3026 (22) F. G. Mann, J. Chem. SOC.,461 (1934). (23) G. W. Wan and W. A. Cude, J. Am. Chem. SOC.,90,6382 (1968). (24) Stanley E . Livingstone, "Comprehensive Inorganic Chemistry", Vol. 3, A. F. Trotman-Dickenson, Ed.. Pergamon, New York. N.Y., 1973, p
1352. (25) See, for example, C. M. Harris, R. S. Nyholm, and N. C. Stephenson, Nature (London), 177, 1127 (1956); C. M. Harris and N. C. Stephenson, Chem. Ind. (London),426 (1957).
Optical Spectra and the Free-Volume Model for the Transport Behavior of Glass-Forming Melts N. Islam,* M. R. Islam, S. Ahmad, and B. Waris Contribution from the Department of Chemistry, Aligarh Muslim University, Aligarh 202001, India. Received July 29, 1974
Abstract: The optical spectra of MX2 ( M = Mn, Co, and Ni; X = CI and Br) -rich mixtures of R4B+X- ( R = propyl, butyl, pentyl, hexyl, heptyl, and octyl, and is either the same or different; B = N and P; and X = C1, Br, and 1) have been identified as due to the presence of tetrahedral, T d tetrahalometalate(l1) ions, MX42-. The band assignments of NiX4*- have been made by constructing the energy level diagrams for the d8 configuration in a cubic T d field based on the four ligand-field (LF) parameters. These parameters for NiC12X22- have been taken as approximately averages of those of NiC1d2- and NiX42-. The optical electronegativity of nickel(II), ~ E ! N , ( I I )has ] . been computed from the corresponding L F parameters and the low-energy charge-transfer (CT) spectrum and I S found to be 2.1. The C T spectra of X- in MX2-rich mixtures of R4N+X- have been found to be unaffected by the low conducting and highly viscous medium containing the species, ((R4N+)2MXd2-J, and may be due to the transitions to n p 5 y ,configuration. The free volume model has been found suitable in explaining the transport behavior of glass-forming melts as supported by almost identical secondary glass transition temperatures, TO,.,and To,,++for MnC14*-, C0c142-, and NiQ2- as 277.23 & 1.27, 276.60 f 0.40, and 269.43 f 2.17'K, respectively, and also by several linear plots.
Tetrahedral tetrahalometalates have been r e p ~ r t e d l -in~ the low-melting organic halides of large [cation]/ [anion] ratio. The metal halide-rich mixtures containing (R4B+)2MXd2- have been found to supercool to glassy states5 The present work deals with the optical spectra of MX2rich mixtures of R4B+X- [ (CdH9)4N+CI-, (C4H9)4P+Br-, (CdH9)4N+Br-, ( C ~ H I ~ ) ~ C ~ H ~ N (C4H9)4N+I-, +B~-, (C5H1 1)4N+1-, (csH13)4N+I-, ( C ~ H I ~ ) ~ N + I and -, (CdH9)3C3H7N+I-O and their comparison with those in the corresponding dilute solutions. The CT and the L F bands of C0Xd2- and NiX42- are recorded. The band assignments of the latter have been made by constructing the energy level diagramsIO based on the four L F parameters and comparing them with those recorded for NiX42- and NiC12X22-, i.e., NiC142-, NiBr42-, NiClzBrz2- and NiC1212*--. The CT spectra of X- in MX2-rich mixtures of R4N+X- have also been recorded. The electrical conductances, densities, and viscosities of MCl2 in molten (C4H9)4N+C1- have been measured at several temperatures and those of CoCl2 in (C4H9)4N+I- as functions of composition and temperature. The applicability of the free-volume m ~ d e l I ' - 'in~ explaining the transport behavior of the glass-forming melts has been examined.
Experimental Section
has been neglected. Density measurements were made in a dilatometer calibrated for 0.005 ml a t several temperatures with f 0 . 3 % accuracy. The viscosities were measured in a calibrated Ubbelohde capillary viscometer with an accuracy of * O . I to 2.5%. Preparation of the samples and the above measurements were carried out in an inert atmosphere in a relay controlled thermostated oil bath of fO.l and f 0 . 2 ' thermal stabilities over 0 to 100 and 100 to 200°, respectively. The energy level diagrams for NiX4*- were constructed'.l0 by computing the energy levels on an IBM-1130 computer.
