- Email: [email protected]
First stage of spinodal decomposition observed by forced rayleigh scattering
55 55 55 55 55 55
Volume 77A, number 1
PHYSICS LETTERS
28 April 1980
FIRST STAGE OF SPINODAL DECOMPOSITION OBSERVED BY FORCED RAYLEIGH SCATTERING Dieter W. POHL 1 IBM Zurich Research Laboratory, 8803 RUschlikon, Switzerland Received 14 February 1980
The dynamics of an isolated concentration fluctuation was studied in a critical mixture of 2,6-lutidine and water. Crossover from exponential decay to growth occurred when the sample temperature exceeded Tc.
Coherent concentration fluctuations with welldefined q-vector and a (small) amplitude ~ can be in a binary liquid mixture (BLM) inside a pair of interfering laser beams by means of absorption, heating, and the Soret effect [1—3].The grating can be probed by forced Rayleigh scattering (FRS) [2— 41. This scheme provides the unique possibility to study the dynamics of a practically isolated concentration mode near a consolute critical point (Cc, Tc) where mutual diffusion becomes “soft”. Furthermore, a BLM with finite ë (at t = 0) can be quenched into the unstable regime, and the response ê() be observed. To explore these possibilities, a critical mixture of 2,6-lutidine—water (LW) was chosen which has an inverted regime of coexistence [5]. Such a system gets “quenched” by heating instead of cooling. It can therefore be brought to instability quite rapidly. Because of this property, LW mixtures have recently been employed for investigations on spinodal decomposition using conventional light-scattering techniques [6]. The LW mixture in a 2 mm cuvette (SC), immersed created
in a bath of paraffin oil, was temperature-stabilized to <1 mK (fig. 1). The temperature T0 could be raised suddenly by L~T~ 100 mK using a light pulse from an argon laser (0.2 or 0.4 s, 2—100 mW, 488 nm, spot size WA = 0.77 mm, beams a, b in fig. I and fig. 2a, top curve). The mixture was slightly colored with 1) methyl at the red to create sufficient absorption (0.2 cm 1
Present address: IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA.
HeNe LASER SHUTTER____________ — HARGON LASER ~ PMI
OSCILLATOR DRIVER
~~SIGNAL AVERAGER LOCK
IN p ‘~
—
=
= :i
—
:
SC. OVEN DETECTOR
Fig. 1. Experimental setup.
frequency of this pump laser. The doping did not markedly change the critical point of the mixture (Cc = 31.1% vol, Tc 32.0°C).The pump pulses also created the temperature grating T(fig. 2a) driving the concentration grating. The latter was probed by the HeNe-laser beam p (WH = 0.45 mm) while r acted as local oscillator for heterodyne detection of beam s, scattered off the grating with amplitude E5 x ~ (scattering from T, confined to a very short time after pulse end, is not considered here). The relative phases of p, r, a, and b could be adjusted by means of the piezomirrors PM1 and PM2. Further, the phase of p was switched periodically (188 Hz) between 0 and ir which inverts E5 allowing lock-in The temporal evolution of the for signal S(t) detection. was investigated for q = 2000, 3430 and 4400 cm1. While decaying exponentially well below T~(A, B in fig. 2b) the signal is preceded by a period of growth for T(t) > T~ 53
Volume 77A, number 1
PHYSICS LETTERS
100 50 0 I
50
H
0.6
pump pulse -
(a) thermal grating
~ —
28 April 1980
o
-
0.4
~ç[schematic]
T~ 0.2
~
~
~1O~f
q
-15 oop5[5[ -10 ~5 TTc [K]
—
4400 cm~
0
_______
-
A
—100
I
cc
0
H ~
-0.2
(b) (0
z~
-0.6 -100 -80 I
0
I
4
8 TIME
-60
-40
-20
020
40
I
12
16
20
[5]
Fig. 2. (a) dashed curves: pump pulse and thermal grating amplitude; solid curves: temperature T(t) — Tc in the zone of interrogation for four combinations of T0 and ~ T (A—D): (b) 8(t) for the above four T(t) curves.
(C, D in fig. 2b). The durations, up to 5 s and more, agree fairly well with the times calculated for cooling below Tc (fig. 2a). When plotted versus T(t), the instantaneous growth rates s (t) ~/S obtained for various values of T0 and L~Tcombine to form a smooth curve (fig. 3) except for short transient times (0.3 s, dashed curves) after the end of the pump Far well belowwith Tc, the s X exponent _(Tc 057~0~04 which pulse. compares fl ±0.015 obtained by classical light scattering 0.554 (inset to fig. 2) [71.Very close to T~,the experimental accuracy is not yet sufficient for a quantitative fit, but after crossing zero at Tc ±5 mK the curve clearly continues with finite slope (~ 0.02 s~/mK)into the “forbidden” zone of the unstable regime. This part may hence be considered a record of the earliest stage of spinodal decomposition. The data for q = 2000 and 3430 cm~are similar to the ones for q = 4400 shown in fig. 3, s being roughly proportional to q2 with the possibility of significant deviations close to Tc. These first results demonstrate that the Soret-FRS technique (as one may call it) is suited to approach —
some interesting problems in the physics of phase transitions and segregation in a new way. Itenerant and earlystage spinodal decomposition [6,8,9], nucleation [8], mode-coupling [101, and finite amplitude effects are specifically to be mentioned here. 54
Fig. 3.
