J . Phys. Chem. 1988, 92, 2990-2992
2990
X-100): The cp value was not affected by the coexistence with the surfactant. On the other hand, the cp value for the 1/4 bilayer was increased to ca. 20° with the surfactant because the surfactant destroys the bilayer structure. This means that the orientation of 2 in the bilayer membrane does not change with stimulation by surfactant because 2 is copolymerized with 4 and is covalently
fixed in the bilayer.
Acknowledgment. This work was partially supported by a grant-in-aid for the Scientific Research on Priority Area of Macromolecular Complexes from the Ministry of Education, Science, and Culture, Japan.
Measurement of the Vapor Pressure of Volatile Liquids by Single Droplet Angle-Averaged Optical Resonance Glenn 0. Rubel US.Army Armament, Munitions, and Chemical Command, Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Maryland 21 01 0-5423 (Received: October 5, 1987; In Final Form: December 7 , 1987)
The evaporation rate of large, volatile droplets is measured by an angle-averaged optical resonance technique. Electrodynamic trapping of single droplets is used to measure the 90' light scattering from evaporating dimethyl phthalate droplets. Periodic resonances in the randomly polarized scattered light are observed during the course of droplet evaporation that are associated with electric and magnetic Mie resonances. From known relationships between the resonance periodicity and the droplet index of refraction, droplet size changes are inferred from the 90' light scattering history. Using continuum mass transport theory, and a rigid-sphere approximation for the dimethyl phthalate gas-phase diffusion coefficient, we are able to find good agreement between the measured dimethyl phthalate vapor pressure and the literature value.
Introduction Rapid, accurate methods to measure the vapor pressure of liquids have always been in demand. In the late 1970s a valuable technique was introduced that significantly reduced the analysis time and increased the accuracy of vapor pressure measurements.' The technique is referred to as single particle electrodynamic balance, and with it it is possible to determine the vapor pressure of liquids from the evaporation rate of individual droplets. For example, by monitoring the time-dependent particle balancing voltage, Rube12 was able to measure the evaporation rate of multicomponent oil droplets and developed semiempirical relationships between the percentage mass evaporated and the liquid vapor pressure. Recently, a new optical method was developed to characterize the condensation dynamics of individual droplets (Fung et al.3). The optical technique involves the measurement of periodic geometrical resonances in the elastic light scattering from growing droplets. Matching Mie theory to experimental light scattering data, Fung et aL3 were able to determine the growth rate of saline droplets. It is the objective of this study to determine the feasibility of using angle-averaged optical resonances to measure the evaporation rate of large volatile droplets and thereby the liquid vapor pressure. We measure the 90° light scattering from evaporating dimethyl phthalate droplets using a randomly polarized helium-neon laser. By monitoring the appearance of electric and magnetic resonances during droplet evaporation, and resorting to theoretical relationships describing the resonance periodicity, we are able to determine the evaporation rate of the phthalate droplet. From continuum mass transport theory, the droplet vapor pressure is expressed in terms of the droplet evaporation rate and the dimethyl phthalate gas-phase diffusion coefficient. Using a rigid-sphere approximation to estimate the gas-phase diffusion coefficient, we determine the vapor pressure of dimethyl phthalate to be 9.37 X mmHg at 20 OC, in good agreement with literature values. (1) Davis, E. J.; Ray, A. K. J . Chem. Phys. 1977, 67, 414. (2) Rubel, G. 0. J . Colloid Interface Sci. 1981, 81, 188. (3) Fung, K. H.; Tang, I. N.; Munkelwitz, H. R. Appl. Opt. 1987, 26, 1282
0022-3654188 12092-2990$01.50 / O
Experiment Electrodynamic suspension of single droplets has proven to be a valuable tool in the investigation of a wide range of phenomena in aerosol physics. The principle for droplet suspension is based on developing a phase lag between the droplet motion and the oscillating electric field (Frickel et a1.4). For linear electric fields, the droplet experiences a net time-averaged force that opposes the weight of the droplet. In addition, if a static electric field that exactly balances the particle weight is impressed across the chamber, the droplet remains stationary at the null point of the oscillating field. Figure 1 shows a schematic of the electrodynamic droplet suspension chamber, approximately 60 cm3 in volume, and the associated electrooptical circuitry. The static electric field is established by impressing a voltage differential across the top and bottom electrodes that are electrically insulated from the central electrode. An oscillating voltage of 500-1000 V is applied to the central electrode that establishes a linear electric field inside the chamber and provides the appropriate restoring force for the charged droplet. As the droplet evaporates, the static voltage differential is reduced to maintain the droplet at the null point of the chamber. Charged dimethyl phthalate (DMP) droplets are generated by applying a high voltage to a capillary tube that contains the DMP (index of refraction of 1.5 138). At a critical voltage, a spray of charged droplets is generated and they are guided into the chamber by focusing fields. All droplets except one are removed from the chamber. The droplet is accurately positioned at the electrodynamic null point by monitoring the light scattered by the droplet at 90° (Figure la). Light from a 2-mW helium-neon laser (6328-A wavelength) is targeted onto the droplet, and the light scattered at 90° is detected with a split photodiode. The split photodiode consists of two diode panels that independently respond to the light scattered by the droplet. The signal from the two diodes is passed through a difference/sum amplifier that outputs into a digital multimeter. If the droplet is positioned at the null (4) Frickel, R. H.; Shaffer, R. E.; Stamatoff, J. B. ARCSL-TR-77041, Chemical Systems Lab., Aberdeen Proving Ground, MD, 1978.
