J. Phys. Chem. 1988, 92, 2032-2036
2032
R~L:’ (L
PSS
(
RuL
‘‘
+ pss)
(camplexed)
bpy, phen, D I P )
Figure 6. Scheme of induced formation of hydrophobic domains by interaction of polypyridyl-ruthenium complexes with poly(styrenesulfonate), PSS, in the presence of a negatively charged quencher, Q-.
where an enhancement of emission intensity of R u ( D I P ) ~ ~bound +, to NaPSS, was observed upon addition of the quencher. This unexpected luminescence behavior could be explained if NaPSS is coiled around the metal complex, forming hydrophobic domains which are difficultly accessible to the quencher, as shown schematically in Figure 6 . The approach of a highly negatively charged quencher molecule to the polyion could increase this hydrophobic effect, resulting in an enhanced interaction between the polymer and the bound metal complex. The lack of any noticeable influence of ferrocyanide on the decays of the ruthenium complexes in the presence of NaPA, together with the observation of an efficient quenching of the luminescence intensity of these systems, leads to the conclusion that this quenching process is static. It thus appears that quenching occurs by ferrocyanide molecules which are close to the metal complexes at the moment of light excitation, whereas the diffusion of the quencher molecules toward the metal centers is inhibited by repulsion due to the negative polyion.
Conclusions It has been shown that the interactions between polypyridylruthenium complexes and polyelectrolytes depend not only on electrostatic factors but also on the hydrophobicity of both the ruthenium complex and the polyelectrolyte. Interaction of the metal complexes with the polymers results in an increase of luminescence intensity and decay times. In case of strong interactions, double-exponential decay behavior was observed, which may be explained by different microenvironments, such as coiled and extended form of the polymer, which are experienced by the probe molecule. The interaction with the anionic polymers leads to protection of the metal complex against a negatively charged quencher, such as ferrocyanide, and to a reduced quenching rate by a neutral molecule, such as oxygen. Quenching by ferrocyanide, in case of interaction of the ruthenium complexes with NaPA, was found to be static. The protection against dynamic quenching is probably caused by repulsion of a free, negatively charged quencher molecule from the polyanion. As an explanation for the absence of any quenching by ferrocyanide upon binding of the ruthenium complexes to NaPSS, especially the surprising enhancement of luminescence intensity with R u ( D I P ) ~ ~the + , formation of hydrophobic domains by the coiling of the polymer chain (so that the metal complex is no longer accessible to the quencher) is proposed.
Acknowledgment. We thank the National Science Foundation, the National Institutes of Health, and the Army Office of Research for their generous support of this research. Registry No. [Ru(bpy),]CI2, 14323-06-9; [Ru(phen),]Cl,, 2357043-6; [Ru(DIP),]CI,, 36309-88-3; NaPA, 9003-04-7; NaPSS, 9080-79-9; [Fe(CN),I4-, 13408-63-4; 02,7782-44-7.
Solvent Interactions at Crystal Surfaces: The Kinetic Story of a-Resorcinol Roger J. Davey,* Chemicals and Polymers Group, Imperial Chemical Industries plc, Runcorn, Cheshire, UK
Bogdan Milisavljevic, and John R. Bourne Technisch Chemisches Laboratorium, Eidgennosische Technische Hochschule, Zurich, Switzerland (Received: June 29, 1987; In Final Form: October 14, 1987)
New kinetic data are reported for the growth of {Ol1) and {OiT)faces of the polar crystal a-resorcinol from aqueous solution. Careful confrontation with crystal growth theory suggests that both surfaces should grow by spiral, dislocation mechanisms. The existence of dead zones in the measured kinetics is in conflict with this prediction and is explained on the basis of solvent adsorption at crystal surfaces. The data suggest that a water molecule is bound more strongly to a growth site on the (011) surfaces than it is on the (Oii]surfaces. This difference in binding energy is estimated to be about 1 kcal mol-’, in good agreement with previous calculations.
