The coexistence curves of {xC6H5NO2+ (1 −x)CH3(CH2)3CH3} and {xC6H5NO2+ (1 −x)CH3(CH2)8CH3} in...
11
J. Chem. Thermodynamics 1998, 30 1049]1059 Article No. ct980364 { The coexistence curves of x C H NO H 6 5 2 ( ) ( ) } 1 I x CH CH CH and 3 2 3 3 { ( ) ( ) } x C H NO H 1 I x CH CH CH 6 5 2 3 2 8 3 in the critical region Xueqin An, Peng Li, Haihong Zhao, a and Weiguo Shen b Department of Chemistry, Lanzhou Uni ¤ ersity, Lanzhou, Gansu 730000, P.R. China Ž .Ž . Ž . Coexistence curves of T , n , T , x , and T , f , where n, x, and f are refractive index, mole Ž fraction, and volume fraction, respectively, for the binary mixtures x C H NO q 1 y 6 5 2 . Ž . 4 Ž . Ž . 4 x CH CH CH and x C H NO q 1 y x CH CH CH have been determined 3 2 3 3 6 5 2 3 2 8 3 within about 10 K of the critical temperatures by measurements of n. The critical amplitude B and the critical exponent b have been deduced and the values of b are consistent with the theoretical ones. The experimental results have been analysed to examine the Wegner correction terms and the behaviour of the diameter of the coexistence curves. The coexistence curves have been successfully described by a combination of the Wegner equation and the expression for the diameter. The power law dependence of critical amplitudes on molar mass has also been discussed. q 1998 Academic Press KEYWORDS: coexistence curve; refractive index; critical phenomena; nitrobenzene; pentane; dodecane 1. Introduction Ž In previous work, we reported coexistence curve measurements of nitrobenzene q . Ž . Ž . Ž tetradecane , nitrobenzene q dodecane , nitrobenzene q octane , and nitro- . benzene q hexadecane near the critical points by using a refractive index technique. Ž 1 ] 4. As a continuing part of the study of the critical phenomena in binary mixtures of chain molecules, here we report the measurements of coexistence Ž . Ž . curves for nitrobenzene q pentane and nitrobenzene q decane . The experi- mental results are analysed to determine the critical exponents b and the critical Ž . amplitudes B, and to examine the behaviour of the differences r y r of 2 1 general ‘‘densities’’ of lower and upper coexisting phases and the diameters r of d the coexistence curves over a temperature range of about 10 K from the critical temperatures. The dependence of critical amplitudes on molar mass for six solutions studied are also discussed. a Present address: Chendu Organic Chemistry Institute, The Chinese Academy of Science. b To whom correspondence should be addressed. 0021] 9614r98r091049 q 11 $30.00r0 q 1998 Academic Press
Transcript of The coexistence curves of {xC6H5NO2+ (1 −x)CH3(CH2)3CH3} and {xC6H5NO2+ (1 −x)CH3(CH2)8CH3} in...