0 1988 American Chemical Societv
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 2991
Vapor Pressure of Volatile Liquids
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(a)
Dimethylphthalate = 42 +m
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3 I
4 I
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,
I
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2
3
4
I
5
6
7
8
9
TIME (minutes)
phthalate droplet as determined from 90° resonances.
Figure 1. Schematic of electrodynamic droplet suspension chamber and associated electrooptical cicuitry. 2
I
1
F w e 3. Square radius as a function of time for an evaporating dimethyl
TELEMICROSCOPE WITH SCANNING GRATICULE
1
17.21
5
6
7
I
I
I
8 I
1 2 3 4 5 6 7 8
-
TIME (MINUTES) 1.15 2.45 3.70 5.00
ai = a(0) - (i - 1)-
6.30 7.80
6.90 10.20
Figure 2. Measured 90' light scattering from an evaporating dimethyl phthalate droplet.
point, then the difference output reads zero. If the droplet moves up or down, the difference output will be nonzero, and the static voltage is adjusted to bring the difference output back to zero. The sum output of the amplifier represents the total light scattered a t 90' by the droplet and is recorded on a y-t plotter that is driven by a quartz drive. The light is projected onto the split photodiode by using a 32-mm objective that is focused onto the droplet. The acceptance angle of the microscope is approximately 4O. The initial droplet size is determined by means of a telemicroscope (lox) that is fitted with a calibrated scanning graticule. Using back-illumination of the droplet, we were able to measure the droplet diameter within 1 pm.
Results and Discussions Figure 2 shows the measured 90° far-field light scattering for an evaporating D M P droplet, the initial diameter of which is 84 pm. Because the chamber is unsaturated with DMP vapors, the droplet evaporates and resonances in the light scattering are observed. The signature of the resonance is that of two sharp peaks followed by a broad peak. The first sharp peak is superimposed onto a broad peak whose amplitude is smaller than the first broad peak. This distinctive pattern was also observed by Ashkin and DziedzicSin the measurement of the radiation pressure on Cargille droplets, the index of refraction of which is 1.51. However, the rwnance pattern observed here differs markedly with that pattern observed by Fung et al.3 Their resonance pattern for the condensational growth of saline droplets consisted of a single sharp peak followed by a single broad peak. This difference might be attributed to the different size parameters studied or to the different material index of refraction used. Interestingly, while the relative amplitudes of the peaks varies, their spacing remains invariant. In the present case, the peak periodicity is 1.3 min. Chylek et a1.6 showed that the sharp and broad peaks are associated with second- and third-order electric and magnetic resonances and that, for sufficiently large size parameters, the resonance separation is only a function of the material index of refraction. For nonabsorbing droplets the size parameter spacing Ax between individual electric and magnetic resonances was shown to take the form tan-' (m2 - I)lI2 Ax = (1) (m2 -
defined as 2?ra/X. This relation is valid for x >> 1 . Therefore at constant wavelength X, one can associate a droplet size change with the appearance of two successive resonances. The timedependent droplet size is expressed in terms of the size parameter spacing as
1)1/2
where m is the index of refraction and x is the size parameter (5) Ashkin, A.; Dziedzic, J. M. Appl. Opt. 1981, 20, 1803. (6) Chylek, P.; Kiehl, J. T.; KO, M. K. W. Appl. Opt. 1978, 17, 3019.