Results and Discussion I. Optical Spectra. Ligand-Field Transitions. T h e optical spectra of N i x 2 R4B+X- have been identified as due to the presence of T d NiX42- on the basis of their comparison with those reported ear1ier.l The L F spectra of NiC142-, NiBrd2-, NiC12Brz2-, and N i C l ~ 1 2 ~have been fitted to their respective energy level diagrams and the assignments of the bands have been made. A. NiC12 RdN+CI-. The d-d spectra of NiCl2 in molten (C4H9)4N+CI- consist of an intense band with peaks at 14,280 and 15,380 cm-' and a shoulder a t -16,660 cm-', and a broad band with a peak at -7500 cm-I. It is apparent from the energy level diagram (Figure 1) that three transitions are spin allowed, two of which are orbital transitions, I'2-5:3Tz(F) I ' I : ~ T I ( F ) , and I ' s : ~ A ~ ( F ) I ' I : ~ T I ( F ) ,and the third one is due to r5:3T1(P) ~ I : ~ T I ( transitions. F) The first transition reported1 at -4000 cm-I has not been recorded due to the overlapping region of the solvent. The remaining two transitions have been reported by several a u t h ~ r s l , and ~ ~ agree - ~ ~ with those found in the present case a t -7500 and 14,280 cm-I. In spite of its inherent limitationsZ5the L F theory rationalizes the spectrum satisfactorily. However, it does not seem to account for the little details of the band, 3 T ~ ( P ) 3Tl(F), as predicted by the theory for I'3:)Tl(P) I ' I : ~ T I ( F ) , l?4:3T~(P) I ' I : ~ T I ( F ) ,and I ' I : ~ T I ( P ) I ' I : ~ T I ( Ftransitions ) a t 14,340, 14,650, and 14,840 cm-I,
+
+
+-
+
+
Tetra-n-alkylammonium (Fluka and Eastman) and phosphonium (Alfa Inorganics) halides, R4B+X-, were used as solvents in the molten state. Anhydrous metal chlorides, MC12, were preparedl8.l9 from their recrystallized hydrated salts (E. Merck) while NiBrz was obtained commercially. The spectra of MX2 in molten RA,B+X- were recorded on digitalized Cary Model 14 and Beckman Model DK-2A spectrophotometers. Electrical conductances were measured with a Philips-PR9500 conductivity bridge at 50 Hz using calibrated capillary type conductivity cells. The dielectric constant was measured with a Sargent Chemical Oscillometer Model V. The capacitive effect of electrolyte-electrode double layer being of the order of pF
Journal of the American Chemical Society J 97:l I 1 M a y 28, 1975
-
---
3027
,
$1"
06
+
-I I
I
1
I1
- 280
T ; 5 : 3i~P~ l c T : 3~~ I F )
I
C
3
W
8,000
~
~
(
~
)
{~Tz(F)
4,000
{~T~(F)
0
50
100
150
250
ZOO
300
350
LOO
D q l c m-Y 5000
7000
Figure 1. Energy level diagram for NiC1d2- in molten (C4H9)4N+CI460 5 00 600 800 950 111 ( A = -275, E = 740, and C/E = 3.97 cm-I). The computed electronic levels were matched closely with those of the observed bands at -7,500 and 14,280 cm-' for Ts?A>(F) ~ I : ~ T ~and ( F )~ s : ~ T ~ ( P ) Figure 2. Spin-forbidden ( I and I11 at 27 and 112') and spin-allowed I'I:3Tl(F) transitions, respectively. (I1 and IV at 112O) ligand-field spectra of tetrabromonickelate(I1) ions in molten (CdH9)4P+Br-.
