1514
J . Phys. Chem. 1985,89, 1514-1 5 19
defects other mechanisms had to be invoked. Conclusion In Table I1 is shown a comparison of FSC cross sections for In this study of the kinetics of Ga(42P,) FSC collisions we have several atomic species in 2P, ( J = 1/2 or 3/2) states. It is apparent demonstrated the application of a two-laser pump and probe that there is a general trend toward smaller cross sections as the technique, involving visible multiphoton dissociation (MPD) of fine-structure splitting increases within the group 13 series Ga, a volatile organometallic and resonant two-photon ionization In, and T1, although several exceptions may be noted. The (R2PI) detection and monitoring of the metal atomic photouniformly large cross sections within this series for oxygen may fragment. The particular feature of the ionization detection be attributable to the occurrence of a general ionic/covalent curve method which makes it a very convenient and practical probe for crossing mechanism. An additional factor favoring a large cross Ga(42PJ) is the availability of a one-photon resonant, two-photon section in the particular case of Tl(62P3/2)/02is the possibility ionization pathway in this case. This means that selective ioniof a near-resonant E-E energy transfer process.I4 It is to be zation of Ga(42PJ) may be induced with a single laser at low expected that irregularities in the above-noted trend would arise power. Similar detection schemes apply in the cases of A1(32PJ) when such near resonances occur. Another example of this is the and In(5*PJ), and since both of these species may be produced relatively large value of the cross section for In(52P3/2)/C0,which by visible MPD of the corresponding trimethyl organometallic^,^^ is attributable to the close match between the In fine-structure the pump and probe technique described here should see further splitting (2213 cm-I) and the CO vibrational fundamental (2143 applications for atom kinetic studies involving these species. For A number of interesting comparisons may be made within detection of atoms for which single-frequency R2PI is not feasible, the group Ga(42P3/2),C S ( ~ ~ P and ~ / ~C1(32P1/2), ), for which the two-color ionization may be ~ o n s i d e r e dbut , ~ ~here the simplicity intramultiplet splittings are comparable in magnitude (see Table and convenience of the ionization detection method begin to be 11). The differences in the cross sections for Ga(42P3/2)and lost. However, the advantages of highly sensitive detection and C1(32P1/2)are quite striking, but perhaps not surprising in view freedom from difficulties associated with optical thickness effects, of the dissimilar chemical nature of these atoms, arising from large such as are encountered in optical detection methods,36 make differences in such properties as ionization potential, electroionization detection quite attractive, particularly in the area of negativity, the radial extent of the valence p-type orbitals, and metal atom kinetics associated with UV/visible MPD of volatile including of course the differing valence electronic configurations. organometallics. Similarly, the relatively large cross sections observed for C S ( ~ ~ P ~ , ~ ) , Registry No. Ga(CH&, 1445-79-0; CH,, 74-82-8; CzH4, 74-85-1; particularly in the case of nitrogen, probably reflect the importance CO, 630-08-0; C02, 124-38-9; SF6, 2551-62-4; N2, 7727-37-9; H2, of specific chemical effects stemming for example from the rel1333-74-0; D2,7782-39.0; 0 2 , 7782-44-7; Ga, 7440-55-3; Ar, 7440-37-1. atively low ionization potential of Cs and the radial diffuseness of the valence charge distribution. We may note in this connection that FSC collisions of C S ( ~ ~ Pwith ~ / N2 ~ )have been discussed in (34) Mitchell. S. A.: Hackett. P. A. J . Chem. Phvs. 1983. 79. 4815. terms of an ionic/covalent curve crossing mechanism.33 (35) Hurst, 6.S.;Payne, M. G.;Kramer, S. D.; Young, J.'P. Reo. Mod. (33) Andreev, E.A.; Voronin, A. I. Chem. Phys. Lert. 1969, 3, 488.
Phys. 1979, 51, 761. ( 3 6 ) Linevsky, M. J.; deHaas, N. J . Chem. Phys. 1982, 77, 6060.
