J . Phys. Chem. 1993,97, 11551-11552
11551
Kinetic Molecular Model Interpretation of Condensation Flux Data: Nonpolar versus Highly Polar Species S. H.Bauer’ and C. F. Wilcox, Jr. Baker Chemical Laboratory, Cornell University, Ithaca, New York 14853 Received: July 6, 1993’
We contrast two different interpretations of the measured temperature-dependent critical supersaturation levels for nonpolar and highly polar molecular species.
Introduction We have presented’ a kinetic molecular model (KKM) for interpreting condensation flux data. It differs fundamentally from classical nucleation theory (CNT) in that it is based on a self-consistent chemical kinetics formulation that incorporates molecular rather than bulk properties. One essential empirical parameter in KKM is the stabilization parameter, SP, which measures the relative efficiency of dissipation of the heat of condensation from the nascent clusters by collisionswith ambient gases. In the absence of a general theory for estimating relative probabilitiesfor v-T energy transfers between vibrationally excited clusters by polyatomic monomers, we consider the derived SP’s as being analogous to @ values that are determined empirically to account for the effects of foreign gases on the shapes of falloff curves in unimolecularreaction rate theories. Thus far, all derived SP values have plausible magnitudes, with a weak temperature dependence, as do f s . To further test the generality of KKM, we reduced temperature-dependent critical supersaturation data in two recently published reports2J according to KKM. In both cases the data were obtained from upward thermal diffusion cloud chamber^.^
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Figure 1. Derived SP values for tetrahedrally symmetric tetrachlorides plotted vs the reduced temperature for J 1-3.
Discussion Measurements on the supersaturated vapors of SiCL2complete an interesting four member sequence: cCl4,’ Sic&: TiC14,6 and SnC14,6 all zero-dipole, tetrahedrally symmetric species. We derived stabilization parameters and plotted them vs reduced temperatures (see Figure 1). Two interesting features appear. (i) Three of the tetrachlorides have closely similar SP’s,with a 0.35total spread of 0.04 unit; they show a small upward trend with n D.cC&-NO, t temperature. As we pointed out previously,’ this is not fully a..o.., 0 CeHs-CHs consistent with the temperature-dependent trends for all the species we examined, other than SnC14 and Fe(CO)S. (ii) At this -Ttime we have no explanation for the larger upward slope found Figure 2. Derived SP values for highly polar species and toluene plotted for SnC14. Other than its considerably higher molecular weight, vs the critical temperature for J 1-3. we have not identified a molecular property that is out of line with the lower molecular weight tetrahedral species. Indeed, as (0.5 D) were included.* The polar species are mutually consistent; was pointed out by El-Shall? it is the titanium compound that all show the typical decline of SP with increasing T (except the is somewhat out of line with respect to its molecular parameters. last two points of benzonitrile). For the structurally analogous In the second study, a group of four compounds with large toluene, the SP‘s are temperature-independent, similar to the dipole moments, 3.92-4.22D, was investigated by Wright et aL3 behavior of 0- and m-xylene, and distinctly different from that All show significant departures from predictions of classical of n-butylbenzene. With respect to the propensity for stabilization nucleation theory (CNT). Thus, at (TIT,) = 0.44,the experby collisions with the ambient gas, dipole moments play a role 1-3) exceed CNT imental supersaturation levels (for J but are not the major factors. estimates by 20% (H3CN02), 50% (H3CCN), 57% (C&N02) We contrast our interpretation of the differences between the and 112% (CsHsCN). Following our established routine, we polar and nonpolar species with that presented by Wright and drew in the =best” envelope curves (on enlarged prints of the El-Shall? Their explanation focuses on the geometric structures corresponding Figures 2-5) and read paired values of S( 77.’ The of the stabilized clusters. They postulated that large dipoles derived temperature-dependent SP’sare plotted in Figure 2.For comparison, values for C&-CH3 (0.36D) and C ~ H S - ~ - C ~ H ~modify the shapes of the liquidlike droplets due to mutual molecular orientations, which either elongate them from spherical shapesor increasetheir effectivesurface tension and thus moderate Abstract published in Aduance ACS Abstracts, October 15, 1993.
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0022-3654/93/2091-1155 lt04.00/0 0 1993 American Chemical Society
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Bauer and Wilcox
11552 The Journal of Physical Chemistry, Vol. 97, No. 44, 1993
the parameters that must be inserted in CNT. Similarly,Kumer et a1.lO proposed that dipoldipole interactions reduced droplet radii and increased total surface energy. For acetonitrile their analysis does lead to a better fit of the experimentalS( T;J) curve than does CNT, but to a poorer fit for chloroform. We consider the dynamics of cluster-collider interactions, i.e., the influence of dipoles for determiningefficiencies of energy transfer between the nascent, vibrationallyhot clusters and their collision partners. Since there is no quantitative theory for v-T energy-transfercross sectionsinvolving complex species, we seek to identify general trends as related to molecular properties. Comparison of magnitudes of SP's for different species at the same temperaturesuggeststhat large SP's are indications of floppy units, such as is present in n-butylbenzene. In general, the more compact the structure of the nascent cluster, the smaller the number of its low-frequency intermolecular vibrations; v-T energy transfers are more efficient for deexciting the lower frequencies, per the LambertSalter re1ation.l' Hence, compact structures decreaseSP's. However, this factor is modulated by the strength of the interaction potential between the nascent clusters and the colliding species; the deeper the well, the more effective the collision; this tends to increaseSP's. Thus, compare toluene with nitrobenzene. Similar arguments apply for a single species over a range of temperatures. When the temperature is lowered, the packing density in the clusters increases; SP should decline. However, at the lower temperature the population of lowfrequency phonons increases (per the Boltzmann distribution) leading to higher SP's. Generally, the second factor dominates. (Recall, to stabilize a nascent cluster, it is necessary to remove with the first collision only enough energy to bring the total intramolecularvibrationalenergy content below the evaporation limit.) Attention is directed to Figure 10 in the report on the polar species.3 In a plot of In S(exp) vs [ ( T C / T ) 11312 interesting differences are muted; they do appear when plotted on a linear scale of S(exp) vs ( T / T , ) . Thus, for flux rates 1-3 drops cm-3 s-*, at ( T / T c )= 0.44, critical supersaturations for the following
six compounds compile as follows: H3C-CN (7.0). HpC-NO2 (8.5), C6HycHs (12.0), C6&