-
-
respectively, while the experimental result corresponds to an intense band a t 15,380 and a shoulder a t -16,660 cm-I. spectra of NiBrz-rich mixtures of molten (CdHg)dP+Br-. T h e latter is close to the computed energy for rs:lT*(G) Upon increasing the [NiBrz] to near stoichiometric point, I ' I : ~ T(F) I transitions. It appears that the close proximity of the ratio of [NiBr42-] to [Br-] increases rapidly and the the intense band for r s : 3 T ~ ( P ) I ' I : ~ T I ( F )transitions and those of weak ' G states renders the actual band positions to melt containing (R4B+)2NiX42- supercools to a glassy mashift toward a position determined by the relative intensity terial. It is interesting to note that the thin film spectrum of of several closely lying overlapping Gaussians, also envelthe glassy material has been found similar to those in the oping some of the extremely weak components. It therefore corresponding dilute solutions. Beer's law has been found to appears reasonable to assign the band a t 14,280 cm-I to be obeyed in fairly concentrated solutions. This indicates r5: T1(P) I ' I : ~ T I ( F )transitions enveloping the compothe presence of the same absorbing species in the two cases. nents predicted at 14,340 and 14,650 for transitions to The shoulder a t -21,500 cm-' appeared as a distinct I ' ~ : ) T I ( P )and r 4 : 3 T ~ ( P )levels, respectively, and the band peak in the glassy material a t 27" and the weak band a t ) Howa t 15,380 cm-I to ~ I : ~ T I ( P I) ? I : ~ T I ( Ftransitions. 10,640 cm-I became somewhat narrower (Figure 2). The ever, all three components, i.e., 14,280, 15,380, and absorbance of all the bands increased and the bandwidth -16,660 cm-', of the intense band are to be considered for near the foot of the band decreased on cooling the concenthe estimation of the oscillator strength as the intensity of trated melt. For example, the absorbance increased by the latter shoulder appears to have been borrowed from the -15% in NiBr42- a t the band maximum while the band3P state. width decreased by -33 cm-' near 16,660 cm-l on lowerB. NiBr2 R4P+Br-. T h e L F spectrum of NiBr2 in moling the temperature from 112 to 27". This phenomenon is ten (CdHg)AP+Br- consists of two weak bands at 18,315 similar in dilute as well as in concentrated solutions which and 21,500 cm-I, an intense band with peaks a t 13,200 and supercool to glassy states. The reasons for such behaviors 14,200, and a shoulder a t -15,000 cm-', followed by a are associated with the creation of holes or an increase in weak band a t 10,640 cm-I and a shoulder a t -9850 c m - ' , the free volume (cf. transport behavior) which in turn lowand a broad band a t -7040 cm-I (Figure 2 ) . ers the density of the absorbing species as well as an inT h e spectrum is analyzed as cited above. The computed crease in the vibronic interaction with successive increases electronic levels were matched with those of the experimenin temperature. tal bands a t -7,040, -10,000, -10,600, and 13,200 cm-I The oscillator strengths of v2, rj:3A2(F) ~I:~TI(F), corresponding to ~ s : ~ A * ( F ) ~ I : ~ T I ( FrS:'T2(D) ), I ' I : ~ T I ( F ) ,transition bands of and v3, I'j:3T~(P) I ? I : ~ T I ( F ) ,T3:'E(D) I ' I : ~ T I ( F ) ,and r j : 3 T ~ ( P ) NiBr42- have been obtained as 1.7 X and 31 X r I :3TI ( F ) transitions, respectively. respectively. Their ratio, f(v3)/f(v*), a t 112 and 27" is I n addition to the limitations of the LF theory cited -18.24. This implies that there was no perceptible change above, the predicted energies for the four components of ' G in the character of Ni*+-Br- bonds in the above temperastate, i.e., r s : ' T * ( G ) ~ I : ~ T I ( FI'4:ITl(G) ), ~ I : ~ T I ( F ) ,ture intervals. , r3:IE(G) I ' I : ~ T I ( F transi) r l : I A I ( G ) +- I ' I : ~ T I ( F )and In view of the above results, the spin-allowed bands of tions a t 15,780, 17,085, 17,205, and 18,540 cm-l, are unacNiC12Xz2- have been recorded in the corresponding thin counted for in a true sense as only two bands a r e obtained films, as their T d geometry remains unaltered by successive a t 18,315 and 21,500 cm-l, respectively. T h e band a t increases in [MCIz] until the glassy materials a r e obtained. 18,315 cm-I is clearly a transition to a ' G state as it lies C. NiClz R4N+X- (X = Br or I). Thin film spectra of very close to that predicted for the I'3:IE(G) level but the NiClz in several organic bromides and iodides consist of theory is expected to underestimate the overall positions of bands similar to those cited above for I'5:3A2(F) the ' G bands by an appreciable amount, and thus the band ~ I : ~ T I (and F ) I ' s : ~ T I ( P ) ~ I : ~ T I (transitions. F) The L F a t 21,500 cm-' is unaccounted for. parameters used in the computation of energy levels for the The second part of this section deals with the absorption corresponding diagrams of NiC12X2*- have been taken as + -
+ -
-
+-
+
-
+ -
-
-
-
+ -
+ -
- -
+
-
+ -
Islam et al.
