-nitrobenzotri fluoride in CCI.j and m-nitro-benzotrifluoride in C" H" yield L2 in close agreement with reported L's although, they showed 'I, == 'T I. Onl y 2-chl oro-6 .. meth yl aniline and 3-chl oro 2-methyl aniline in C"H" showed va lues of 'I I in excellent agreement wi th the ca lcul ated values of 'I,. For the rest di-substituted anilines va lues of 'II agree we ll with the calcul ated values of 'I" but the agreement is not better with the measured va lues of 'I from Eqs ( IS) and ( 16). It thus reveals that, a part of the di-substituted anilines i ~ rotatin g, obey ing symmetric re laxati on behav iour, while most of the di -substituted benzenes showed asy mmetri c relaxation process for their whole molecular rotati ons.

The relative weighted contri buti ons CI and £:2

towards dielectric di spersions due to ""[ I and 1 2 are estimated and placed in Tab le 3, by using Frohlich's Egs (6) and (7). They are compared with the experimental C I and C2 from the fitted curves of

DUTTA el a l.:DOUBLE RELAXATION PHENOMENA 813

X; j'IX";1 and Xt IX,,;j against WI in the limit Wj~O of Figs 5 and 6. The non-linear fit with onl y five points for III (- 0 - ) and IV (-e-) of Fig.5 appeared to be not convincing and in fact mi sguidin g, but three accurate experimental points are enough for such a fit. However, the fit is done with a PC and appropriate software. All the curves of Figs 5 and 6 vary u su a ll / ~ except the convex curve V for o-nitrobenzotrifluoride in Cr,Hr,. The variations of XIJ'IX ,,;j with Wj are, however, concave and convex in nature for all systems as observed elsewhere l2. The left hand sides of Eqs ( I) and (2) vary with values of W j in concave and convex manner according to Figs 5 and 6 are now fi xed for 1 1 and 1 2 once estimated from intercept and slope of Eq. (3) to yield experimental C I and C ~ va lues from Eqs (4) and (5) at Wj~O .

Thi s study is supposed to yield the accurate va lues of C I and C2 unlike the earlier onel ~ , based on the graphica l ex trapolated va lues of (£,,'- £~ ;j)/(£" ; I­

£~ , ,) and £/'/( £,, ;j- £~ ; I ) at Wj~O, drawn on the basis of sc ientifi c judgement. Although, the nature of vari ati ons remains unaltered, it is evident from Table 3 that, C2 va lues are often negati ve for 4-chl oro 3-nitrobenzotrifluoride In CCI ~ ,

m-nitrobenzotrifluoride in C"Hr, and for all the di­substituted anilines unlike other systems. Thi s perhaps signifies that the rotation of the fl ex ibl e parts of the polar molec ules are not in accord with the whole molecular rotati on due to inherent inerti a of the substituted parts of the molecules under hf elec tri c fi e ld . The theoreti cal va lues of C I+ C2 are found to be greater than the sum of the experimental olles as li sted in Table 3.

The ex perimental va lues of (' 1+ C 2 == I fo r almost a ll the non-spherical polar liquid molecul es. But (I I) 4-chl oro 3-nitrobenzotrifluoride in CC I ~ (-6-), eX) 4-chl oro 2-methyl anil!ne (-V'-) and (X I) 5-chl oro 2-methyl aniline (- [8] --) in Cr,H(, show considerabl y lower values of C I H '2' Thi s may indicate the reliability of Eg. 0 ) so far deri ved fo r such mo lecules, although they show hi gh correlati on coeffi cients (r) and the corresponding very low % of

rro rs to gel the intercept and slope of Eq. (3). The largest theoreti cal (' 1+(.' 2 va lue fo r (IV) 4-chl oro 3-nit ro to luene in CCL (-e-) is 1.34, showin g a dev iati on of nea rl y 34 %, unlike the other systems. The poss ible ex istence of more than two broad Debye-type di spersions may be taken into account

for such molecules of vary1l1g compl ex ities as reported in tables and fi gures.