Adsorption and Surface Tension Reduction at the Vapor-Liquid Interface D. J. Lee, M. M. Telo da Gama, and K. E. Gubbins* School of Chemical Engineering, Cornell University, Ithaca, New York 14853 (Received: November 30, 1984)
We report a study of the vapor-liquid interface of a mixture of components A and B, in which A is a liquid solvent and B is a volatile (often supercritical) solute, using the methods of molecular dynamics (MD) simulation and mean field theory (MFT). In such mixtures the volatile component B is often strongly adsorbed at the surface, leading to a substantial reduction in the surface tension. We have used MD to calculate the density profiles, adsorption, and surface tension for such a mixture composed of Lennard-Jones molecules and have compared the results with MFT. The MFT gives a good account of the adsorption of the volatile component. We also use MFT to predict the effect of varying the temperature, composition, and potential parameter ratios ~ g B / c f i and U B B / U U on the density profiles, adsorption, and surface tension for Lennard-Jones mixtures. The adsorption is particularly pronounced for small ~ g g / t A Aratios and low temperatures, particularly if uBB/uAA is relatively large. For such mixtures the solute can cause a lowering of the surface tension by 90% or more.
1. Introduction When a volatile solute is added to a liquid solvent it may be strongly adsorbed at the vapor-liquid surface, leading to a large reduction in the surface tension. This phenomenon has important practical applications in industrial separation processes such as distillation, liquid extraction, and adsorption, and in oil recovery. In gas-injected oil recovery, for example, a light component such as carbon dioxide or liquid petroleum gas is injected into the oil reservoir.' The adsorption of the light component at the oil-solid (1) See, for example: Dake, L. P. 'Fundamentals of Re-servior Engineering", Fayers, F. J., Ed.; Elsevier: New York, 1978. "Enhanced Oil Recovery"; Elsevier: New York, 1981.
0022-3654/85/2089-1514$01.50/0
interface greatly reduces the surface tension and changes the wetting behavior of the oil, making the trapped oil mobile. Although experimental studies have been made of the reduction in surface tension for a number of mixtures, the detailed mechanisms involved remain poorly understood. Systematic computer s i m ~ l a t i o nand ~ * ~theoretical3-' studies have, for the main part,
'
(2) Chapela, G. A.; Saville, G.; Thompson, S. M.; Rowlinson, J. S. J. Chem. SOC.,Faraday Trans. 2, 1971, 73, 1133. (3) Lee, D. J.; Telo da Gama, M. M.; Gubbins, K. E. Mol. Phys. 1984, 53, 1113. (4) Carey, B. S.; Scriven, L. E.;Davis, H. T. AIChE J . 1980, 26, 705. Davis, H. T.; Scriven, L. E. Adu. Chem. Phys. 1982, 49, 357. (5) Telo da Gama, M. M.; Evans, R. Mol. Phys., 1980, 41, 1091.
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1515
Vapor-Liquid Interface Study
TABLE I: Details of M D Runs" run 1 2
NA/N 0.875 1 .oo
system size 1024 1024
no. of stepsb 35 000 25 000
surface tension/dyn cm-' MD MFT 21.9 & 0.1 18.0 26.10 0.05 23.4
step size/s 1 x 10-14 1x
*
1044
" For both runs the cell dimensions were xL = yL = 37.0A,zL = 74.0 A.
adsorption X 102/A-2 MD MFT 1.80 0.05 2.10
bAfter equilibration.