/ Transport Behavior of Glass-Forming Melts
3028 Table I. Band Positions for Nix,,- (cm-,)
Table V. CT Bands of MX,’- (cm-’)
Band positions for NiC1,BrZZ-
Transitions
Predicted = aver ages of those of NiCI,,- + NiBr,’-
3T1(P)+ 3T1(F) 3T1(P) ’T,(F) 3A,(F) +- 3T,(F)
13.740 14,790 -7,270
-
Obsd
Predicted averages of those of NiC1,’- + Ni1,’-
Obsd
13,800 14,600 -7,240
12,810 13,765 -7.275
12,820 13,417 -7,270
Table 11. L F Parameters for
(cm-I)
Parameters
B C/B D4
Band positions for NiC1,I’-
NiC1,’-
NiBr,’-
Ni1,’-
740 3.97 358
680 3.88 332
537 5.51 331
42,735
NiC1,BrzZ- NiClzIz’710 3.92 345
638.5 4.74 344.5
Table 111. Comuuteda Band Positions for Nix.’- (cm-’) Transitions
NiCl,Br,’-
r,:3A,(F) r,:3T;(F) r,:3T,(P) t r , : 3 T , ( F )
7,290 13,790
CoC1,’in R,N+CI-
NiC1,IZ2-
46,083
CoCl,Br,’in R,N+BI-
CoCI,IZ2- NiC1,2in in R,N+IR,N+CI-
-35,460 (sh) 37,735
30,030
35,460
32,786
38,460 42,550
NiCl,Br,’in R,N+BI-
NiBr,’in R,P+BI-
-31,950
28,409 30,303 34,480 37,175
between 6660 and 4000 cm-l and a n intense resolved band which extends from 16,660 to -12,000 cm-’ may be assigned to 4 T ~ ( F ) 4Az(F) and 4 T ~ ( P ) 4A2(F) transit i o n ~ , ~ -respectively. ~ ~ , ~ ~ -The ~ ~latter has also some contributions from 2G due to overlapping. T h e L F spectra of c0x42-in several systems a r e summarized in Table I V . E. MnXz R4N+X-. The visible spectrum of has not been obtained in thin films because of their low intensity as all of the L F transitions are spin forbidden. A band has been recorded in the ultraviolet region a t 37,740 cm-I which resembles one of the bands reported for MnXd2-. Td geometry may be assumed for the absorbing R4N+X- on the basis of those respecies in MnX2 ported30 for MnBr2 R4P+Br-. Charge-Transfer Spectra of MXdZ-. T h e CT spectra of MX42- recorded in the ultraviolet region (Table V) suggest a predominant covalent character in the metal-ligand bond.3 The CT transition is attributedl to an electron j u m p from a filled y 4 subshell to the partially filled 75 subshell. The y4 subshell has r-type two-center symmetry and is nonbonding in metal-ligand directions in the L C A O - M O model that ignores metal orbitals above 4p. The lowest energy CT band has been employed in calculating the optical electronegativity, OE, of nickel(I1) relative to the y4 subshell. J4rgensen3[ has associated this quantity with the electron bonding. The basic relation in OE is given by the relation, ucorr = 3 X 1 0 4 ( O E p ] - O E [ M I ) where , ucorr and 3 X l o 4 stand for the corrected transition energy and the conversion factor of Pauling electronegativity scale to reciprocal centimeters, respectively. The ucorr is given by
-
-
+
+ +
7,300 12,790
QNiCl Br,’-: A = -275, B = 713.75, C/B = 3.93, Dq = 345. NiCI,IZ2’: h = -275, B = 639.75, CIB = 4.7, and Dq = 345 cm-’.