J. Chem. Thermodynamics 1998, 30 1049]1059Article No. ct980364
{The coexistence curves of xC H NO H6 5 2( ) ( ) }1 I x CH CH CH and3 2 3 3{ ( ) ( ) }xC H NO H 1 I x CH CH CH6 5 2 3 2 8 3in the critical region
Xueqin An, Peng Li, Haihong Zhao,a and Weiguo Shenb
Department of Chemistry, Lanzhou Uni ersity, Lanzhou,Gansu 730000, P.R. China
Ž . Ž . Ž .Coexistence curves of T , n , T , x , and T , f , where n, x, and f are refractive index, mole� Žfraction, and volume fraction, respectively, for the binary mixtures xC H NO q 1 y6 5 2
. Ž . 4 � Ž . Ž . 4x CH CH CH and xC H NO q 1 y x CH CH CH have been determined3 2 3 3 6 5 2 3 2 8 3within about 10 K of the critical temperatures by measurements of n. The critical amplitudeB and the critical exponent b have been deduced and the values of b are consistent with thetheoretical ones. The experimental results have been analysed to examine the Wegnercorrection terms and the behaviour of the diameter of the coexistence curves. The coexistencecurves have been successfully described by a combination of the Wegner equation and theexpression for the diameter. The power law dependence of critical amplitudes on molar masshas also been discussed. q 1998 Academic Press
KEYWORDS: coexistence curve; refractive index; critical phenomena; nitrobenzene; pentane;dodecane
1. Introduction
ŽIn previous work, we reported coexistence curve measurements of nitrobenzene q. Ž . Ž . Žtetradecane , nitrobenzene q dodecane , nitrobenzene q octane , and nitro-
.benzene q hexadecane near the critical points by using a refractive indextechnique.Ž1 ] 4. As a continuing part of the study of the critical phenomena inbinary mixtures of chain molecules, here we report the measurements of coexistence
Ž . Ž .curves for nitrobenzene q pentane and nitrobenzene q decane . The experi-mental results are analysed to determine the critical exponents b and the critical
Ž .amplitudes B, and to examine the behaviour of the differences r y r of2 1general ‘‘densities’’ of lower and upper coexisting phases and the diameters r ofdthe coexistence curves over a temperature range of about 10 K from the criticaltemperatures. The dependence of critical amplitudes on molar mass for six solutionsstudied are also discussed.
a Present address: Chendu Organic Chemistry Institute, The Chinese Academy of Science.b To whom correspondence should be addressed.
0021]9614r98r091049 q 11 $30.00r0 q 1998 Academic Press
X. An et al.1050
2. Experimental
Ž .The nitrobenzene, obtained from Beijing Chemical Factory A.R. grade , was driedover calcium chloride for 5 d and distilled slowly under reduced pressure. Themiddle part of the distillate was collected and passed through a column of driedchromatographic alumina. The purified nitrobenzene was stored in the dark andover 0.4 nm molecular sieve. The pentane and decane, mass fraction 0.99, weresupplied by Aldrich Chemical Co. and Fluka Co., respectively, and were dried andstored over 0.4 nm molecular sieve.
The coexistence curves were determined by measurements of the refractiveindices. The apparatus and experimental procedure for refractive indexmeasurements, and the techniques for determination of the critical mole fractionsx and the critical temperatures T have been described in detail previously.Ž5.c cDuring measurements, the temperature was constant to "0.002 K. The accuracyand the precision in measurements of temperature were better than "0.01 K and
Ž . Ž . Ž . � Ž . Ž . 4TABLE 1. Coexistence curves of T , n , T , x , and T , f for xC H NO q 1 y x CH CH CH .6 5 2 3 2 3 3Refractive indices n were measured at wavelength l s 632.8 nm, and T s 297.104 K. Volume fractionc
