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Critical resistivity in impurity doped binary liquid mixtures
Volume 62. number 2
CHEMICAL
CRITICAL. RESLSTIVITY Anil KUMAR
and ESR
IN IMPURITY
1 April 1979
PHYSICS LETTERS
DOPED BINARY
LIQUID MIXTURES
GOPAL
Depvrmenr of Phpks. Indizn Insritu?eof Science. Bangalore i60012. India Received 1 November 1978; in final form 1I December 1978
The electricatresistanceof the critical binary liquid system C~H~Z+(CH~CO)=O is measured both in the pure form and uhen the system is doped with small amounts (= 100 ppm) of Hz0 impurities. Near T, the resistance varies as dR/dT = A +A2(T-Tc)-b with b = 035 Neither the critical exponent b nor the amplitude ratio A l/A+ are affected by the impuritiei A sig reverti of dR/dT is noticed at bGghtemperaturesT S T,
The universality in the anomalous behaviour of thermodynamic properties near the gas-liquid critical points, Curie temperatures and other second-order continuous phase transitions is now \\eil established [I z]_ In the case of non-equilibrium transport properties_ the situation is still not clear_ The electrical resistivity, for example, has a divergence in dRfdT_ The behaviour near T, is represented by the relation dR/dT =Arb+___V where t = (T-T&T,_ Recent experiments [&5] in binary liquid systems give the value of the critical exponent b as close to 035_ On the other hand, in magnetic and aliied systems [5], both experiments and theories give b = Q == I/S, where a is the critical exponent characterizing the divergence of the specific heat _ There is thus a possrbility that the universal critical behaviour breaks down in binary liquids for a transport property_ Hence it is important to confirm the value of b and also to consider the factors that could influence it_ An important factor, which can affect the nature of critical anomalies. is the presence of impurities [2]_ This is most relevant to the case of polar i-nonpolar Binary iiquids where essentially impurity conduction prevaiIs [4_5]. Since the magnitude ofelectrical resistivity is easily altered by impurities, this is a FavourabIe case for studying impurity effects on a transport property. Further, there is no agreed value of the critical exponent [6,7] for other transport properties such as viscosity, thermal conductivity, mutual diffucion coefficient, etc., even in “pure” systems_ We have measured the electrical resistance of the 306
polar f nonpolar binary liquid system C6 H12 + (CH3CO)20. The measurements were performed at a frequency of I kHz using a standard ac resistivity techniqtie [s]_ For r-hisbinary liquid system, the critical composition and the critica temperature are accurately known [8]_ Analytical reagent grade chemicals were used. However, the polar liquid acetic anhydride has great affinity For water and in the pure sampIe Hz0 traces of nearly 50 ppm were indicated by a gas-chromatographic analysis. AI1 the measurements were done while cooiing the system From the one-phase to the two-phase region- Each run lasted for approximately 1 week_ T, was approached to 1 mK (r = 3 X 10e6)_ The water used For doping was distilled and deionized_ The measured resistance data over the extended range were fitted to the equation R =R CT- JI’~‘-~
+B’t 9
0)
which gives (R - R,)/tR,
= At-b
•tB ,
(2)
where R, is the resistance as T+ T, R,. T, and b were treated as parameters adjustable in the ieastsquare fitting oFdata_ To avoid gravity effects [3,51 or,Iy the data in the temperature range 1W5Sr ,<10m2 were used For analysis_ A least-square fit to the data gave the values ofA. b and B as noted in table 1. The observations on the “pure” system and on the sample doped with 300 ppm of H,O are shown in fig_ 1. It is seen from fig. 1 that For the doped samples there is a reversal in the sign of dR/dT for T > T,_ It
CHEMICAL
Vohune 62, number 2
PHYSICS LETTERS
Table I Best-tit values of the critical exponent (6) and the amplitude ratio (A/B) in eq. (2) for the entire range of data; b’ and C/D are the corresponding values for the data without the contribution from the high-temperature non-critical (T ) Tc) region System a)
pure 50 ppm 100 ppm 200 ppm 300 ppm
b (+o.os)
Hz0 HZ0 ki20 Hz0
0.3 1 0.49 0.40 0.3 1 0.40
b’ (?0.05)
C/D (20.05)
0.31 0.50 O-40 0.31 0.40
0.239 0.100 0.122 0.235 0.120
A/B (kO.05)
0.249 0.340 -0.122 -0.235 -0.120
a) Impurity content in terms of voIume of (CH3CO)zO. The data for the 50 ppm impurity run are less reliable because of interruptions of the run due to power failures_