1. Introduction a-Resorcinol belongs to the space group Pna2, and grows from aqueous solution as ( 110) prisms bounded by the (011) and (OTi) faces. It was Wells in 1949, who first pointed out that because of the noncentric nature of the resorcinol structure, the c axis was polar and hence one end of the crystal must be “hydroxyl-rich” and the other “benzene-rich”. In addition, the existence of inclusions in only one of the c-axis growth sectors suggested that there was a significant difference in crystal growth rate between the (011)and (OTi}faces. Wells was unable to assign the absolute direction of growth along the c axis but surmised that strong adsorption of water on the hydroxyl-rich end would impede its (1) Wells, A. F. Discuss. Faraday SOC.1949, 5 , 197.
0022-3654/88/2092-2032$01 S O / O
growth and that the fast-growing end was in fact benzene-rich. More recently, firstly M i l i s a ~ l j e v i cand ~ ~ ~then Shimon et aL4s5 have returned to this problem and concluded that Well’s assignment was in fact incorrect and that the hydroxyl-rich end is actually the faster growing. This conclusion has been arrived at (2) Miliivljevic, B. C. Ph.D. Thesis, Swiss Federal Institute of Technology (E.T.H.), Zurich, Switzerland, 1982, Dissertation N6898. (3) Davey, R.J.; Milisavljevic, B. C.; Bourne, J. R. Paper presented at a Discussion Conference ‘Crystallisation Processes in Condensed Phases”; Faraday Division of the Royal Society of Chemistry; Girton College, Cambridge, England, July 1983. (4) Shimon, L.J. W.; Wireko, F. C.; Wolf, J.; Wiessbuch, I.; Addadi, L.; Berkovitch-Yellin, 2.;Lahav, M.; Leiserowitz, L. Mol. Cryst. Liq. Cryst. 1986, 137, 67. ( 5 ) Wireko, F. C.; Shimon, L. J. W.; Frolow, F.; Berkovitch-Yellin, 2.; Lahav, M.; Leiserowitz, L. J . Phys. Chem. 1987, 91, 472.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 2033
Kinetic Story of a-Resorcinol
0.044
20
0 040
0.033
10
0 028
0.022 0.014
" 0
500
1000
1500
2000
Rotational Speed
n[rpml
Figure 1. Influence of rotational speed and supersaturation on growth rates of the (OTT)faces of a-resorcinol. 0
ik._J
by a number of methods. Milisavljevic2 found that nucleation 0.04 0.08 of resorcinol crystals at low supersaturations onto silica supports Relative created crystals with their fast-growing surfaces in contact with Supersaturation, Inix/xd the silica. Considering the known adsorptive properties of silica toward polar organic molecules, this observation suggested that Figure 2. Kinetics of growth of a-resorcinol crystals at 15 "C: (0)the the hydroxyl-rich end was in contact with the silica and hence (Oii)faces, ( 0 )the (011) faces, (-) fitted curves. was faster growing. In addition, Milisavljevic2 also found that small amounts of the amine dye Variamine Blue B reduced the rate of growth of the fast-growing end presumably because it hydrogen bonded to the hydroxyl groups. Thus, M i l i s a ~ l j e v i c ~ ~ ~ made the reverse assignment to Wells, and this result has been confirmed recently by Shimon et al.435both by the elegant use of tailor-made additives and by the Bijvoet method of anomalous X-ray scattering. These workers have also reexamined the crystallography of the (OTT]and (011) faces and redefined the benzene-rich hydrophobic (011) faces as hydrogen-rich and acidic, while the (07I), hydroxyl-rich, hydrophilic faces are oxygen rich and basic. Viewed in this way it is not obvious which surfaces would bind water more strongly. Detailed calculations5 of the van der Waals and Coulomb energy potentials of the surfaces suggest that in fact water may be bound more strongly (to the extent of 1 kcal mol-') in channels on the (011) faces. This explains how the (017)surfaces are able to be the faster growing. 0 In this paper, this problem is viewed from a kinetic standpoint. 0.04 0.08 Relative Growth rate data for the (011) and (Oii)faces growing from Supersaturation, aqueous solution are presented and interpreted in the light of the Inixix,) absolute assignment of the polar axis. It will be shown that these Figure 3. Kinetics of growth of or-resorcinol crystals at 20 OC: (0)the data are consistent with the calculations of Wireko et aLS {OTT)faces, ( 0 ) the (011) faces, (-) fitted curves. 2. Experimental Section Following earlier studies6 a rotating disk configuration has been utilized for kinetic measurements. Disks were constructed from single-crystal faces incorporated in powdered Teflon. Pressing in a mold to -3 bar gave disks that could be mounted for crystal Growth 0.6 growth studies. The disk holder was of 3.5-cm diameter and held Rate a disk 2.5 cm in diameter and 0.4 cm thick. This was held on R, a stirrer shaft and immersed in supersatured solution contained b m s-l) in a 1-L vessel at constant (f0.02 "C) temperature. Rotational speeds in the range 0-2000 rpm were used, and the crystal growth rates were obtained from in situ measurements of the displacement 0.4 of the crystal interface using a microscope fitted with a micrometer eyepiece. Solution concentrations were measured with a Paar precision density meter. The single-crystal surfaces were cut from either the slow (01I] or the fast (OiT)ends of specially grown seed crystals.