is denoted by f. Subscripts 1 and 2 relate to upper and lower phases, respectively
Ž .T y T rK n n x x f fc 1 2 1 2 1 2
0.002 1.4242 1.4304 0.373 0.405 0.345 0.3760.005 1.4237 1.4309 0.370 0.408 0.342 0.3780.010 1.4230 1.4316 0.367 0.411 0.339 0.3820.013 1.4226 1.4320 0.365 0.413 0.337 0.3840.015 1.4222 1.4324 0.362 0.415 0.335 0.3860.020 1.4206 1.4329 0.354 0.418 0.327 0.3880.026 1.4211 1.4335 0.357 0.421 0.329 0.3910.036 1.4203 1.4343 0.352 0.425 0.325 0.3950.044 1.4198 1.4348 0.350 0.428 0.323 0.3980.061 1.4189 1.4357 0.345 0.432 0.318 0.4020.066 1.4187 1.4360 0.344 0.434 0.317 0.4040.084 1.4179 1.4367 0.340 0.437 0.313 0.4070.102 1.4172 1.4374 0.336 0.441 0.309 0.4110.119 1.4167 1.4380 0.333 0.444 0.307 0.4140.144 1.4160 1.4389 0.330 0.448 0.303 0.4180.178 1.4153 1.4395 0.326 0.451 0.300 0.4210.236 1.4142 1.4407 0.320 0.457 0.294 0.4270.297 1.4133 1.4418 0.315 0.463 0.289 0.4330.385 1.4121 1.4430 0.308 0.469 0.283 0.4380.684 1.4091 1.4466 0.292 0.486 0.267 0.4561.018 1.4066 1.4496 0.278 0.501 0.254 0.4701.435 1.4044 1.4526 0.265 0.515 0.242 0.4842.208 1.4019 1.4561 0.250 0.531 0.228 0.5012.980 1.3990 1.4607 0.231 0.551 0.211 0.5224.010 1.3965 1.4650 0.215 0.570 0.195 0.5415.106 1.3946 1.4685 0.201 0.585 0.183 0.5565.764 1.3937 1.4706 0.195 0.594 0.177 0.5656.739 1.3924 1.4734 0.185 0.605 0.168 0.5777.772 1.3913 1.4762 0.176 0.617 0.160 0.5898.859 1.3903 1.4789 0.167 0.627 0.152 0.6009.769 1.3895 1.4810 0.160 0.636 0.145 0.609
� 4Coexistence curves of C H NO q n-alkane6 5 2 1051
Ž . Ž . Ž . � Ž . Ž . 4TABLE 2. Coexistence curves of T , n , T , x , and T , f for xC H NO q 1 y x CH CH CH .6 5 2 3 2 8 3Refractive indices n were measured at wavelength l s 632.8 nm, and T s 295.964 K. Volume fractionc
is denoted by f. Subscripts 1 and 2 relate to upper and lower phases, respectively
Ž .T y T rK n n x x f fc 1 2 1 2 1 2
0.006 1.4619 1.4687 0.550 0.600 0.391 0.4400.012 1.4613 1.4693 0.545 0.604 0.386 0.4440.019 1.4609 1.4697 0.542 0.607 0.383 0.4470.030 1.4603 1.4703 0.538 0.611 0.379 0.4520.036 1.4597 1.4709 0.533 0.615 0.375 0.4560.042 1.4594 1.4713 0.531 0.618 0.372 0.4590.056 1.4590 1.4717 0.528 0.620 0.370 0.4620.071 1.4585 1.4722 0.524 0.624 0.366 0.4650.097 1.4578 1.4729 0.518 0.628 0.361 0.4700.128 1.4571 1.4738 0.512 0.634 0.355 0.4770.184 1.4560 1.4750 0.503 0.642 0.347 0.4850.261 1.4549 1.4762 0.494 0.650 0.339 0.4940.352 1.4538 1.4774 0.485 0.658 0.331 0.5020.451 1.4528 1.4785 0.476 0.664 0.323 0.5100.530 1.4521 1.4794 0.470 0.670 0.318 0.5160.667 1.4512 1.4803 0.462 0.675 0.311 0.5221.000 1.4493 1.4829 0.445 0.691 0.296 0.5401.317 1.4478 1.4848 0.431 0.701 0.284 0.5521.730 1.4464 1.4869 0.417 0.713 0.273 0.5662.270 1.4449 1.4892 0.401 0.725 0.260 0.5813.255 1.4427 1.4928 0.377 0.743 0.241 0.6034.106 1.4412 1.4953 0.359 0.755 0.227 0.6184.914 1.4400 1.4977 0.344 0.767 0.216 0.6335.666 1.4391 1.4995 0.332 0.774 0.207 0.6436.551 1.4383 1.5015 0.320 0.783 0.198 0.6557.815 1.4373 1.5042 0.304 0.794 0.187 0.6709.037 1.4363 1.5066 0.288 0.804 0.176 0.683
10.005 1.4357 1.5084 0.278 0.810 0.168 0.692
"0.001 K, respectively. The accuracy of measurement was "0.003 K for theŽ .temperature difference T y T , "0.0002 for the refractive index in each coexistingc
phase, and "0.001 for the critical mole fraction x .c
3. Results and discussion
The critical mole fractions and the critical temperatures were determined to beŽ . Ž . � Žx s 0.386 " 0.001 and T s 297.1 " 0.2 K for xC H NO q 1 yc c 6 5 2
. Ž . 4 Ž . Ž .x CH CH CH , and x s 0.574 " 0.001 and T s 296.0 " 0.2 K for3 2 3 3 c c� Ž . Ž . 4xC H NO q 1 y x CH CH CH .6 5 2 3 2 8 3