perhaps implies a change in the mechanism of conduction. Thus, to get a realistic estimate of the exponent b and the amplitude ratio A/B of the singular to the analytic term in the critical region, this high-temperature resistance contribution was taken as a linear term in the region far from T, and was subtracted from the
SYSTEM : CaHr2t(CH3C0)z CONPoStTION
C
- CRITICAL
PURE SYSTEM DOPED
Wlitr
300
ppm
Hz0
i
t 16510
z
h
z
total measured resistance_ The remaining data (AR)_ which are relevant to the critical behaviour. were fitted to the equation (AR - AR,)/rAR,
(3)
Notice also that the scale and the nature of unpurities chosen, essentially simuIate a physica conduion lihely in any system. ppm levels of mipurittes dre not easy to avoid. It may be noted that another factor 1%hlch could influence the anomaly is the frequency used to me;\sure the electrical resistance (R)_ As the frequency used to measure R I>y all the workers in the case of binxy liquids is = ! kHz, II could Mitch with the time constant of the deca! ofthe concentration fluctuations (due to critical slowing down). Such J “frequencymatching” effect could lead to dielectric dispersion trical resistance. ing effect
only,
[9]
and hence
to an anomaly
If b is a consequence then it must
in elec-
of such a march-
be 3 strong
function
of
R. A recent study [IO] reveals that b is not affected appreciably by the frequency used in the experimenta measurements of the resistance_ We therefore conclude that the critical exponent b describing the divergence of dR/dris not influenced by impurities which cause conduction in polar + nonpolar binary liquids. Since Lj is neither affected by the frequency used for the resistance measurement. the value b = 0.3 5 must be considered genuine, which diffrequency
Fig. 1. Plot of eIectricai resistance versus tT- T,) for the pure acetic anhydride + cyclohexane sqstem and for the system doped with 300 ppm of water.
= Cr-“’ + D.
The best-fit values for b’and C/D are also given in table 1; 6’ should be equal to b, except for small differences caused by the data analysis. As one notes from tab!e 1, there IS a small spread in the values of the exponent b = b’, which is probably due to scatter in the data- One could possibly conclude that there is no effect of impurities on the exponent b and neither on the amplitude ratio C/D in the critical region. This IS in consonance with the observation of Shaw and Goldburg [3]. who studied one fixed doping ofKC1 in the water f phenol systemThere is a rapid fall in resistance when the pure system is doped \\clthH,O impurities. This result confirms dn earlier speculation that Hz0 impurities cause conduction in polar + nonpolar binary hquids [a_5 ] _ The present stud) is encouraging in the sense that impurities do not seem to affect the value of the critical exponent b. within the limits of the experiments-
and absorption te eao
1 Aprli 1979
used to measure
307
Volume 62. number 2
CHEMICAL
PHYSICS LEl-l-ERS
fers appreciabl_v from the specific heat exponent
a=
I/S. -
A more detailed account of the experiments the results will be presented elsewhere.
and
The authors thank their colleagues for cooperation in the textFinzmciaf support from a PL4SO scheme as we11 as a DST(NTPP) scheme is also gratefully acknowIedged.
and a referee for suggesting improbements
References [ 11 II-E_ Stanley. Introduction to phase transitions and critical phenomena (Oxford Univ. Press. London. 1971); SX_ Mn. Modern theory of cririczl phenomern (Benjamin, New York, 5976).
I April 1979
[Z] &LA- Anisimov, Soviet Phys- Uspekhi I? (1975) 72L [3 1 C-H. Shaw and \%‘_I_ Goldburg. J. Cbem. Phys 65 (1976) 49@6[4 1 ES.R. Cop& XV. LeIe. N. Xamjan. J. Rrtmakrishnan and P- Chandm Sekhar. Phys. Letten63A (1977) 139. [-Cl J. Ramakrishnan. N. Nagarajan, A. I&mar, ES-R Gopal, P. Chandra Sekhar and G. Ananthakrishna. J. Chem. Phyr 68 (1978) 4098. and references therein [6] J-V. Sengers. A_I_P_Conference Proceedings I1 (1973) 229_ [7] PC. Hohenbeg and 5.1. Halperin. Rev. hIod_ Phys 49 (1977) 435. 181 ES-R- Gopal. P_ Chandra Sekhjr. G_ Amnthdaishm, R Ramacbandra znd S-V_ Submmanyam, Proc Roy_ Sot A350 (1976) 9L [9] P.hL CammeII and CA. Angeli. Phys. Letters 40A (1972) 49; J. Chem- Phys- 60 (1974) 584. [ 101 A. Kumar. M-K. Tiustri ;tnd E.S.R_ Gopsl, Chem. Phys. Letters 56 (1978) 507; Chem. Phys., to be published.