1
-
J.
0.2
3. Results The relationship between growth rate and rotational speed is as expected with asymptotic values of growth rate being reached a t high speeds. This is seen in Figure 1, the asymptote being reached more rapidly a t lower supersaturations. The values of surface-limited growth rates have been obtained from these data by extrapolation to infinite rotational speed using an equation of the form
0
0.08 Relative Supersaturation
0.04
In(x/xs)
(6) Bourne, J. R.; Davey, R. J.; Gros, H.; HungerbOhler, K.J. Crysr. Growth 1976, 34, 221.
Figure 4. Kinetics of growth of a-resorcinol crystals at 25 "C: (0)the (011) faces, ( 0 )the (01l } faces, (-) fitted curves.
2034
Davey et al.
The Journal of Physical Chemistry, Vol. 92, No. 7 , 1988 R, = R , - B / ( Q 4- C )
(1)
Thus, Figures 2, 3, and 4 show the measured surface kinetics at temperatures of 15, 20, and 25 O C , respectively, for the (OTT] faces and the {011) faces. The data are clearly nonlinear and have been fitted to both birth and spread surface nucleation and spiral growth models by using the relationships R = Au5i6 exp(- @ / u )
(2)
and
R = (C/ul)u2 tanh (ul/u)
(3)
respectively.' These data clearly confirm the kinetic differences between the (011 ) and {OTT) surfaces with the latter growing faster at all temperatures. Supersaturations have been expressed as u =
In ( X / X , )
(4)
in which X i s the actual mole fraction and X , the saturation mole fraction at the growth temperature.* The solubility data used in this work were taken from ref 2 and compare well with previous mea~urements.~
4. Interpretation of Data Having thus confirmed and quantified the kinetic differences between the fast-growing {OTT) surfaces and the slow-growing {011 ) surfaces of resorcinol, the question now arises as to whether such data can throw any light on the differences in their surface structure and interaction with water. To this end the data can be examined from various standpoints. 4.1. Morphological Theory. A Hartman-Perdok analysis'O of the resorcinol structure has never been carried out. It is important to note, however, that because Hartman's habit controlling factor," Eatt,is the same at both ends of a polar direction, this structural approach would predict Rlolil= R,,lil and hence could not give rise to a polar morphology. The basis of the unequal growth rates for the two surfaces is related structurally to the different polarization and relaxation phenomena occurring on either end of the polar axis. These cannot at present be easily accounted for theoretically. 4.2. Kinetic Laws and Solvent Effects. A useful basis on which to explore kinetic differences is to consider a very simple functional relationship between growth rate and surface and solution properties, namely R = f(solubility)(supersaturation) (no. of growth sites) X (fraction of sites available) (5)
The solubility and supersaturation define the total surface flux and driving force for crystal growth. These are determined by control of bulk parameters such as solvent, solution composition, and temperature. The number of growth sites and fraction of sites available are controlled partly by solid-state properties and partly by the nature of solute-solvent and solute-solute interactions at the surface. Thus, the number of growth sites is related to the energetics of the surface and ease of creating steps and kinks on an interface. The a factor, originally defined by Jackson and later refined by Jetten et al.,'* may be. used as a rough indicator of these energetics. (7) Bennema, P.; Boon, J.; van Leeuwen, C.; Gilmer, G. H. Krist. Tech. 1973,8,659. .Burton, W. K.; Cabrera, N.; Frank, F. C. Philos. Trans. R. Soc. London, A 1951, 243. (8) Cardew, P. T.; Davey, R. J.; Garside, J. J. Cryst. Growth 1979,46, 534. (9) Loskit, K. Z. Pys. Chem. Stoechiom. Venvandtschaftsl.1928,134, 135 and 156.