XAX
2?r
where i is the ith resonance and a, the droplet radius at that resonance. By monitoring the periodicity of the resonance, one then has a quantitative measure of the droplet evaporation rate. Figure 3 shows the time-dependent square radius of the evaporating dimethyl phthalate droplet as determined from eq 2 and Figure 2. In agreement with theory, the data show a linear relationship between the square radius and time with a slope that is proportional to the droplet vapor pressure. Using a least-squares regression analysis, we find that the average evaporation rate of the dimethyl phthalate droplet is 1.074 X lo-' cm2/s. One can use this droplet evaporation rate to determine the liquid vapor pressure using relevant mass transport considerations. For Knudsen numbers (ratio of gas mean free path to droplet radius) much less than unity, gas fluxes can be detetmined from continuum theory. In the continuum regime, the molar flux is given by dC
J = 4?ra2Ddr
(3)
where Dg is the gas-phase diffusion coefficient of the volatile component, and c(r) is the molar concentration field of the volatiles exterior to the droplet. Under steady-state and isothermal conditions, the molar concentration field satisfies Laplace's equation and is expressed as
The isothermal assumption is valid due to the small latent heat of evaporation for DMP. Substituting eq 4 into eq 3, and using the ideal gas law, we obtain the following expression for the droplet vapor pressure
p = - - PRT da2 2DgMw
dt
(5)
In the derivation of eq 5 , we set the back-pressure P(-) equal to zero since a vapor-free environment is established within the electrodynamic balarice. This is achieved by introducing an external gas flow into the chamber such that the chamber volume replenishment time is much less than the time required to establish a steady-state concentration profile in the chamber. The gas-phase diffusion coefficient for dimethyl phthalate in air is calculated from the molecular theory of gases (Hirschfelder et al.') through 2.628 X 10-3(p(m, + mJ)/2mjm,)'l2 D, =
Aa,;n*('J),(
Pi,)
(6)
(7) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954.
J. Phys. Chem. 1988, 92, 2992-2997
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Here A is the total pressure in atmospheres, mi is the molecular weight of the diffusing species, and mj is the molecular weight of the gas through which the ith species diffuses. The first-order collision integral fl is a complicated function of the interaction parameters describing the forces between the ith and j t h species. Due to a lack of fundamental data on the interaction parameters for dimethyl phthalate in air, a rigid-sphere approximation is used. For rigid spheres, fl*('-'), = 1 and ui,= (ri rj),where ri is the spherical equivalent radius of the diffusing dimethyl phthalate molecule. The rigid-sphere approximation tends to overestimate the diffusion coefficient for the phthalate esters by 15%.* Using eq 6, we find that Dg = 0.062 cm2/s. With M , = 194.19 g/mol and p = 1.1905 g/cm3, we obtain a liquid vapor pressure of 9.37 X lo4 mmHg a t 20 O C . This value is in good agreement with
+
(8) Davis, E. J.; Chorbajian, E. Ind. Eng. Chem. Fundam. 1974,13, 272.
the literature value of 1.0 X
mmHg as reported by Frostling?
Conclusions Angle-averaged optical resonance is used to measure the evaporation rate of phthalate droplets, the size parameter of which exceeds 400. By use of a simple system consisting of a particle trap, a visible laser, and a photodiode detector, light scattering resonances are observed for evaporating dimethyl phthalate droplets. By use of well-known relations between resonance periodicity and liquid index of refraction, single droplet evaporation rates are inferred. Using continuum mass transport theory and rigid-sphere approximations to estimate dimethyl phthalate gas-phase diffusion coefficients, we find the measured vapor pressure to be in good agreement with literature values. (9) Frostling, H. J . Aerosol Sci. 1970, 1 , 341.