—
———
T-T~ [mK] s(t) for various T 0 and ~T.
—
Common
tangent curve. Inset: comparison with width of Rayleigh line.
The author wishes to acknowledge stimulating discussions with R.W. Gammon, University of Maryland. and competent technical assistance by V. Irniger. References
[11 C.
Soret, Arch. Sci. Phys. Nat. 2 (1879) 48. 121 K. Thyagarajan and P. Lallemand, Opt. Commun. 26 54. 131 (1978) D.W. Pohi, in: Proc. Workshop on Quasielastic lightscattering studies of fluid and macromolecular (CISE, Milan, 1979) (Plenum), to be published.solutions
141
15] 161 17] 181
191
D.W. Pohl, S.E. Schwarz and V. Irniger, Phys. Rev. Lett. 31(1973) 32; H. Eichler, G. Saije and H. Stahl, J. AppI. Phys. 44 (1973) 5383. A.W. Loven and O.K. Rice, Trans. Faraday Soc. 59 (1963) 2723. Y.C. Chou and W.I. Goldburg, Phys. Rev. A, to be published. E. Gülari,Phys. A.F. Collings, Schmidt and C.J. Pings, J. Chem. 56 (1972)R.L. 6169. See, for example, J.S. Langer, M. Baron and H.D. Miller, Phys. Rev. All (1975) 1417; K. Binder, Phys. Rev. B15 (1977) 4425; K. Kowasaki and T. Ohta, Prog. Theor. Phys. (Japan) 59 (1978) 362. N.C. Wong and C.M. Knobler, J. Chem. Phys. 69 (1978)
725.
I
a 5
[101 See, for example, R.A. Ferrell, Phys. Rev. Lett. 24 (1970) 1169 and references therein,
a a a a a a a a a 55
a a a a a a
Volume 77A, number 1
PHYSICS LETTERS
28 April 1980
FIRST STAGE OF SPINODAL DECOMPOSITION OBSERVED BY FORCED RAYLEIGH SCATTERING Dieter W. POHL 1 IBM Zurich Research Laboratory, 8803 RUschlikon, Switzerland Received 14 February 1980
The dynamics of an isolated concentration fluctuation was studied in a critical mixture of 2,6-lutidine and water. Crossover from exponential decay to growth occurred when the sample temperature exceeded Tc.
Coherent concentration fluctuations with welldefined q-vector and a (small) amplitude ~ can be in a binary liquid mixture (BLM) inside a pair of interfering laser beams by means of absorption, heating, and the Soret effect [1—3].The grating can be probed by forced Rayleigh scattering (FRS) [2— 41. This scheme provides the unique possibility to study the dynamics of a practically isolated concentration mode near a consolute critical point (Cc, Tc) where mutual diffusion becomes “soft”. Furthermore, a BLM with finite ë (at t = 0) can be quenched into the unstable regime, and the response ê() be observed. To explore these possibilities, a critical mixture of 2,6-lutidine—water (LW) was chosen which has an inverted regime of coexistence [5]. Such a system gets “quenched” by heating instead of cooling. It can therefore be brought to instability quite rapidly. Because of this property, LW mixtures have recently been employed for investigations on spinodal decomposition using conventional light-scattering techniques [6]. The LW mixture in a 2 mm cuvette (SC), immersed created
in a bath of paraffin oil, was temperature-stabilized to <1 mK (fig. 1). The temperature T0 could be raised suddenly by L~T~ 100 mK using a light pulse from an argon laser (0.2 or 0.4 s, 2—100 mW, 488 nm, spot size WA = 0.77 mm, beams a, b in fig. I and fig. 2a, top curve). The mixture was slightly colored with 1) methyl at the red to create sufficient absorption (0.2 cm 1
Present address: IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA.