concentrated on mixtures of two similar liquids, where adsorption and surface tension reduction effects are small. The theoretical calculations have usually been based on the square gradiente or mean field3J0J1approximations. The mean field theory is related to the integral equation version of the original van der Waals theory; it is convenient to use and seems to reproduce the major features of- the vapor-liquid interface well. In a recent paper3 we have carried out a detailed comparison of the results of mean field theory (MFT) and molecular dynamics (MD) calculations for the interfacial properties of mixtures of Lennard- Jones molecules, with parameters chosen to model Ar and Kr. We found that the agreement between theory and simulation for these almost ideal mixtures was generally good, the main differences being due to the fact that MFT underestimates the bulk liquid densities. In this paper we use MFT and MD simulation methods to study the liquid-vapor interface of mixtures in which the volatile component (which in most cases is a supercritical vapor) exhibits pronounced surface activity. Mixtures of this type exhibit a rich interfacial structure. Furthermore, the accurte prediction of their interfacial properties provides a strict test of the MFT. We have also used MFT to study the dependence of the interfacial properties of the mixture (especially the surface tension and adsorption) on the parameters characterizing the volatile component and on temperature and composition. Our paper is arranged as follows. In section 2 we give a brief outline of the theory and of the simulation method. In section 3 we present our results. In section 3.1 we compare the results for the surface tension, density profiles, and adsorption obtained from MFT and M D simulation for a binary mixture of truncated and shifted Lennard-Jones fluids in which one of the components is a supercritical vapor. We study the effects of the adsorbed vapor on the interfacial properties of the system by comparing the properties of the mixture with those of a pure liquid. In section 3.2 we report theoretical predictions for the interfacial properties of a series of Lennard-Jones mixtures for different ratios of the parameters characterizing the intermolecular potentials, and over a wide range of temperature and composition. Finally in section 4 we make some concluding remarks.
j" is the free energy density of a uniform mixture characterized
2. Theory and Simulation Method
€AA/k = 299.5
by the repulsive intermolecular interactions, and (ii) the contribution from the long-range attractive interactions ut can be treated in a mean field approximation. The equilibrium densities are calculated by solving the coupled integral equations which are obtained by minimizing Q with respect to pi, i.e. Mi
= fif(lpi)) + ~ J d f p , ~ ut(lr ) - fl)
i = 1,2
where pf is the chemical potential of species i in the repulsive reference fluid. In the absence of external fields or boundaries the equilibrium value of the functional (1) is the grand potential of the system, which for a planar interface of area A is
n = -pV+
yA
(3)
where p is the equilibrium pressure and y the interfacial tension. Once the equilibrium density profiles have been obtained by solving eq 2 the surface tension is easily obtained from (3) and (1). In order to implement this theory we require some means of calculating?, the free energy density of the repulsive system. We have chosen to divide the potentials using the Weeks, Chandler, and Andersen method.12J3 The free energy of the uniform reference system is then approximated by that of an equivalent system of hard-spheres with appropriately chosen diameters, in the compressibility Percus-Yevick appro~imation.'~Consistent with eq 1 for Q, the attractive part of the potentials are treated in a mean field approximation, and therefore the bulk thermodynamic functions for this system are given by simple analytic expressions.1° The equilibrium bulk densities are calculated at each temperature and composition by solving the equations for the two-phase system,14keeping pressure and chemical potentials constant. These densities provide the boundary conditions for the Euler-Lagrange equations for the density profiles (eq 2), which can then be solved numerically by an iteration method." 2.2. Molecular Dynamics Method. We have carried out a molecular dynamics simulation for a mixture of truncated and shifted Lennard-Jones (LJ) molecules with Lorentz-Berthelot mixing rules, with parameters:
K,
€gB/k = 119.8 K, and
UM= uBB
=
uAB
CAB
= (€AA€BB)'/~
= 3.405 A
so that BBB/CAA = 0.4 and cM/cgB = 1. The potentials were ~ ~were ~ shifted by the value of the truncated a t rc,J = 2 . 5 and L J potential at the cutoff distance, so that the actual intermolecular potentials ua&) go to zero at rc,aB,i.e. Uafi(r)
where pi is the number density of species i, bi is the chemical potential of that species, is the external potential that couples to pi, and Vis the volume of the system. In writing (1) for Q we have assumed that (i) the contribution to the free enrgy due to the short-range repulsive interactions can be treated locally, Le.,
+ Vi(r)
(2)
2.1. Mean Field Theory. The mean field grand potential functional Q for a nonuniform binary mixture can be written as3J0,1 1
J
= 4$r) - u$(rc,a,d, r
< rqap
= 0, r 3 rc,a6 where u$ is the usual L J potential
(6) Telo da Gama, M. M.; Evans, R. Faraday Symp., Chem. SOC.1981, 16, 45.