averages of those of NiC14*- and NiX4*- as supported by the following consideration. The dilute solutions of NiC12 or NiBr2 and NiCl2 or NiI2 in several molten bromides and iodides, respectively, yield essentially the same spectra as those of NiBr42- and Ni142-. On the other hand, the absorbing species in NiC12rich mixtures of molten R4N+X- have been identified as NiC12Xz2- on the basis of the following comparison (Table I ) . Thus it may be assumed that each metal ion in the glassy material is essentially present in a T d field of two chloride and two bromide or iodide ions (Table 11). T h e best fitted values a r e taken as approximately close to those which describe the experimental results (Table 111). A comparison of these computed energy levels as well as the predicted band positions (Table I) based on the averages of those of NiC14*- and NiX4*- for NiC12X22- with the experimental band positions reinforces the above deductions for the L F parameters. Similarly MXz-rich mixtures of molten R4B+X- result in (R4B+)zMX42- unlike those in dilute solutions. Such species are expected to be weakly dissociated and a t the same time highly viscous. The transport behavior is therefore examined later. D. Cox2 R4N+X-. The spectra of Cox*-rich mixtures of R4NfX- consist of a broad band with structure located
+
Ucorr
= vobsd
- lo&
+ D [ ( s (s+ 1) - s(s + I ) ) ]
where the bracketed term is -2/3 for Ni(I1) ions and D is the spin-pairing energy parameter obtained from the L F parameters as shown by the relation D = (7k)[(5/2)B C ] . The low-energy C T bands of NiC12Xz2- taken as the averages of Uobsd for NiC142- and NiXd2- are supported by the same O E p I ( ~ viz. ~ ) ] 2.1 obtained in all the five cases (Table V I ) . This fits well with Jqhgensen’s ~ o r r e l a t i o n The . ~ ~ shift of bands toward lower energies in the order NiCId2- >
+
Table IV. Band Positions of COX,’- (cm-’) Systems
Coci, + (c,H,),N+I
4T,(P)
4T,(F) 4A,(F) +
c o c i , + (c,H,),N+cICOCI, + (c,H,,),c,H,N+B~-
-
cOci,+ ( c ~ H , , ) ~ N + I c o c i , + (c,H,,),N+ICoC1, + (C,H,,),N+I-
4444 5154 4376 4282 4405 5263
5714
5571 (sh) 4424 5128 -5279 (sh) 4424 5167 4347 4273
5405
5464
5714
Journal of the American Chemical Society / 97:l I / M a y 28, 1975
+
“A,(F)
14,490 15,150 13,986 14,285
16,000 15,479
16,390
13,157 13,793
14,184 -15,503 (sh)
13,157 13,698 14,285 -15,384 (sh) 13,245 13,947 -14,492 (sh) -13,245 13,698 14,084 14,492 (sh) 15,625
3029 Table VI. Optical Electronegativities Obtained from CT Spectra and the L F Parameters Parameters in Pauling units of 3 x lo4 cm-'
Parameters in cm-I
Ab sorbing species NiC1,'NiCl,Br,'NiBr,'NiCl,I,' Ni1,'-
B
C
1ODq
'13
740 713.75 680 639.75 5 37
2938 2805 2638 3007 2959
0.1 19 0.112 0.11 0.112 0.11
-0.124 -0.1 18 -0.112 -0.1 18 -0.115
0
O E [ x ] for NiCI2X2' -are taken as averages of those of NiCI,'-and
a v o b s d and
Vobsd
Vcorr
OE[X]
OE[Ni(II)]
1.184 -1.06SQ 0.947 -0.798a 0.65b
0.939 0.832 0.725 0.568 0.425
3.0 2.90 2.8 2.65a 2.5
2.06 2.07 2.08 2.08 2.08
Nix,'-.
bReference 1.
Table VII. Computer-Fitted Least-Squares Representation for Specific and Equivalent Conductancesa and Fluiditiesb as a Function of Temperaturec for MX,-Rich Mixtures of Molten R,N+X-
System (C,H,),N+Cl- + MnCl, (24.5 mol %) (c,H,),N+c~- + CoCI, (26.6 mol %) (C,H,),N+CI-+ (22.1 mol %)
NiC1,
Equation no.
k or A
(i) (ii) (iii) (i) (ii) (iii) (i) (ii) (iii)
0.1789 X lo-, 0.2367 382.5 0.1386 X lo-' 0.0947 210.3 0.0708 X lo-, 0.0551 160.2
b
a
C
@
k or A
@
3.3487 -0.4223 x 923.8 36.226 605.1 5226.0 5.4064 -0.3143 X 198.97 743.1 617.8 12737.0 3.9199 -0.1783 X lo-, 663.63 69.24 621.7 8377.8
-0.07901 295.03 712.68 -0.10124 682.08 916.17 -0.08283 437.02 875.01
Std Dev i n k , A/@
@
k or A
0.2622 X l o d 6 0.4662 X 243.4 321.75 278.5 275.96 0.184 X 0.4869 X lo-' 267.2 290.08 276.21 277.0 0.4442 X lo-' 0.1158 X 309.13 272.10 267.26 27 1.6
0.025 f 0.005 0.025 i 0.005 0.012 t 0.006 0.015 * 0.005 0.015 i 0.005 0.012 i 0.008 0.02 0.02 0.01 i 0.006
QTemperaturerange for conductance: 373-413 O K . bTemperature range for fluidity: Mn2+, 393-428 "K; Goa+, 398-433 "K, and NiZ+, 393-428 O K . C f , 'C, T, "K. (i) Y = a + bt + cf'; (ii) Y = a exp[-b/(T - c)] ; and (iii) Y = QT-", exp[-b/(T - c)] in which c corresponds to T0C4 $1. oe 6
65
LIN-T~D ~ 1 0 3 7.0 75
8.0
8.5
I 07
1.5
06
*I
0
-
10-
r* -z
m
- 0.5.