CHEMICAL
CRITICAL. RESLSTIVITY Anil KUMAR
and ESR
IN IMPURITY
1 April 1979
PHYSICS LETTERS
DOPED BINARY
LIQUID MIXTURES
GOPAL
Depvrmenr of Phpks. Indizn Insritu?eof Science. Bangalore i60012. India Received 1 November 1978; in final form 1I December 1978
The electricatresistanceof the critical binary liquid system C~H~Z+(CH~CO)=O is measured both in the pure form and uhen the system is doped with small amounts (= 100 ppm) of Hz0 impurities. Near T, the resistance varies as dR/dT = A +A2(T-Tc)-b with b = 035 Neither the critical exponent b nor the amplitude ratio A l/A+ are affected by the impuritiei A sig reverti of dR/dT is noticed at bGghtemperaturesT S T,
The universality in the anomalous behaviour of thermodynamic properties near the gas-liquid critical points, Curie temperatures and other second-order continuous phase transitions is now \\eil established [I z]_ In the case of non-equilibrium transport properties_ the situation is still not clear_ The electrical resistivity, for example, has a divergence in dRfdT_ The behaviour near T, is represented by the relation dR/dT =Arb+___V where t = (T-T&T,_ Recent experiments [&5] in binary liquid systems give the value of the critical exponent b as close to 035_ On the other hand, in magnetic and aliied systems [5], both experiments and theories give b = Q == I/S, where a is the critical exponent characterizing the divergence of the specific heat _ There is thus a possrbility that the universal critical behaviour breaks down in binary liquids for a transport property_ Hence it is important to confirm the value of b and also to consider the factors that could influence it_ An important factor, which can affect the nature of critical anomalies. is the presence of impurities [2]_ This is most relevant to the case of polar i-nonpolar Binary iiquids where essentially impurity conduction prevaiIs [4_5]. Since the magnitude ofelectrical resistivity is easily altered by impurities, this is a FavourabIe case for studying impurity effects on a transport property. Further, there is no agreed value of the critical exponent [6,7] for other transport properties such as viscosity, thermal conductivity, mutual diffucion coefficient, etc., even in “pure” systems_ We have measured the electrical resistance of the 306
polar f nonpolar binary liquid system C6 H12 + (CH3CO)20. The measurements were performed at a frequency of I kHz using a standard ac resistivity techniqtie [s]_ For r-hisbinary liquid system, the critical composition and the critica temperature are accurately known [8]_ Analytical reagent grade chemicals were used. However, the polar liquid acetic anhydride has great affinity For water and in the pure sampIe Hz0 traces of nearly 50 ppm were indicated by a gas-chromatographic analysis. AI1 the measurements were done while cooiing the system From the one-phase to the two-phase region- Each run lasted for approximately 1 week_ T, was approached to 1 mK (r = 3 X 10e6)_ The water used For doping was distilled and deionized_ The measured resistance data over the extended range were fitted to the equation R =R CT- JI’~‘-~
+B’t 9
0)
which gives (R - R,)/tR,
= At-b
•tB ,
(2)
where R, is the resistance as T+ T, R,. T, and b were treated as parameters adjustable in the ieastsquare fitting oFdata_ To avoid gravity effects [3,51 or,Iy the data in the temperature range 1W5Sr ,<10m2 were used For analysis_ A least-square fit to the data gave the values ofA. b and B as noted in table 1. The observations on the “pure” system and on the sample doped with 300 ppm of H,O are shown in fig_ 1. It is seen from fig. 1 that For the doped samples there is a reversal in the sign of dR/dT for T > T,_ It
CHEMICAL
Vohune 62, number 2
PHYSICS LETTERS
Table I Best-tit values of the critical exponent (6) and the amplitude ratio (A/B) in eq. (2) for the entire range of data; b’ and C/D are the corresponding values for the data without the contribution from the high-temperature non-critical (T ) Tc) region System a)
pure 50 ppm 100 ppm 200 ppm 300 ppm
b (+o.os)
Hz0 HZ0 ki20 Hz0
0.3 1 0.49 0.40 0.3 1 0.40
b’ (?0.05)
C/D (20.05)
0.31 0.50 O-40 0.31 0.40
0.239 0.100 0.122 0.235 0.120
A/B (kO.05)
0.249 0.340 -0.122 -0.235 -0.120
a) Impurity content in terms of voIume of (CH3CO)zO. The data for the 50 ppm impurity run are less reliable because of interruptions of the run due to power failures_