(7) Telo da Gama, M. M.; Evans, R. Mol. Phys. 1983, 48, 229. (8) Telo da Gama, M. M.; Evans, R. Mol. Phys. 1983, 48, 251. (9) Falls, A. H.; Scriven, L. E.; Davis, H. T. J . Chem. Phys. 1983, 78, 7300. (10) Tarazona, P.; Telo da Gama, M. M.; Evans, R. Mol. Phys. 1983,49, 283. (1 1) Tarazona, P.; Telo da Gama, M. M.; Evans, R. Mol. Phys. 1983,49, 301.
The molecular weights of the two species were mA = mB = 39.948. We carried out simulations of the liquid-vapor interface for two (12) Weeks,J. D.; Chandler, D.; Andersen, H. C. J . Chem. Phys. 1971,
54, 5231.
(13) Lee, L. L.; Levcsque, D. Mol. Phys. 1973, 26, 1351. (14) For details of these calculations see. ref 5 and 6.
Lee et al.
1516 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 30
0.025
25
0.020 c)
Q
20
0.015
‘E 15 -o \
0.010
x 10
0.005
5
I
OO
I
d
0.05
0.15
0.10
0.20
0.25
Figure 1. Equilibrium density profiles pa and pe at the liquid-vapor interface of a truncated (and shifted) LJ mixture with t g e / e h = 0.4 and uh = uBBat a bulk liquid composition xB = 0.047 and at a temperature T* = kT/cA, = 0.6. Component B is strongly adsorbed at the interface: (-) MD simulation; (- - -) MFT.
systems: one for an AB mixture with 896 molecules of species A and 128 molecules of species B and one for a pure A fluid ( 1024 molecules) at a temperature T = 179.7 K (kT/eAA= 0.6). Details of each run are given in Table I. The N molecules were confined to a prism of dimensions xL,y L (= xL) and zL (> xL) for both runs. The usual periodic boundary conditions in the surface plane (the xy plane) were applied. The liquid was confined to the center of the cell with the vapor phase at each end, as in our previous work,3 and we have also used periodic boundary conditions in the z dire~ti0n.I~The initial configuration was an fcc lattice of the appropriate liquid density with the particles randomly distributed on lattice sites. After 2000 steps of conventional bulk liquid simulation, the z boundaries were shifted away from the liquid slab, allowing the vapor phase to develop. Another equilibration stage (25 000 time steps for the mixture, 10000 for the pure fluid) followed during which the temperature was kept constant by scaling the momenta; the velocity of the center of mass was corrected to zero. For the mixture this second equilibration stage was longer than that required for mixtures of Ar and Kr due to the strong adsorption of the supercritical coms and the ponent B at the interface. The time step size was temperature was scaled a t each step. Further details of the run are given in Table I. For a description of the numerical algorithm see ref 3. 3. Results and Discussion 3.1. MD and MFT Results for Cutofland Shifted W Mixture. In Figure 1 we plot the results for the equilibrium density profiles of an AB mixture with t B B / t A A = 0.4 and uAA= uBB a t a bulk liquid composition xB= 0.047 and at a temperature T = 179.7 K (P= kT/tM = 0.6). The MFT underestimates the bulk liquid densities by -lo%, but it predicts the shape of the profiles quite accurately. In particular, the large adsorption of B at the interface obtained by M D is quite accurately predicted by MFT; both the height and width of the maximum of pB at the liquid-vapor interface (Le., the “surface density” and “surface width” of component B) are given correctly by the theory. The width of the peak in p B is about three molecular diameters, and therefore B is not adsorbed at the interface as a monolayer. This broad interface arises because the temperature at which we did the simulation (which is just above the bulk triple point of component A) is above the bulk critical temperature of component B. For other systems (as we will see in the next section) for which the liquid range of the two fluids overlaps, the adsorption of B can (15) Rao, M.; Levesque, D. J . Chem. Phys. 1976,65, 3233.