Dipole moments Il~ and II I due to rotati on of the whole molecule as well as the fl ex ible parts were, however, measured from Eq. e 19) using dimensionless parameters (b) in vo lved with 1 ' S by both the methods and sl ope ~ I ' s of X/ versus \1/1

curves of Fig. 4. The measured values of Il ~ and III are presented in Table 4 . The variations of a ll the XIJ' va lues of polar-nonpolar liquid mi xtures are found to be paraboli c with values of \'V, of polar compounds as ev ident from FigA. They are found to cut the ordinate axis at WI = 0 within 0.0238 :s X,,' :s 0.0645 except 4-chl oro 3-nitrobenzotriflu oride in CCl 4 (- .6.- ), 4-chloro 3-nitrotoluene in CC l ~ (-e- ). This behaviour probabl y refl ects the so lvent effects on the polar compounds under in ves ti gati on. The interacti on of solute on so lvent CC l~ may occur due to slightl y pos iti ve charge c)+ on C atom of CC l ~ and negati ve charge (). on CI atom of the substituted group in the benzene ring, as seen in F ig. 8. All the systems are of similar nature hav ing monotonic

increase of XIJ' with WI '

The dipole moments ~t ~ and ~t l are also deri ved from the conductivity measurement technique of Eq. (26) using the slope ~ 2 'S of O',j versus H ', curves of Fig.7 and are pl aced in Table 4 for compari son. The total hf conducti vity 0';1 of all the polar-nonpolar liquid mixtures increase monotoni call y with \\"1 and cut the ordinate ax is within the range 1.2233 :s 0'" :s 1.2646 at H'I=O as seen in Fig.7. The sli ght di sagreement of III and /1 2 de ri ved from both the methods is due to the fact that the hf conducti vity inc ludes the fas t polari zati on probab ly for the bound molecul ar charge assoc iated with the molecule. All values of ~t 2 for di -substituted benzenes and va lues of /1 1 for di -substituted anilines are fo und to agree with the reported va lues of ~L presented in Table 4 . Thi s indicates that, the fl ex ibl e parts of the d i-substituted benze nes are ITIore rig id in cOlllpari son

to di -substituted anilines.

The hf d ipole moment ~t l' s are cal cul ated by using T from both the methods of direct slope of Eq. ( 15) and the rati o of the indi vidual slopes of Eq. ( 16) in order to place them in .

Values of Ilj by using 1 from the rati o of the individual slopes are in c lose agreement with the reported va lues, sugges ting that, the latter method to

814 INDIAN J PURE & APPL PHYS, VOL 40, NOVEMB ER 2002

obta in 1 is more rea li stic . In such a case, one po lar mo lecule is surrounded by a large number of non­po la r so lvent mo lecul es and re mains in a qu as i­isol ated state.

A specia l attenti on is, the refore, pa id to obta in the conformat ional structures of some of the complex mo lecules as shown schematica ll y in F ig. 8. The inducti ve, e lectromeri c and resonance effects combined with mesome ri c effec t of the substituted po lar groups play the key role to yie ld

the theoreti cal dipo le moment ~th"" depending on the

e lectron affinity of C-atom of the benzene ring. The

mo lecules have C~CF1 ' Cf-NH2 (L I42°), C~N02.

C~C I Cf-C Hl po la r groups of bond moments 9.53 x 10 1°, 4.93 X 10-1°, 14. lOx 10 1°, 5.63 X 10-1°, 1.23 X 10-10 C-m (Coul omb-metre) respec tive l l 2. 1~

a ligned in di ffe rent angles in a pl ane to y ie ld ~thc ...

O ut of these, onl y -NO~ and - NH, groups are in the

hab it to show resonance effect (-R or +R ) in the molecul es ei the r by pulling or pushing e lectrons

towards C- alom of the benzene ring. Thi s reson ance effec t is stronger than induc ti ve effec ts (+1 or - 1) to

ex hibit the peculiar behav iours as seen in the Xi/IX"ij

versus Wj and XL/'IX,,, j versus Wj curves fo r the di ­substituted benzenes II , IV , V, VI inc luding a ll the di-substituted anilines.

The structure o f these po lar mo lecules is of spec ia l inte rest as ske tched in F ig. 8 in view of rearrangement of charge-density in them . A ll the di­

subs tituted anilines inc lude -CI, -NH~ and - CHl

po lar groups, of which -CI and - CH l have very weak inducti ve effects (+1 or - 1). T hey are eas il y influenced by the G Hz e lectri c f ie ld to show the rotati on of the ir fl ex ible parts. Furthe r, the observed

d iffe rence in ~. values for a polar mo lecul e in two aproti c nonpo lar solvents may ari se due to weak po larity of CC I4 as shown in Fig. 8. The diffe rence

between ~thCL> and experimenta l va lues of ~j

establi shes the non-consideration of inducti ve and mesomeri c effects. A ll these effects may be taken

into account by the fac tor ~cxp/~ the" to y ie ld the exact ~ I and ~1 values of the mo lecules. A ll the polar molecules have Sp 1 hybridi zed carbon atoms of benzene ring and the substituted parts a re assoc iated with sp' orbita l. The interac ti on o f orbita ls may lead to ga in know ledge on accumul ati on of charge on the substituted groups in additi on to various effects present in them. The confo rmati onal structures of

othe r molecules except six of F ig. 8 were a lready shown e lsewhere 11.1') .