perhaps implies a change in the mechanism of conduction. Thus, to get a realistic estimate of the exponent b and the amplitude ratio A/B of the singular to the analytic term in the critical region, this high-temperature resistance contribution was taken as a linear term in the region far from T, and was subtracted from the
SYSTEM : CaHr2t(CH3C0)z CONPoStTION
C
- CRITICAL
PURE SYSTEM DOPED
Wlitr
300
ppm
Hz0
i
t 16510
z
h
z
total measured resistance_ The remaining data (AR)_ which are relevant to the critical behaviour. were fitted to the equation (AR - AR,)/rAR,
(3)
Notice also that the scale and the nature of unpurities chosen, essentially simuIate a physica conduion lihely in any system. ppm levels of mipurittes dre not easy to avoid. It may be noted that another factor 1%hlch could influence the anomaly is the frequency used to me;\sure the electrical resistance (R)_ As the frequency used to measure R I>y all the workers in the case of binxy liquids is = ! kHz, II could Mitch with the time constant of the deca! ofthe concentration fluctuations (due to critical slowing down). Such J “frequencymatching” effect could lead to dielectric dispersion trical resistance. ing effect
only,
[9]
and hence
to an anomaly
If b is a consequence then it must
in elec-
of such a march-
be 3 strong
function
of
R. A recent study [IO] reveals that b is not affected appreciably by the frequency used in the experimenta measurements of the resistance_ We therefore conclude that the critical exponent b describing the divergence of dR/dris not influenced by impurities which cause conduction in polar + nonpolar binary liquids. Since Lj is neither affected by the frequency used for the resistance measurement. the value b = 0.3 5 must be considered genuine, which diffrequency
Fig. 1. Plot of eIectricai resistance versus tT- T,) for the pure acetic anhydride + cyclohexane sqstem and for the system doped with 300 ppm of water.
= Cr-“’ + D.
The best-fit values for b’and C/D are also given in table 1; 6’ should be equal to b, except for small differences caused by the data analysis. As one notes from tab!e 1, there IS a small spread in the values of the exponent b = b’, which is probably due to scatter in the data- One could possibly conclude that there is no effect of impurities on the exponent b and neither on the amplitude ratio C/D in the critical region. This IS in consonance with the observation of Shaw and Goldburg [3]. who studied one fixed doping ofKC1 in the water f phenol systemThere is a rapid fall in resistance when the pure system is doped \\clthH,O impurities. This result confirms dn earlier speculation that Hz0 impurities cause conduction in polar + nonpolar binary hquids [a_5 ] _ The present stud) is encouraging in the sense that impurities do not seem to affect the value of the critical exponent b. within the limits of the experiments-
and absorption te eao
1 Aprli 1979
used to measure
307
Volume 62. number 2
CHEMICAL
PHYSICS LEl-l-ERS
fers appreciabl_v from the specific heat exponent
a=
I/S. -
A more detailed account of the experiments the results will be presented elsewhere.
and
The authors thank their colleagues for cooperation in the textFinzmciaf support from a PL4SO scheme as we11 as a DST(NTPP) scheme is also gratefully acknowIedged.
and a referee for suggesting improbements
References [ 11 II-E_ Stanley. Introduction to phase transitions and critical phenomena (Oxford Univ. Press. London. 1971); SX_ Mn. Modern theory of cririczl phenomern (Benjamin, New York, 5976).
I April 1979
[Z] &LA- Anisimov, Soviet Phys- Uspekhi I? (1975) 72L [3 1 C-H. Shaw and \%‘_I_ Goldburg. J. Cbem. Phys 65 (1976) 49@6[4 1 ES.R. Cop& XV. LeIe. N. Xamjan. J. Rrtmakrishnan and P- Chandm Sekhar. Phys. Letten63A (1977) 139. [-Cl J. Ramakrishnan. N. Nagarajan, A. I&mar, ES-R Gopal, P. Chandra Sekhar and G. Ananthakrishna. J. Chem. Phyr 68 (1978) 4098. and references therein [6] J-V. Sengers. A_I_P_Conference Proceedings I1 (1973) 229_ [7] PC. Hohenbeg and 5.1. Halperin. Rev. hIod_ Phys 49 (1977) 435. 181 ES-R- Gopal. P_ Chandra Sekhjr. G_ Amnthdaishm, R Ramacbandra znd S-V_ Submmanyam, Proc Roy_ Sot A350 (1976) 9L [9] P.hL CammeII and CA. Angeli. Phys. Letters 40A (1972) 49; J. Chem- Phys- 60 (1974) 584. [ 101 A. Kumar. M-K. Tiustri ;tnd E.S.R_ Gopsl, Chem. Phys. Letters 56 (1978) 507; Chem. Phys., to be published.