x
’
,,’
I’
,”
Lrn
4 -
MFT
2MO I
I
/ I
o 0i
I
0.05
0.10
0.15
0.20
J
0.25
xB Fgrre 3. Adsorption of B (re)with respect to the Gibbs dividing surface of A at the liquid-vapor interface of a truncated (and shifted) LJ mixture with t g B / t M = 0.4 and u u = ~ g at g T, = 0.6 as a function of the bulk liquid composition of B. The adsorption of B at small xBis much larger than the adsorption of Ar at the liquid-vapor interface of mixtures of Ar and Kr:) ( 0 )MD simulation; (- -) MFT.
-
be more localized, and it approaches a monolayer under certain conditions. In Figure 2 we plot the surface tension (y) of the truncated (and shifted) L J mixture as a function of the bulk liquid composition of the more volatile component, B. At this temperature B is above its bulk critical temperature, and the surface tension decreases rapidly as the concentration of B increases. The relative decrease in y, A y = ( ~ ( x B = O ) - y ( x B ) ) / y ( x Bis) -22% at a concentration xB 0.05. This is about a factor of 5 larger than the corresponding decrease for mixtures of Ar and Kr.3 The agreement between the MFT and M D results is fair; the theory underestimates y by 15%. This is related to the fact that the theory also underestimates the bulk liquid densities. The MFT predictions for the surface tension of this type of mixture are at least as accurate as the predictions for the simpler Ar and Kr mixture^,^ however. In the present work the simulation system is much larger than those used in our previous simulations of Ar and Kr mixtures. Consequently, we expect the finite size corrections to y to be considerably smaller. In particular, the finite
-
-
The Journal of Physical Chemistry, Vol. 89, No. 8,1985 1517
Vapor-Liquid Interface Study uAA= uBs=
0.02c
aAA/k CBB/CAA.
50
3.405
= 299.5K 0.3 0.7
-
0.020
40
-
k
?'
'9
30
0.015
'0 % \
x
Q
h
0.010
20
vapor
10
0.005
0 0
20
40
z/i
80
60
* = use= 3.405 A = 299.5K
eAA/k
r
c
~
~
kT/cAAz
3 520
-
1
0.05
I
I
0.10
0.15
0.20
0.25
XB %A
3.025
100
/
0.3 c ~- 0.7 ~ =
Figure 5. Surface tension y of (full) LJ mixtures at Ts = 0.6, with uM = uBB and a series of cBB/eM values. The lower the ratio tBB/cM the more rapidly *, decreases with xB. For large values of cBB/cM,y varies almost linearly with xB. See Figure 4 for u, t values.
0.6
P,
/---O
W
XB
0
20
40
z
/i60
ao
IO0
Figure 4. Equilibrium density profiles pa and pB at the free interface of M (0.3, (full) LJ mixtures, with uM = uBBand a series of B B B / ~values 0.4, 0.5,0.6, 0.7) at Ts = kT/eM = 0.6. The bulk liquid composition of B is xB= 0.05 in (a, top) and xB= 0.20 in (b, bottom): (-) t g ~ / e l \ ~ 0.3, (---) t g c g / t U = 0.4, (-.-*) t ~ ~ / e= u0.5, (-**-..)Q B / ~ M = 0.6, and tgB/tM = 0.7. The surface density of B increases as the ratio e B B / t M decreases. (----e)
size correction due to the suppression of capillary waves is less than 4%. We e x p t other finite size corrections to be even smaller (see ref 3 for more details). In Figure 3 we plot the adsorption rB of B with respect to the Gibbs dividing surface of component A, Le.