(10) Hartman, P. In Crystal Growth: An Introduction; Hartman, Ed.; North-Holland: Amsterdam, Netherlands, 1973. (11) Hartman, P.; Bennema, P. J. Cryst. Growth 1980, 49, 145. ( 12) Jackson, K. A. In Liquid Metals and Solidification; American Society for Metals: Cleveland, OH, 1958; p 174. Jetten, L. A. M. J.; Human, H. J.; Bennema, P.; Van der Eerden, J. P. J . Cryst. Growth 1984, 68, 503.
TABLE I: Fitted Kinetic Parameters surface temp, K A, pm s-l
p
fO11l
288.15 293.15 298.15
61.0 130.0 15.0
0.57 0.36 0.083
(oii)
288.15 293.15 298.15
20.0
0.15
C,Fm SKI
10.7 17.5
uI
0.097 0.038
Normally, for facetted growth forms a is greater than 3 and growth can proceed only in a stepwise manner with growth sites present as kinks along the steps. The availability of kink sites to solute molecules is then determined by the strength of the adsorption of solvent. It turns out, therefore, that the observed influence of a solvent on growth kinetics may be the result of changes in either of these surface effects. Only careful experimentation and calculation of a factors can help differentiate the effects.13 For the present results calculation of a factors and modeling of the kinetic data are used as a means of gaining insight into which is most important at each end of the polar resorcinol crystal. 4.3. Calculation of a and Possible Growth Mechanics. As discussed above, the density of steps and kinks on a surface is related, at least at low supersaturation, to the surface energy factor (the Jackson factor), a. This is defined, for systems forming ideal solutions, asi4 a = thkXAH/RT- In X,)
(6)
in which AH is the heat of melting, T the melting temperature, X , the solubility, and thkl the crystallographic anisotropy factor, a exhibits a critical value below which step and kink formation is energetically favored, giving a molecularly rough surface, and above which steps are formed only by surface nucleation or emergent dislocations. In the statistical mechanics derivation of a,&, the interaction energy between solid and fluid blocks, is generally given a single value. In a polar crystal, although it will have a different value normal to the polar surfaces, this will not affect the overall energetics of surface roughening. Thus, a will be identical for the two polar ends of the crystal. For the (011) and ( O i T J surfaces of a-resorcinol t i= based simply on the numbers of nearest neighbors in the bulk and surface. The heat of fusion for a-resorcinol is not known due to the existence of a phase transition before the melting point, but the heat of fusion of the @-polymorphcorrected to 20 OC is 21.3 kJ mol-' , I 5 The aqueous saturation mole fraction of a-resorcinol at 20 "C is 0.192, and the solutions are nearly ideal.* Equation 6 then gives a = 5.2. This value lies well above the critical value of a i= 3 and suggests that both surfaces should grow by a layer mechanism. This is indeed confirmed by the strongly nonlinear growth kinetics reported in section 3 and agrees with similar calculation made for melt growth of resorcinoLi6 The original calculations made by Milisavljevic2were done prior to the development of eq 6 and are certainly incorrect. Mechanistically, it is expected that the source of growth steps would probably be dislocations emergent at the growth surfaces. The value of a is too high for surface nucleation to be favored at low supersaturations. The existence of inclusions in the (OTT) growth sector would certainly give rise to many dislocations, and the existence of etch pits on the (011) faces4 implies that here also there are emergent dislocations. Thus, a reasonable prediction would seem to be that both the slow-growing 1011) and the fast-growing {OTT) surfaces will grow by step growth with many emergent dislocations available to provide step sources. (1 3) Davey, R.J.; Mullin, J. W.; Whiting, M. J. L. J . Cryst. Growth 1982, 58, 304. (14) Elwenspoek, M. J. Cryst. Growth 1986, 78, 353. (15) Walker, W. H.; Collett, A. R.; Lazzell, C. L. J . Phys. Chem. 1931, 35, 3259. (16) Sharma, B. L.;Sharma, N. K.; Bassi, P. S. J . Cryst. Growth 1984, 67, 633.