Conclusions

The study of re laxati on pheno mena of d i­substituted benzenes and anilines in Cr,HI> and CCI4

by the modern establi shed symbo.l s of d ie lectri c

ori entati onal susceptibilities XLi measured under a single frequency e lec tri c fie ld is very encourag ing. It seems to be more topica l, s igni fican t and useful contri bution to predict the confo rma ti o na l struc tures and vari ous mo lecul a r assoc iations of the mo lecul es at any given te mperature. The inte rcept and s lope of the de ri ved li near Eq . (3) by the regress io n ana lys is

on the measured data of XLj o f d iffe re nt va lues of H 'I

are used to get 11 and 11, The met hodo logy so far deve loped in SI units is superior because of the uni fied , coherent and rati ona li zed nature of the establi shed symbo ls of di e lectric te rmino logies and parameters, w hich arc d irec tl y linked with ori entati onal pola ri za ti on of the mo lecul es. T he

s ignificant Eqs ( 15) and ( 16) to obta in va lues of 1,

and hence va lues of ~j from Eq. ( 19) he lp the future workers to shed more li ght on the re laxat ion phenomena of the complicated non-sphe ri ca l po la r liquids and liquid c rys ta ls. The prescribed method to

obta in values of 1j from Eq. ( 16) w ith the use of the

ratio of the ind iv idual s lopes of X;;" versus Wj and X;;'

versus Wj curves at Wj~O is a s ignificant improvement over the ex isting ones, as it e liminates

po lar-po lar inte rac ti on a lmost completely in 1j'S and

~j'S respecti ve ly.

Values of 1 j and ~j are usua ll y c la imed to be accurate w ithin 10 % and 5 %, respec tive ly. But, the corre lati on coeffic ient r and % e rrors o f Eq . (3)

demand that, va lues of 1 and ~ are more than accurate . The non-spherica l di-substituted benzene and aniline mo lecules absorb e lec tri c energy much more strong ly, nearly 10 GHz e lectric fie ld, at

which the va lue of E" fo r absorption against

frequency co showed a peak. Th is in vited the

attenti on to get the doubl e re laxati on t imes 11 and 11 fro m Eq . (3) . The corresponding sum of the experimenta l and theoretica l va lues o f weighted contributi ons CI and C2 towards di e lectri c di spersions

due to estimated 12 and 11 diffe r sign ificantly to indicate more than two Debye type re laxati ons in such mo lecules because of the ir complex ity. The

va lues of 1 for di -substituted benze es as seen in

DUTTA et (l1.:DOUBLE RELAXATION PHENOMENA 815

Table 2 show the whole molecular rotation, while the fl ex ible parts of the di-substituted anilines rotates unde r 10 GHz electric field.

Di-substituted anilines exhibit the symmetric re laxation behaviour, whil e the asymmetric re laxation behaviour occurs III di-substituted benzenes In Cr,Hr, except 4-chloro 3-nitrobenzotrifluoride in CCI 4 and m-nitro

benzotrifluoride in C(,H(" respect ive ly. Values of ~2

and ~ I due to 1 2 and 1 1 are expec ted to be smalle r when they are measured from the susceptibility measurement technique rathe r than the hf

conductivity method , where the approximation of (jij

== (jij" is usuall y made. The diffe rence of /ll for the

first six systems and of ~ I for the rest five systems of Table 4 , between conductivity and susceptibility measurement may arise, e ithe r by e longation or reducti on of the bond moments of the substituted

polar groups by the factor /lcxpi / /l,hc" in agreement with the measured values of ~ to take into account of the i nduc ti ve, mesomeric and e lectromeric effects of the polar groups in the molecules. Thus, the correlation between the conformational structures with the observed results enhances the scientific content to add a new horizon of understanding to the eXIstlllg knowledge of die lectric relaxation phenomena.

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