where zAis the Gibbs dividing surface of A and pBII,pB,vare the coexisting bulk densities of B. The adsorption of B at xB= 0.047 is about one order of magnitude larger than the adsorption of Ar a t the liquid-vapor interface of mixtures of Ar and Kr.3 The agreement between theory and simulation is again similar to that found in the simpler Ar and Kr mixtures.' Again there is a fairly large uncertainty in the calculation of rB from the simulation results, which is almost entirely due to the uncertainty in the bulk densities. 3.2. MFT Results for (Full) U Mixtures. In this section we report extensive MFT results for the dependence of the interfacial properties (density profile, surface tension, adsorption) of (full) L J mixtures on the parameters characterizing the intermolecular
Figure 6. Adsorption of B (rB)with respect to the Gibbs dividing surface
of A at the free interface for (full) LJ mixtures with uU = uBB and a series of cBB/eMM,at 7" = 0.6. For these values of tgB/eM, rBincreases with the bulk composition of B, and also as the ratio eBp/tM decreases. For large values of cBB/cM, revaries almost linearly with xB. See Figure 4 for u, c values.
potentials, tgB/tM and aBB/aM, as well as on temperature and composition. Many of the mixtures were studied at a temperature which is above the bulk critical temperature of the more volatile component B, so that our results are relevant to studies of adsorption of supercritical vapors a t liquid-vapor interfaces. In Figures 4-6 we show the effect of varying the ratio e B B / , t M on interfacial properties. In Figure 4 we plot the equilibrium density profiles a t the free interface of a series of (full) Lennard-Jones mixtures with uAA = uBB and eBB/eAA in the range 0.3-0.7, a t a fixed temperature T* = kT/eAA= 0.6 and at two liquid compositions of B, xB = 0.05 (Figure 4a) and xB= 0.20 (Figure 4b). The interfaces studied are liquid-vapor interfaces. However, in the case of the mixtures with the lowest e B B / e M ratio, 0.3, the two phases have similar densities and are close to a critical point. The surface density of B (Le., the maximum of pB) at the liquid-vapor interface increases by a factor of -5 as eBB/6AA decreases from 0.7 to 0.3. For comparison, the density profile of Ar, pAr, at the liquid-vapor interface of a LJ mixture of Ar 0.93) exhibits a and Kr (t&Ar/€rrKr C 0.73 and UArAr/UKrKr maximum at this temperature which is weaker3 than that corresponding to the mixture with eBB/eAA = 0.7 and bgB/(TAA = 1 (see also Figure 7 and following discussion). In Figure 5 we show the effect of varying CBB/efi on the surface tension, the conditions being the same as in Figure 4. For large
Lee et al.
1518 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 0.0%
r
0.015
1
0.010
t
m
0.005
uBa/uAA = 0.6
I
I
'IVU'
I
vapor
01 0
I
0.05
1
I
0.10
0.15 xB
fiB
Figure 8. Surface tension y of (full) LJ mixtures with tgg/eM = 0.5 and ~ at 7" = 0.6. The higher the ratio bgB/(rAA. a series of U ~ B / Uvalues, the more rapidly y decreases with xB. For small values of bgB/UAA, y varies almost linearly with xB. See Figure 7 for cr, c values.
2 /A
0.025
r
Oa0
t 0
1
0.20
I L!