05
-
a
4-
Jo
04
8
2
0 0
Figure 4. Plots of log Y T ' I 2vs. l / ( T molten (C4H9)4N+CI-.
03
02
01
1.11
, 80
ZOO
220
240
260
280
300
320
-.
-.340
Wovelength I n m )
Figure 3. Charge-transfer spectra of MC1d2- and CI- in MC12 ( M = I , Co, 11, Ni; and 111, Mn) -rich mixtures of molten (C4H9)4N+CI-,
NiC12Br22- > NiBr42- > NiCl~12~> Ni142- is consistent with the decrease in B and O E p ] values from chloride to iodide. CT Spectra of X- in Thin Film of MX2-Rich Mixtures of RdN+X-. In addition to the CT spectra of MX4'- (Figure 3), still more intense bands a t higher energies have been recorded for X- as the ratio of [(R4N+)2MX42-] to [X-] increases in the MX2-rich mixtures of R4N+X- and are unaf-
- To) for MCI*-rich mixtures of
fected by the viscous medium containing the species of the type {(R4N+)*MX4*-), ( M = Mn, Co, and Ni) for a given X-. The band separation of 0.87 to 0.97 eV in iodide is c ~ m p a r a b l e with ~ ~ ? the ~ ~ calculated value of 0.889 eV for the doublets in transitions to psyl configuration. The splitting of the doublet in CI- being 0.103 eV is too small to be observed (Figure 3). The CT bands of X- may be as~ i g n e d ~either ' . ~ ~to X-nps(n 1)s Xnp6 or (XnpS a quasi-continuum of delocalized states of one electron) Xnp6, p5yi p6y4 transitions. 11. Transport Behavior. Free-Volume Model for the Electrical Conductances and Viscosities of Glass-Forming Melts. The transport properties have frequently been described by the rate process t h e ~ r y .However, ~ ~ , ~ ~ the electrical conductances and fluidities of molten mixtures of MCl2 and R4N+X- measured as functions of temperature and composition show a non-Arrhenius type behavior and are therefore least-squares fitted to several functional forms based on the free-volume model."-" The computed parameters a r e listed in Table VII. It is significant that the To values a r e found to be independent of t h e method employed in
-
Islam et al.
+
-
-
+
/ Transport Behavior of Glass-Forming Melts
3030 Table VIII. Energies of Activation of Conductances and Fluidities for MX,-Rich Mixtures of R,N+X at Several Temperatures T , "K
373 378 383 388 393 398 403 408 413
aRT2 + ' / , R T , a kcal/mol
Ek,
@J'
Ek,@2s
E k , O3
kcal/molb
Emrr A, a), kcal)mol
0.540 0.550 0.560 0.570 0.580 (0.39 1) 0.5 9 1 (0.395) 0.601 (0.400) 0.612 (0.405) 0.623 (0.410)
System: (C,HJ,N+Cl-+ MnC1, (24.5 mol %) 15.02 15.20 16.00 14.84 14.47 14.47 14.25 13.81 13.71 13.52 13.2 1 12.80 12.78 12.66 12.56 (17.37)C (17.84) (16.59) 12.09 12.16 12.17 (15.6 1) (1 5.97) (15.22) 11.47 11.70 11.42 (14.24) (14.42) (15.21) 10.91 11.27 10.65 (13.15) (13.12) (12.98) 10.41 10.88 10.28 (12.26) (12.01) (12.57)
15.95 15.14 14.48 13.75 13.25 (17.66) 12.73 (16.00) 12.13 (15.02) 11.55 (13.49) 11.15 (12.69)