HeNe LASER SHUTTER____________ — HARGON LASER ~ PMI
OSCILLATOR DRIVER
~~SIGNAL AVERAGER LOCK
IN p ‘~
—
=
= :i
—
:
SC. OVEN DETECTOR
Fig. 1. Experimental setup.
frequency of this pump laser. The doping did not markedly change the critical point of the mixture (Cc = 31.1% vol, Tc 32.0°C).The pump pulses also created the temperature grating T(fig. 2a) driving the concentration grating. The latter was probed by the HeNe-laser beam p (WH = 0.45 mm) while r acted as local oscillator for heterodyne detection of beam s, scattered off the grating with amplitude E5 x ~ (scattering from T, confined to a very short time after pulse end, is not considered here). The relative phases of p, r, a, and b could be adjusted by means of the piezomirrors PM1 and PM2. Further, the phase of p was switched periodically (188 Hz) between 0 and ir which inverts E5 allowing lock-in The temporal evolution of the for signal S(t) detection. was investigated for q = 2000, 3430 and 4400 cm1. While decaying exponentially well below T~(A, B in fig. 2b) the signal is preceded by a period of growth for T(t) > T~ 53
Volume 77A, number 1
PHYSICS LETTERS
100 50 0 I
50
H
0.6
pump pulse -
(a) thermal grating
~ —
28 April 1980
o
-
0.4
~ç[schematic]
T~ 0.2
~
~
~1O~f
q
-15 oop5[5[ -10 ~5 TTc [K]
—
4400 cm~
0
_______
-
A
—100
I
cc
0
H ~
-0.2
(b) (0
z~
-0.6 -100 -80 I
0
I
4
8 TIME
-60
-40
-20
020
40
I
12
16
20
[5]
Fig. 2. (a) dashed curves: pump pulse and thermal grating amplitude; solid curves: temperature T(t) — Tc in the zone of interrogation for four combinations of T0 and ~ T (A—D): (b) 8(t) for the above four T(t) curves.
(C, D in fig. 2b). The durations, up to 5 s and more, agree fairly well with the times calculated for cooling below Tc (fig. 2a). When plotted versus T(t), the instantaneous growth rates s (t) ~/S obtained for various values of T0 and L~Tcombine to form a smooth curve (fig. 3) except for short transient times (0.3 s, dashed curves) after the end of the pump Far well belowwith Tc, the s X exponent _(Tc 057~0~04 which pulse. compares fl ±0.015 obtained by classical light scattering 0.554 (inset to fig. 2) [71.Very close to T~,the experimental accuracy is not yet sufficient for a quantitative fit, but after crossing zero at Tc ±5 mK the curve clearly continues with finite slope (~ 0.02 s~/mK)into the “forbidden” zone of the unstable regime. This part may hence be considered a record of the earliest stage of spinodal decomposition. The data for q = 2000 and 3430 cm~are similar to the ones for q = 4400 shown in fig. 3, s being roughly proportional to q2 with the possibility of significant deviations close to Tc. These first results demonstrate that the Soret-FRS technique (as one may call it) is suited to approach —
some interesting problems in the physics of phase transitions and segregation in a new way. Itenerant and earlystage spinodal decomposition [6,8,9], nucleation [8], mode-coupling [101, and finite amplitude effects are specifically to be mentioned here. 54
Fig. 3.
—
———
T-T~ [mK] s(t) for various T 0 and ~T.
—
Common
tangent curve. Inset: comparison with width of Rayleigh line.
The author wishes to acknowledge stimulating discussions with R.W. Gammon, University of Maryland. and competent technical assistance by V. Irniger. References
[11 C.
Soret, Arch. Sci. Phys. Nat. 2 (1879) 48. 121 K. Thyagarajan and P. Lallemand, Opt. Commun. 26 54. 131 (1978) D.W. Pohi, in: Proc. Workshop on Quasielastic lightscattering studies of fluid and macromolecular (CISE, Milan, 1979) (Plenum), to be published.solutions
141
15] 161 17] 181
191
D.W. Pohl, S.E. Schwarz and V. Irniger, Phys. Rev. Lett. 31(1973) 32; H. Eichler, G. Saije and H. Stahl, J. AppI. Phys. 44 (1973) 5383. A.W. Loven and O.K. Rice, Trans. Faraday Soc. 59 (1963) 2723. Y.C. Chou and W.I. Goldburg, Phys. Rev. A, to be published. E. Gülari,Phys. A.F. Collings, Schmidt and C.J. Pings, J. Chem. 56 (1972)R.L. 6169. See, for example, J.S. Langer, M. Baron and H.D. Miller, Phys. Rev. All (1975) 1417; K. Binder, Phys. Rev. B15 (1977) 4425; K. Kowasaki and T. Ohta, Prog. Theor. Phys. (Japan) 59 (1978) 362. N.C. Wong and C.M. Knobler, J. Chem. Phys. 69 (1978)
725.
I
a 5
[101 See, for example, R.A. Ferrell, Phys. Rev. Lett. 24 (1970) 1169 and references therein,
a a a a a a a a a 55
a a a a a a