The refractive indices n were measured for each coexisting phase atvarious temperatures. The results are listed in columns 2 and 3 of table 1 for� Ž . Ž . 4 � ŽxC H NO q 1 y x CH CH CH , and of table 2 for xC H NO q 1 y6 5 2 3 2 3 3 6 5 2. Ž . 4 Ž . Ž .x CH CH CH . They are also shown in figures 1 a and 2 a .3 2 8 3
We assumed that the refractive index n of a pure liquid or a mixture may be
X. An et al.1052
Ž . Ž . Ž . � ŽFIGURE 1. Coexistence curves of: a, T , n ; b, T , x ; and c, T , f for xC H NO q 1 y6 5 2. Ž . 4x CH CH CH . v, experimental values of concentration variables r of the coexisting phases; ',3 2 3 3
experimental values of diameter r of the coexisting phases; }}}, concentration variables r andd caldiameter r of the coexisting phases from calculation.d
expressed as a linear function of temperature in a certain temperature range:
.n T , x s n T8, x q R x T y T8 , 1Ž . Ž . Ž . Ž . Ž .R x s xR q 1 y x R , 2Ž . Ž . Ž .A B
Ž .where R x is the derivative of n with respect to T for a particular composition x,Ž .and R and R are the values of R x for x s 1 and x s 0, respectively. In theA B
previous works,Ž1,5 ] 7. we made a series of measurements of refractive indices ofsolutions with various known compositions at various temperatures, and found that
Ž . Ž .equations 1 and 2 fitted the experimental data very well with a standardŽ .deviation of less than 0.0002 in refractive index. The validity of equations 1 and
� 4Coexistence curves of C H NO q n-alkane6 5 2 1053
Ž . Ž . Ž . � ŽFIGURE 2. Coexistence curves of: a, T , n ; b, T , x ; and c, T , f for xC H NO q 1 y6 5 2. Ž . 4x CH CH CH . v, experimental values of concentration variables r of the coexisting phases; ',3 2 8 3
experimental values of diameter r of the coexisting phases; }}}, concentration variables r andd caldiameter r of the coexisting phases from calculation.d
Ž . Ž .2 allowed us to obtain n T , x as a function of T and x simply from measurementsŽ .of R x for two pure components at various temperatures, and measurements of
the refractive indices for mixtures with various known compositions at a fixedtemperature above the critical point. The refractive indices n of pure pentane anddecane at various temperatures were measured and are listed in table 3.Table 4 gives the measured refractive indices of a series of binary mixtureswith known values of mole fraction x in the one phase region at T s 297.54 K for� Ž . Ž . 4 �xC H NO q 1 y x CH CH CH , and T s 296.88 K for xC H NO q6 5 2 3 2 3 3 6 5 2Ž . Ž . 4 Ž .1 y x CH CH CH . Fitting equation 1 to the results listed in table 3 gives3 2 8 3
. y4 y1 . y4 y1R s5.99 10 K for pentane and R s y4.41 10 K for decane. TheB B. y4 y1 Ž1.value R s y5.13 10 K was reported previously. The values of n at variousA
compositions and given temperatures listed in table 4 were fitted with a polynomial
X. An et al.1054
Ž . Ž .TABLE 3. Refractive indices n at wavelength l s 632.8 nm for CH CH CH and CH CH CH3 2 3 3 3 2 8 3at various temperatures
TrK n TrK n TrK n TrK n
Ž .CH CH CH3 2 3 2
285.961 1.3584 287.923 1.3571 290.371 1.3556 292.966 1.3541295.435 1.3527 296.438 1.3521 297.081 1.3516 297.350 1.3515
Ž .CH CH CH3 2 8 3
286.010 1.4135 287.910 1.4127 290.497 1.4116 293.304 1.4103294.420 1.4098 295.562 1.4094 296.148 1.4090 296.925 1.4087
Ž . Ž . � Žform. We obtained equations 3 and 4 for xC H NO q 1 y6 5 2. Ž . 4 � Ž . Ž . 4x CH CH CH and xC H NO q 1 y x CH CH CH , respectively:3 2 3 3 6 5 2 3 2 8 3
n 297.54 K, x s 1.35151 q 0.20802 x y 0.06046 x 2 q 0.08425x 3 y 0.03840 x 4 ,Ž .3Ž .