Kinetic Story of a-Resorcinol
4.4. Model Confrontation. Using nonlinear regression analysis, we have fitted the experimental growth rates to the surface nucleation and spiral growth laws of eq 2 and 3. The fitted curves are shown in Figures 2, 3, and 4, and the best values of A , B, C, and uI are given in Table I. A number of important observations arise from this exercise. Firstly, it is found that of all the data only that measured on the (Oii)faces at 298.15 and 293.15 K can be fitted by spiral growth curves. The temperature dependence of C obtained yields a value of approximately 16 kcal mol-I for the activation free energy for a resorcinol molecule entering the adsorption layer. This value compares well with that estimated for other molecular systems" and is presumably associated with desolvation of both the arriving molecule and the surface site. Since a hydrogen bond is -4 kcal mol-', this may correspond to the desolvation of approximately four hydroxyl groups. Secondly, the kinetic data for the slow-growing (011) surfaces and the faster growing (OTT)faces at 288.15 K can be fitted only by surface nucleation type curves. The reason for this is the existence in each case of regions at low supersaturations for which the growth rate is effectively zero. This implicitly excludes a fit to the spiral growth law, eq 3. Thirdly, when the data are used to obtain an overall activation energy, E A , for growth, by plotting In R versus 1/ T, unrealistically high values are found. For the (Oii)faces E A i= 40 kcal mol-' and for the (011) faces EA i= 107 kcal mol-', both evaluated at a supersaturation of 4.5%. Consideration of the data suggests that these values are the result of the large increase in the dead zone which occurs at 288.15 OC and are thus associated with an abrupt change in some surface process. Overall then a picture emerges in which despite the likely existence of emergent dislocations on the growing surfaces only the (OTi)faces at 298 and 293 K exhibit the expected spiral growth law. A drop in temperature-t_o 288.15 K causes a zone of zero growth to appear for the (011) surfaces as indeed exists at all temperatures for the (011) surfaces. These data can again only be fitted by an exponential surface nucleation law. 5. The Solvent Effect Having established that the significant mechanistic differences which exist between the growth of the (011) and (071) surfaces are not related to their molecular roughness (afactor), it must be concluded that adsorption of water molecules at growth sites is a key factor to be considered. Thus, it may be postulated that the unexpected appearance of surface nucleation-like growth curves is the result of blocking of dislocation step sources by adsorbed water molecules. This leads to the idea that the dead zones at low supersaturation are due, not to an inherent nucleation law, but to a form of blocking mechanism similar to that observed in the presence of additives as predicted by the Cabrera and Vermilyea model.'* The value of supersaturation at which growth begins on these faces may then be used as a measure of the strength of this solvent adsorption process. On the (01 1) face the dead zone expands with falling temperature as the water molecules become more difficult to displace. The size of these dead zones gives an estimate of the chemical potential driving force Ap for solute molecules to enter a solvent occupied growth site. Further, since Ap = Ah - TAs it is possible, by plotting Ap as a function of temperature, to identify the magnitude of the enthalpy barrier, Ah, associated with solvent removal from the surface. Such a plot is shown in Figure 5 . A linear regression analysis yields a value of 1.06 kcal mol-' for Ah and 3.54 eu for As. The fact that a spiral growth process can operate (with no dead zones) on the (Oil)faces at temperatures above -20 OC suggests (17) Bourne, J. R.;Davey, R. J. J. Cryst. Growrh 1976, 36, 287. (18) Cabrera, N.; Vermilyea, D. A. In Growrh and Perfection of Crystals; Doremus, R.H., Roberts,B. W., Turnbull, D., Eds.; Wiley: New York, 1968; p 441. Black, S.N.; Davey, R.J.; Halcrow, M. J. Cryst. Growth 1986, 76, 765.