(0.415)
(11.52)
(1 1.06)
(11.66)
(11.83)
(0.420)
(10.89)
(10.23)
(11.24)
(11.21)
(0.425)
(10.36)
(10.55)
0.538 0.548 0.558 0.568 0.578 0.589 (0.395) 0.599 (0.4 00) 0.610 (0.405) 0.621 (0.4 10)
(9.51) (10.51) System: (C,H,),N+CI-+ CoCl, (26.58 mol %) 17.97 18.33 18.28 17.17 16.72 17.83 17.05 16.14 15.22 15.92 15.22 14.85 14.82 14.40 13.71 13.82 13.66 12.79 (17.97) (18.43) (18.28) 12.93 12.99 11.42 ( 17.28) (17.29) (17.26) 12.17 12.39 10.51 (16.33) (16.23) (16.13) 10.50 11.84 9.69 (15.08) (15.34) (1 5.30)
18.73 17.83 16.70 15.90 14.89 14.01 (1 8.62) 13.05 (17.68) 12.30 (16.64) 11.30 (15.65)
(0.415)
(14.4 1)
(14.47)
(14.62)
( 14.92)
(0.420)
(13.57)
(13.73)
(1 3.7 1)
(14.09)
(0.425)
(12.82)
( 1 3.05)
(12.98)
(13.38)
( 0.430)
(12.16)
(12.44)
(12.11)
(12.67)
0.521 0.530 0.540 0.550 0.559 (0.391) 0.569 (0.395) 0.579 ( 0.400) 0.588 (0.405) 0.598 (0.410)
System: (C,H,),N+Cl-+ NiC1, (22.13 mol %) 17.79 18.02 18.28 16.39 16.80 17.37 15.08 15.73 15.99 13.94 13.78 14.85 12.96 13.94 13.7 1 (19.73) (19D7) (18.46) 12.13 13.18 12.80 (17.53) (17.42) (17.27) 11.41 12.49 11.99 (16.00) (16.01) (16.13) 10.80 11.19 11.43 (14.73) (14.7 9) (15.2 1) 10.27 11.33 10.65 (13.67) (13.73) (13.85)
18.55 17.38 16.14 15.07 14.10 (19.36) 13.27 ( 17.80) 12.54 (16.47) 11.73 (15.16) 11.35 (14.16)
(0.415)
(12.79)
(12.80)
(13.16)
(13.33)
(0.420)
(12.04)
(11.98)
(12.68)
(12.65)
(0.425)
(11.39)
(11.26)
(11.52)
(11.82)
A
1.333 1.256 1.238 1.168 1.138
418 423 428
373 378 383 388 393 398 403 408 413
1.329 1.354 1.352 1.385
418 423 428 433
37 3 378 383 388 393 398 403 408 413
1.373 1.341 1.313 1.306 1.247
418 423 428 a '/,
R T is added to E&,.bEk @! from the derivative of a + bt + ct' ;Ek,@' from the derivative of u exp[-b/(T - c)] and Ek,$3 from the slope of Arrhenius plot log ( k , @Ivs. 1/T. cE@values are given in parentheses.
studying the transport behavior as To,., = TO,@ (Table VII). Thus the plots of log Y(k,4) vs. 1 / T become linear by the introduction of a third adjustable parameter, To as shown in the plots (Figure 4) of log YT'12 vs. 1 / ( T - T o ) . The energies of activation, Ek,@,were evaluated from the
derivatives d In Y / d ( T - ' ) by making use of the three parameter equations (Table VII) for the transport behavior, and also from the successive pairs of points at 5' intervals from the plots of log Y vs. 1 / T . The plot of the averages of Ek,41 Ek,s2 E k , 4 3 as a function of composition shows
Journal of the American Chemical Society f 97:ll f May 28, 1975
+
+
303 1
Figure 5. Test of
,
,
1/Vr
5.0 , Ill
4:6
4;4
1
I1 $\ \0, ; .2; .0
0.29
,
- 0.23 -0.03 8.
8
-g
-
0,
- -0.13
012-.o.o
-a 02--019
- -0.33
-0.22
-y9
5.25
5.$5
4.9
47
5 L
I1
I
5.1
1
1 /Vf
Figure 6. Plots of log 6 vs. l / u r for MCIZ-rich mixtures of molten (CdHq)dN+CI-.