n 296.88 K, x s 1.40888 q 0.05928 x q 0.08019 x 2 y 0.05352 x 3 q 0.05064 x 4 ,Ž .4Ž .
Ž . Ž .with a standard deviation of less than 0.0002. Equations 1 to 4 were used toconvert refractive indices of the coexistence curve to mole fractions. The volumefraction f of C H NO for both solutions was then calculated from the mole6 5 2fraction by:
1rf s 1 y K q Krx , 5Ž . Ž .K s d M rd M , 6Ž .A B B A
where d is mass density, M is the molar mass, and subscripts A and B relate tonitrobenzene and n-alkane, respectively. The value of d and d were obtainedB A
� ŽTABLE 4. Refractive indices n at wavelength l s 632.8 nm for xC H NO q 1 y6 5 2. Ž . 4 � Ž . Ž . 4x CH CH CH and xC H NO q 1 y x CH CH CH at temperatures of 297.54 K3 2 3 3 6 5 2 3 2 8 3
and 296.88 K, respectively
x n x n x n x n
� Ž . Ž . 4xC H NO q 1 y x CH CH CH6 5 2 3 2 3 3
0.0000 1.3514 0.1025 1.3726 0.2066 1.3924 0.2992 1.41010.3989 1.4295 0.5002 1.4484 0.6211 1.4719 0.6840 1.48420.7874 1.5042 0.9014 1.5261 1.0000 1.5450
� Ž . Ž . 4xC H NO q 1 y x CH CH CH6 5 2 3 2 8 3
0.0000 1.4089 0.1001 1.4155 0.1974 1.4234 0.2944 1.43230.3808 1.4412 0.4954 1.4545 0.5942 1.4675 0.7022 1.48350.7872 1.4990 0.8964 1.5204 1.0000 1.5455
� 4Coexistence curves of C H NO q n-alkane6 5 2 1055
Ž .TABLE 5. Values of critical amplitudes B and critical exponents b for coexistence curves of T , n ,Ž . Ž . � Ž . Ž . 4 � ŽT , x , and T , f for xC H NO q 1 y x CH CH CH and xC H NO q 1 y6 5 2 3 2 3 3 6 5 2
. Ž . 4 Ž . Ž .x CH CH CH in equation 7 ; t s T y T rT3 2 8 3 c c
Order t - 0.034 t - 0.003
parameter B b B b
� Ž . Ž . 4xC H NO q 1 y x CH CH CH6 5 2 3 2 3 3
n 0.284 " 0.006 0.332 " 0.002 0.28 " 0.01 0.329 " 0.006x 1.49 " 0.03 0.332 " 0.002 1.45 " 0.07 0.329 " 0.006f 1.45 " 0.03 0.332 " 0.002 1.40 " 0.07 0.329 " 0.006
� Ž . Ž . 4xC H NO q 1 y x CH CH CH6 5 2 3 2 8 3
n 0.223 " 0.002 0.332 " 0.002 0.210 " 0.008 0.325 " 0.005x 1.63 " 0.02 0.332 " 0.002 1.50 " 0.06 0.326 " 0.005f 1.60 " 0.02 0.331 " 0.002 1.52 " 0.06 0.325 " 0.005
Ž .from references 8 and 9. The values of x, f of coexisting phases at varioustemperatures are listed in columns 4 to 7 of tables 1 and 2, and are shown in partsŽ . Ž .b and c of figures 1 and 2.