The Journal of Physical Chemistry, Vol. 92, No. 7. 1988 2035 454035-
Chemical Potential, A P (cals)
3025-
'
51
\\
10-
5286 288 290 292 294 296 298 300
Temperature (K)
Figure 5. Relationship between chemical potential and temperature estimated from measure dead zones.
that the corresponding value of Ah on this surface is effectively zero. Now identifying Ah as is the binding energy of a water molecule at a surface in which site and E b u l k its binding energy in solution, it follows that
Taking the above values for Ah, it is concluded that the binding energy of a water molecule to a site on an acidic (011) surface exceeds that on the basic (Oii)surface by about 1 kcal mol-'. This order of magnitude is in excellent agreement with the theoretical calculations of Wireko et al.435and leads directly to the view that the polar habit of resorcinol results from the greater inhibition of (011) growth rates by water adsorption. Following these arguments, the sudden appearance of the dead zone in the growth of the (Oii]faces a t 15 OC must be due to a temperature-induced change in interfacial structure enhancing the binding of water molecules to this surface. It is conceivable that a reconstruction process may occur with relaxation of resorcinol molecular positions and structuring of the surface layer of water. This could lead to enhanced blocking of the surface by water molecules. Such an idea is consistent with all available solution chemistry for aqueous solutions which suggests that at a temperature of about 10 OC the solution properties change from solvated resorcinol molecules at high temperatures to nonsolvated at lower temperatures. This is evidenced by comparison of measured solubility and predicted ideal solubility,*J5 cryoscopic measurement^,'^ and dew point data.20 It is conceivable that the reduction in solvation with decreasing temperature corresponds to an increase in water structure. This may be enhanced by the oxygen rich (OTi)surfaces. 6. Conclusions Measured kinetic data for the (011)and (Oii)surfaces of resorcinol growing from aqueous solutions have confirmed that the (Oii)oxygen rich surfaces are faster growing over a range of temperatures and supersaturations. Careful confrontation of these data with crystal growth theories confirms that solvent adsorption is the cause of the polar morphology in resorcinol. The observed surface nucleation curves appear to be the result of surface blocking by adsorbed solvent and not due to the existence of an inherent surface nucleation growth law. This conclusion is in overall agreement with the calculations of Shimon et al.495for interaction energies of water with the (Oii)and (011) faces or resorcinol. In addition, the (19) Carallaro, L.;Indelli, A. Gam. Chim.Ital. 1958, 88, 369. (20) Chatterji, A. C.;Rastogi, R. P. J . Indian Chem. SOC.1954, 31, 63.
J . Phys. Chem. 1988, 92, 2036-2039
2036
dramatic mechanistic change observed on the ( O i i ) faces between 20 and 15 OC suggests that the structural nature of the interface may change at lower temperatures. Comparison with available solution chemistry confirms this possibility and predicts that the water molecules will become more self-associated and may interfere more strongly with the growing oxygen-rich surface. In the general context of crystal growth theory and data interpretation it is worth noting that apparent surface nucleation
curves should be interpreted with care. It may be that commonly observed dead zones are due not to the problem of nucleation on a surface but to adsorption of solvent.
Acknowledgment. We thank Drs. S . N. Black and P. T. Cardew for helpful discussions during the preparation of this Registry No. Resorcinol, 108-46-3.
Study of Nonequlllbrium States of a Binary Mixture with Misclblllty Gap in the Vicinity of Its Crltkal Polnt In the Homogeneous One-Fluid-Phase Region Werner Mayer and Dietrich Woermann* Institute of Physical Chemistry, Universitat Koln, 0-5000 Koln 41, West Germany (Received: July 1 , 1987; In Final Form: October 7 , 1987)
The temperature of a homogeneous 2,6-dimethylpyridine/watermixture of critical composition is raised by a fast temperature jump (Joule heating pulse; characteristic heating time 711 E 0.4 ms, amplitude of temperature jump 0.04 K < 6Th < 0.2 K) bringing the system closer to its lower critical temperature. The delayed increase of intensity of scattered light is measured as a function of time at different scattering angles (e = 20°, 30°, 40') and different temperature differences ( T , - T,) ( T , and Tf, critical temperature and final temperature of the sample after the temperature jump, respectively). This corresponds to a change of the scaling variable k& (k, absolute value of scattering wave vector; Ef, correlation length of local concentration fluctuationsat Tf)in the range 0.1 < k& < 1.5. The measured relaxation curves are always single exponentials (7= tl,experimental relaxation time). For k ~ 0.4) the structure factor relaxes more slowly: 7hyd/7expt] decreases with increasing k&. Plots of 7hyd/7exptl versus k& show no dependence on the parameters Ef/Ei and ( T , - T,) within the error limits over the entire k& range.