that Ek,$ is composition independent in the cases of dilute solutions unlike those in the glassy material. The energies of activation have been found to increase considerably a t low temperatures and decrease slowly with an increase in temperature (Table VIII). The corrected activation energies, E,,rr~.,,4), were calculated from the expressions E,,,,(.~) = a R T 2 ('/2)RT ( E k ) and E,,,,($) = Y2RT (E$)= k,R[ T / ( T - T0)l2,respectively, using the ( E k . 6 ) values and the coefficient of cubical expansion, cy, evaluated a t several temperatures from the density data expressed by the least-squares fit P I = 1.1975 - 0.58099 X 10-3(T)
+
+
p11 = pill
+
1.2006 - 0.58397 X 10-3(T)
= 1.1894 - 0.5208 X 10-3(T)
+
+
for ( I ) MnCl2 (C4H9)4N+CI-, (11) CoCl2 (C4Hg)dN+CI-, and (111) NiCl2 (C4H9)4N+CI-, respectively. The applicability of the free-volume model in explaining the transport behavior of the glass-forming melts under discussion is further supported by the linear plots as expected on the (Figure 5) of E,,,, vs. [ T / ( T basis of the equation, E,,,, = A [ T / ( T - T o ) ] 2 B based on such a model. An increase in Ecorr($) with a decrease in temperature (Table VIII) as well as an increase in [ M X 2 ] in molten R4N+X- suggests the presence of increased molecular association/intermolecular forces3' as apparent from an approximately constant ratio of E,,/EAi and the nonlinear plots of viscosity, 7 vs. [MX2].
+
+
2 .o
I .o
44.0
48.0
v-vo
52.0
560
600
64.0
(crn31 mole)
Figure 7. Plots of $ vs. v - vo for MCl2-rich mixtures of molten (C+tHg)+th+X-.
The applicability of the free-volume model to these systems is further supported by the linear plots of TOvs. cationic p ~ t e n t i a l . To ~ ~has . ~ ~been found to decrease with successive increases in [ C O C I ~as ] a result of complex formation which leads to an eventual supercooling to glassy states. A t low temperatures the association of such species {(R4B+)2MC12X22-)x, in which x depends on the polymeric tendency of these species, results in a highly viscous liquid. This view may also be supported by a high E,,, and the low electrical conductances. The linear plots of log 4 vs. 1 / v f (Figure 6) for MX2 R4N+X- justify the applicability of Doolittle's expression based on the free-volume model. Similar expression^^^ have recently been used in explaining the fluidities as a function of free volume, v f . For example, Hildebrand's equation 4 = B ( v - V O ) / V O has been found suitable in few systems since volume expansion has been mentioned as the primary cause for the ease of viscous flow. Linear plots of 4 vs. (v - v o ) and 4 vs. ( v - vO)/vo have been reported40 in different ranges of temperature. However, in the present investigations the plots of 4 vs. ( v - V O ) are linear only in the high-
+
Islam et al.
/ Transport Behavior of Glass-Forming Melts
3032 were possible even a t temperatures lower than those in the corresponding dilute solutions as the melts become soft with successive increases in [MX2]. T h e plots of 4 vs. ( v - V O ) are found to be nonlinear (Figure 7 ) presumably because of much increased molecular interactions/associations. Similar behaviors are shown by these systems in the plots of 4 vs. ( v - V O ) / V O (Figure 8). In such cases the molecules are expected to be closely packed and the linear relation between the fluidity and molal volume is violated.40 The viscosity anomalies a t lower temperatures have earlier been ascribed to a scarcity of free space whi,ch does not permit free rotation of molecules in the liquid. This may lead to the formation of “clusters” or “network7-like arrangements” due to the increased intermolecular forces. However, the electrical conductances of ionic melts may be explained satisfactorily by the expression, = B.,[(v V O ) / V O ] , as shown in Figure 9, for several systems. This may lead to the assumption that the mechanism of ionic conductance is presumably different from that of viscosity, as the former involves the exchange of ions with the free volume while the latter has to overcome a potential energy barrier in laminar flow of clusters.
I
P
I
’
I
I
/
Iv-vo ) I vo
Figure 8. Plots of 6 vs. ( v - v o ) / v o relative volume expansion for MC12-rich mixtures of molten ( C ~ H ~ ) A , N + X - .
Acknowledgment. It is a pleasure to thank Dr. Pedro Smith of O a k Ridge National Laboratory for helping us in computer programming, and Professors B. R . Sundheim and Wasi-ur-Rahman of New York University and Head of the Department of Chemistry, Aligarh Muslim University, respectively, for providing the necessary facilities. Financial assistance to three of us (M.R.I., S.A., and B.W.) from the C.S.I.R. (New Delhi) is gratefully acknowledged. References and Notes
I V - 20 3
I1
V I - 31 5
VII-MnClZ
I C q H g ) 4 NCI
V I I I ~ C O C’(C4 I ~ H& NCI IX-NICIZ * ( C 4 H914 NCl
9
‘