In the region sufficiently close to the critical temperature, the coexistence curvecan be represented by:
r y r s Bt b , 7Ž .2 1
Ž .where t s T y T rT , T is the critical temperature, B is the critical amplitude,c c cb is the critical exponent, r is the ‘‘density’’ variable, and r and r are the values1 2
Ž .of r in upper and lower coexistence phases. The differences r y r obtained in2 1Ž .this work were fitted with equation 7 , with all points equally weighted, to obtain
b and B. The results are listed in table 5. The values of b and B depend on thecutoff values of t , but for t F 0.003 the values of the exponent b aremax max
Ž .consistent with that of other solutions of nitrobenzene q n-alkane reportedpreviously Ž1 ] 4. and approach the theoretical value of 0.327.
With the critical exponents b and D to be fixed at the theoretical valuesŽ . Ž10 ] 11.b s 0.327, D s 0.50 , a weighted non-linear least-squares programme wasused to fit the Wegner equation,Ž12.
r y r s Bt b q B t bqD q B t bq2D q ??? , 8Ž .2 1 1 2
to obtain the parameters B and B . The total uncertainties used in weighting1Ž .included the errors in measurements of r y r and standard deviations2 1
Ž .propagated from measurements of T y T . The results are summarized in table 6.cDiameters r of coexistence curves for the three choices of the ‘‘density’’d
variable were fitted to the form:
r s r q r r2 s r q Dt Z , 9Ž . Ž .d 2 1 c
to test the presence of a 2b term and to examine the goodness of the selected
X. An et al.1056
Ž . Ž . Ž . Ž .TABLE 6. Coefficients of equation 8 for coexistence curves of T , n , T , x , and T , f for� Ž . Ž . 4 � Ž . Ž . 4xC H NO q 1 y x CH CH CH and xC H NO q 1 y x CH CH CH6 5 2 3 2 3 3 6 5 2 3 2 8 3
� Ž . Ž . 4 � Ž . Ž . 4xC H NO q 1 y x CH CH CH xC H NO q 1 y x CH CH CH6 5 2 3 2 3 3 6 5 2 3 2 8 3
Order parameter B B B B1 1
n 0.2784 " 0.0002 0.2188 " 0.00020.2732 " 0.0007 0.039 " 0.005 0.2137 " 0.0006 0.040 " 0.004
x 1.444 " 0.003 1.601 " 0.0031.413 " 0.009 0.24 " 0.07 1.558 " 0.009 0.34 " 0.07
f 1.404 " 0.004 1.580 " 0.0041.37 " 0.01 0.28 " 0.09 1.55 " 0.01 0.25 " 0.09
Ž .order parameters. The apparent exponent Z in equation 9 was fixed at the valuesŽ .1 y a s 0.89, and 2b s 0.654 in separate fitting procedures. The results are
Ž .compared in table 7. The quality of the fit with equation 9 is indicated by thevalues of standard deviations listed in table 7. The difference D s of the standarddeviations between the fits with Z s 1 y a and with Z s 2b was used to showthe goodness of the order parameter.Ž13. The smaller the value of D s, the better
� Ž . Ž . 4the order parameter is. For xC H NO q 1 y x CH CH CH , the values of6 5 2 3 2 8 3. y5 . y3D s are 7.0 10 and 1.1 10 for f and x, respectively. The difference between
two D s values is significant, indicating that f is a significantly better order� Ž . Ž . 4parameters than x. However, for xC H NO q 1 y x CH CH CH , the6 5 2 3 2 3 3
. y4 . y4values of D s are y1.0 10 and y1.6 10 for f and x, respectively, whichalthough suggesting that x is slightly better than f, the difference is trivial. This is
Ž .consistent with what the symmetry of the coexistence curves indicates: the T , fŽ . � Žcurve is obviously more symmetric than the T , x curve for xC H NO q 1 y6 5 2
. Ž . 4 Ž .x CH CH CH , but the difference in the symmetry between the T , x curve3 2 8 3Ž . �and the T , f curve is too small to be observed in figure 1 for xC H NO q6 5 2
Ž . Ž . 41 y x CH CH CH . The experimental values of n listed in table 7 were3 2 3 3 cobtained by extrapolating refractive indices against temperatures in the one-phaseregion to the critical temperatures. The experimental values of x and f listed inc ctable 7 were determined by the technique of ‘‘equal volumes of two coexistence
Ž . Ž .phases’’ and calculated by equations 5 and 6 . The uncertainties of optimalparameters reported in table 7 included no systematic uncertainties contributed byconverting n to x, and x to f. Such uncertainties in x and f were estimated to beabout "0.002. Thus the values of x and f obtained from extrapolation ofc c
Ž .equation 9 are consistent with those from observations. It is evident that nosignificant critical anomaly is present in refractive indices and that they wereproperly converted to mole fractions and volume fractions in our treatments.