1. Introduction
Binder' has published a kinetic equation to describe the relaxation of the structure factor S( T,k,t) after fast changes of the temperature in the homogeneous, stable one-fluid-phase region of binary liquid mixture of critical composition near the critical consolute temperature. In the hydrodynamic limit ( k 0, t a) the time dependence of the structure factor is given by
- -
S(Tf,k,t)= S(Tf?k)+ (S(Ti,k) - S(Tf,k)) eXP(-2t/Thyd)
(1)
[S( T,k),equilibrium structure factor; S( T,k,t),structure factor at time t after the fast temperature jump; k, absolute value of scattering wave vector ( k = 47rn/X, sin (8/2); 8,scattering angle; n, index of refraction; Xo, wavelength of incident light in vacuum; T, thermodynamic temperature (Ti,initial temperature before the temperature jump; T,, final temperature after the temperature relaxation time in the hydrodynamic limit]. jump); The relaxation time 7hyd is related to the mutual diffusion coefficient of the mixture and the correlation length of local concentration fluctuations by 1/7hyd
(2)
= D(Tf)/62(Tf)Q2(x)
where
+
n(x) = y4{1 x2 + ( x 3 - l / x ) arctan (x)) x = k [ ; D = Doey*;
= &"
[ D , mutual diffusion coefficient (Do,critical amplitude); [, correlation length of local concentration fluctuations (Eo, critical amplitude); e, reduced temperature difference (e = ( T , - T)/T,); Y and v*, critical exponent (theoretical values v = 0.630, v* = 0.671 (v* = v(l + XJ), theoretical value x, = 0.065)]. (1) Binder, K. Phys. Rea. E : Solid State 1977, IS, 4425.
0022-3654/88/2092-2036$01.50/0 , , I
-
~
To test ( I ) Wong and Knobler2 have performed pressure-jump experiments with critical mixtures of isobutyric acid/water. They concluded from their results that the observed time dependence of the scattered intensity is in good agreement with the model proposed by Binder. However, the agreement between the value of the mutual diffusion coefficient derived from the decay time q,yd and the value obtained from dynamic light scattering experiments was poor.3 Jefferson, Petschek, and Cannel14 have reported results of pressure-jump experiments with critical mixtures of 3-methylpentane/nitroethane which indicate that in the range 0.2 < ktf < 1.6 the structure factor relaxes more slowly then expected on the basis of linear response. The present study was stimulated by the poor agreement between the value of the mutual diffusion coefficient derived from the decay time 7hyd and the value obtained from dynamic light scattering experiments reported in ref 3. It is its purpose to test again the kinetic equation of the structure factor proposed by Binder' by experiments with another binary mixture using a temperature-jump technique instead of the pressure-jump technique. The experiments are carried out with critical mixtures of 2,6-dimethylpyridine/water near the lower critical point, keeping the mixtures in the stable onefluid-phase region. The temperature jumps are generated by discharging an electric capacitor through the mixture. This technique can be applied to the system 2,6dimethylpyridine/water because the electrical conductivity of a critical mixture is high enough to generate fast temperature jumps with a characteristic heating time 7 h < 1 ms. However, the strong critical opalescence of that system limits the range of k [ f values (2) Wong, N. C.; Knobler, Ch. M. Phys. Rev. Lett. 1979, 43, 1733. (3) Wong, N. C.; Knobler, Ch. M. Phys. Rev. Lett. 1980, 45, 498. (4) Jefferson, C.M.; Petschek, R. G.; Cannel1 D. S.Phys. Rev. Leu. 1984, 52. 1329.
0 1988 American Chemical Society