20
40
100
60 z/i
Figure 7. Equilibrium density profiles p A and pB at the liquid-vapor interface of (full) LJ mixtures with c B B / f u = 0.5 and a series of U B B / U ~ values (1.1, 1.0, 0.9, 0.8, 0.7, 0.6) at rC = 0.6. The bulk liquid composition of B is xB = 0.05 in (a, top) and XB = 0.20 in (b, bottom): (-) U B B / U ~ = 0.6, (---)u ~ B / u=~0.7, (-*-*) u ~ B / u=~0.8, UBB/U~ = 0.9, (---) uBB/uAA= 1.0, and (--) U B B / U ~= 1.1. The surface ~ Here crM = 3.405 density of B increases as the ratio u ~ B / uincreases. A, c A A / k = 299.5 K. (-*e-**)
values of tgB/eAA, y varies almost linearly with xB,as we found in the case of mixtures of Ar and Kr.3 However, as the ratio e g B / t A A decreases the slope dy/dxB a t xB = 0 becomes more negative and the surface tension of the mixture decreases initially much more rapidly with the concentration of B. As xB increases ~ dependence dy/dxB becomes less negative, and for small t g the of y on xB can be highly nonlinear. These trends can be easily related to the behavior of the adsorption of B (re)at the liquid-vapor interface. This is illustrated in Figure 6 where we plot This figure shows that, as a function of xBfor various corresponding to the large reduction in y at small concentrations of B, there is a rapidly increasing relative adsorption of B at the interface. Again, the curves of rBvs. xBare almost linear for the largest values of eBB/eAA, in agreement with the results for mixtures of Ar and Kr. As t g B / t A A decreases the nonlinearity of the plots of increases and for t B B / t U = 0.3, xB 1 0.05 the adsorption r B exhibits a maximum at small xB. The effect of varying the molecular size ratio, uBB/uAA, on the interfacial properties is shown in Figures 7-9. In Figure 7 we plot the equilibrium density profiles at the liquid-vapor interface of a series of LJ mixtures with tBB/eAA = 0.5 and uBB/uAA in the range 0.6-1.1; we use the same temperature, T* = 0.6, and bulk compositions of component B, xB = 0.05 (Figure 7a) and xB =
I
/
0
Ob5
/
O.'lO
0:15
0:20
xB Figure 9. Adsorption of B (re)with respect to the Gibbs dividing surface of A at the liquid-vapor interface of (full) LJ mixtures with cBB/cAA = 0.5 and a series of uBB/uAa values, at T1 = 0.6. re increases as the bulk composition of B increases and as the ratio u ~ ~increases. / u ~For small values of bgB/bAA, r B varies almost linearly with xB. See Figure 7 for cr, c values. 0.20 (Figure 7b), as before. These mixtures exhibit liquid-vapor equilibrium at this temperature. The surface density of B decreases very rapidly as the ratio u B B / u U decreases, and for tgg/eU = 0.5 the maximum in pB is suppressed for values of QBB/uAA I 0.6. In Figure 8 we plot the corresponding results for the surface tension. For small values of UBB/UAA (which correspond to the mixtures with very little adsorption at the interface) the plots of y vs. xBare almost linear, whereas for larger values of uBB/uAA the slope dy/dxB becomes less negative as xBincreases from zero. Thus the behavior of the surface tension of mixtures (at fixed t B B / t U ) with increasing u B B / u A A is similar to the behavior of the surface tension of mixtures a t fixed uBB/uAA and decreasing cBB/cAA. The reduction in the surface tension at small concentrations of B becomes greater as decreases and/or uBB increases. The variation of the adsorption with xBand uBB/uAA is illustrated in Figure 9 and is again directly related to that of the surface tension. At fixed xBthe magnitude of re increases as uBB/uAA increases. At small xB (-0.05), increases by a factor of 25 when uBB/uAA increases from 0.6 to 1.1. Finally, in Figures 10-12 we summarize our results for the temperature dependence of the interfacial properties of these mixtures. As the temperature increases the bulk liquid density decreases, the vapor density increases, and the interfacial region broadens (Figure 10). An increase in temperature would, in general, be expected to lead to a decrease in surface tension, and this is observed at concentrations of B of xB = 0.15 and 0.20
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1519
Vapor-Liquid Interface Study
I'
0.025
A
T * = 0.4
_ _ _ _ _ _ _-. . ...--..-. -.-.. .--. .--.. -..
-_
0.020
,
.,\
pure vapor
10
0
20
40
60
2
/i
80
01 0.3
100
0,025r
-
-0.15 020
I
0.4
J
I
0.5
0.6
0.7 kT/cAA
0.8
0.9
Figure 11. Surface tension y of a (full) LJ mixture with ~ g B / t u= 0.5, uBB = uM at several bulk liquid compositions xB,as a function of the temperature Tz. See Figure 7 for u, c values. 25
20 N