Ž . Ž .Combination of equations 8 and 9 yields:
r s r q Dt z y 1r2 Bt b y 1r2 B t bqD , 10Ž . Ž . Ž .1 c 1
r s r q Dt z q 1r2 Bt b q 1r2 B t bqD . 11Ž . Ž . Ž .2 c 1
� ŽFixing Z, b , D, and T at 0.654, 0.327, 0.5, and 297.1 K for xC H NO q 1 yc 6 5 2
� 4Coexistence curves of C H NO q n-alkane6 5 2 1057
Ž .TABLE 7. Coefficients of equation 9 and standard deviations s in r for diameter of coexistencedŽ . Ž . Ž . � Ž . Ž . 4 �curves of T , n , T , x , and T , f for xC H NO q 1 y x CH CH CH and xC H NO q6 5 2 3 2 3 3 6 5 2
Ž . Ž . 4 Ž .1 y x CH CH CH . r is the critical value of the order parameter determined by the3 2 8 3 c expttechniques described in the text
Ž . Ž . Ž .T , n T , x T , f
� Ž . Ž . 4xC H NO q 1 y x CH CH CH6 5 2 3 2 3 3
Ž .r 1.4273 " 0.0002 0.386 " 0.001 0.358 " 0.001c expt
Z s 0.89
r 1.4272 " 0.0001 0.387 " 0.001 0.360 " 0.001cD 0.167 " 0.001 0.273 " 0.007 0.374 " 0.007
y4 y4 y4. . .s 1.2 10 5.4 10 5.6 10
Z s 0.654
r 1.4269 " 0.0001 0.386 " 0.001 0.360 " 0.001cD 0.072 " 0.002 0.117 " 0.004 0.161 " 0.003
y4 y4 y4. . .s 3.5 10 7.0 10 6.6 10
� Ž . Ž . 4xC H NO q 1 y x CH CH CH6 5 2 8 2 8 3
Ž .r 1.4652 " 0.0002 0.574 " 0.001 0.415 " 0.001c expt
Z s 0.89
r 1.4563 " 0.0001 0.573 " 0.001 0.416 " 0.001cD 0.1382 " 0.0005 y0.64 " 0.02 0.300 " 0.005
y5 y3 y4. . .s 4.1 10 1.4 10 4.0 10
Z s 0.654
r 1.4650 " 0.0001 0.575 " 0.001 0.415 " 0.001cD 0.060 " 0.001 y0.283 " 0.002 0.131 " 0.001
y4 y4 y4. . .s 2.7 10 3.1 10 3.3 10
. Ž . 4 � Ž . Ž . 4x CH CH CH or 296.0 K for xC H NO q 1 y x CH CH CH ,3 2 3 3 6 5 2 3 2 8 3respectively, and taking the values of D, r , B, and B from tables 6 and 7, r , r ,c 1 d 1
Ž . Ž .and r were calculated from equations 9 to 11 . The results are shown as lines in2figures 1 and 2. The values from calculation are in good agreement withexperimental results.