Effects of Alkyl Chain on Dlaza Macrocycilc Llgands Compiexing Barium Ion in Water: Conductometric and Surface Tensiometric Evldence Bianca Sesta Department of Chemistry, University 'La Sapienza", 001 85 Rome, Italy
and Alessandro D'Aprano* Institute of Physical Chemistry, University of Palermo, 901 23 Palermo, Italy (Received: June 8, 1987; In Final Form: October 28, 1987)
The conductance of barium chloride in water and in aqueous solutions of 1,7,10,16-tetraoxa-4,13-diazacyclooctadecane (D2) (RD2) has been measured at 25 O C . The results and N-methyl-N'-dodecyl-1,7,10,16-tetraoxa-4,13-diazacyclooctadecane show that the diazacrown and its alkyl derivative induce different effects on the molar conductance of aqueous barium chloride solutions that cannot be justified in terms of the complexation processes occumng in these systems. Because of the amphiphilic character of the ligand RD2, a coupling between micellizationand complexation process is suggested to explain these differences. The micellization of RD2 in pure water and in aqueous solutions of barium chloride has been investigated by surface tension measurements in the temperature range 15-35 O C . From the temperature dependence of the cmc, the thermodynamicparameters of micellization and adsorption have been calculated.
Introduction The unique cation-selective complexation properties of the crown ethers and their use in several technological fields'" have promoted extensive research in the past few years. In addition, heterocyclic crown ethers exhibit interesting features associated with the presence of different functional groups. Diazacrown ethers and their derivate compounds are typical examples of this class of macrocycles. Recently, several alkyl diazacrowns have been by substitution of a hydrogen atom of the diazacrown molecule with a long hydrophobic alkyl chain. The effect of this replacement on the chelating properties of 1,7,10,16-tetraoxa4,13-diazacyclooctadecane(D2) has been investigated in different solvents.I1 It was found that while in aprotic acetonitrile the Dz (1) Hong Qiand, Z.; Cussler, E. L. J . Membr. Sci. 1984, 19, 259. (2) Aalmo, K. M.; Krone, J. Acta Chem. S c a d . , Ser. A 1982, A36, 227, (3) Shono, T.; Okohara, M.; Ikeda, I.; Kimura, K.; Tonura, H. J . Electroanal. Chem. Interfacial Electrochem. 1982, 132, 99. (4) Fyles, T. M.;Melik-Diemer, V. A,; Whitfield, D. M. J. Can. Chem. 1981,59, 1734. ( 5 ) Kale, K. K.; Cussler, E. L.; Evans, D.
F.J . Phys. Chem. 1980.84, 593. ( 6 ) Lehn, J. M.; Mantovani, F. Helv. Chim. Acra 1978, 61, 67. (7) Ikeda, I.; Yamamura, S.; Nakatsuji, Y.; Okahara, M. J . Ora. Chem.
1980,45, 5355. ( 8 ) Kuo, P. L.; Miki, M.; Ikeda, I.; Okahara, M. JAOCS, J. Am. Oil Chem. SOC.1980, 57, 227. (9) Cinquini, M.; Tundo, P. Synthesis 1976, 516. (10) Le Moigne, J.; Simon, J. J . Phys. Chem. 1980, 84, 170
0022-3654188 12092-2992SO1SO10 , I
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and its alkyl derivative N-methyl-N'-dodecyl- 1,7,10,16-tetraoxa-4,13-diazacyclooctadecane(RD2) have the same capability to complex the potassium cation (stability constants were log K, = 4.47 and log K, = 4.43, respectively), in isodielectric protic methanol their behavior is quite different (i.e., absence of complexation for the D2 and complexation capability as in acetonitrile for the RD2). Such a peculiar behavior has been rationalized on the basis of the proton donor-acceptor properties of the D2, Le., hydrogen bonding with methanol. We report an extension of these investigations to water. It can be anticipated that in this solvent the amphiphilic character of the RD2 produces metallic supermolecular structures that complicate the complexation process. Conductometric investigations of aqueous solutions of barium chloride with and without D2 or RD2, as well as the micellar properties of RD2in water and in aqueous BaC12solution, obtained by surface tension measurements, are presented and discussed in this paper. Experimental Section Materials. 1,7,10,16-Tetraoxa-4,13-diazacyclooctadecane (Dz) (Merck product M W 262.35) was purified as described elsewhere.' N-Methyl-N'-dodecyl-l,7,10,16-tetraoxa-4,13-diazacyclooctadecane (RD,) (MW 444.53) synthesized according to the lit-
'
(11) D'Aprano, A,; Sesta, B. J . Phys. Chem. 1987, 91, 2415
0 1988 American Chemical Society