The power law dependence of critical amplitudes on molar mass has beenderived from a Landau-Ginsburg-Wilson type model for chain molecule solutions
TABLE 8. Critical amplitudes B and critical volume fractions f forf c� 4C H NO q n-alkane . M is the molar mass of n-alkane6 5 2
y1.Ž .n-alkane Mr g mol f Bc f
Pentane 72.15 0.358 1.404Octane 114.22 0.392 1.521Decane 142.28 0.415 1.580Dodecane 170.33 0.434 1.625Tetradecane 198.40 0.452 1.636Hexadecane 226.44 0.464 1.661
X. An et al.1058
y1 .865 Ž .FIGURE 3. A ln-ln plot of B f against molar mass M for nitrobenzene q n-alkane .f c
of both small molecules and polymers.Ž13. This dependence for the amplitude Bf
Ž .relating to T , f coexistence curve may be expressed as:
B fy1 .865 A M b , 12Ž .f c
where b is a universal M-exponent with a theoretical value of 0.29.Ž14. Theexperimental values of B and f for six solutions are summarized in table 8. Af c
Ž .ln-ln plot in equation 12 is shown in figure 3. Least-squares fitting gives b s0.28 " 0.02. It is in excellent agreement with the theoretical prediction of 0.29
Ž .and the experimental values of 0.29 " 0.04 for demethylacetamide q n-alkane ,Ž .0.26 " 0.04 for 3-octanone q polymethylmethacrylate , and 0.30 " 0.02 for
Ž . Ž15.methylcyclohexane q polystyrene . It supports the assumption that equationŽ .12 is universal for chain molecule solutions of both small molecules and polymers.
ŽThis work was supported by the National Natural Science Foundation Project
� 4Coexistence curves of C H NO q n-alkane6 5 2 1059
.29673019 , the State Education Committee, and the Natural Science Foundation ofŽ .Gansu province No. ZR-96-009 , P.R. China.
REFERENCES
1. An, X.; Zhao, H.; Jiang, F.; Mao, C.; Shen, W. J. Chem. Thermodynamics 1997, 29, 1047]1054.2. An, X.; Zhao, H.; Jiang, F.; Shen, W. J. Chem. Thermodynamics 1998, 30, 21]26.
Ž .3. An, X.; Jiang, F.; Zhao, H.; Chuanyin, C.; Shen, W. J. Chem. Thermodynamics in press .4. An, X.; Jiang, F.; Zhao, H.; Shen, W. Acta Chimica Sinica 1998, 56, 141]146.5. An, X., Shen, W.; Wang, H.; Zheng, G. J. Chem. Thermodynamics 1993, 25, 1373]1383.6. An, X.; Liu, X.; Shen, W. J. Chem. Thermodynamics 1997, 29, 669]675.7. An, X., Zhao, H.; Shen, W. J. Chem. Thermodynamics 1996, 28, 1165]1172.8. Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Sol ents: 4th edition. Techniques of chemistry,
Vol. II. Wiley-Interscience: New York. 1986.9. Thermodynamics Research Centre, API 44 Tables, Selected Values of Properties of Hydrocarbons and
Related Components, Vol. I. 1972.10. Alpert, D. Z. Phys. Re¨. 1982, B25, 4810]4814.11. Le Guillou, J. C.; Zinn-Justin, J. Phys. Re¨ . 1980, B21, 3976]3998.12. Wegner, F. J. Phys. Re¨ . 1972, B5, 4529]4536.13. An, X.; Zhao, H.; Jiang, F.; Shen, W. J. Chem. Thermodynamics 1996, 28, 1221]1232.14. An, X., Jiang, F.; Chen, C.; Shen, W. Chem. Phys. Letters 1998, 282, 403]408.
Ž .15. An, X., Jiang, F.; Chen, C.; Shen, W. Pure and Applied Chem. in press .
( )Recei ed 6 January 1998; in final form 17 February 1998
WE-115
