COMMUP\'IC.\TIONS TO THE EDITOR
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1Ve considered the trajectxies of two ions starting with equal velocities b u t in opposite direction from a point in the plane of the mass spectrometer electron beam. These trajectories are parts of a parabola. The trajectories can be replaced by the trajectories of two hypothetical ions starting in the top of the parabola, with the same velocity componeiits as the former ions in directions perpendic(6) Fellow of the Alfred P Sloan Foundation ( 7 ) Katronal Science Foundation Cooperati\ e Felloir l ~ l f ~ l - l i l h 2 ular to the repeller field and no velocity in the DEPARTMEST OF CHEMISTRY direction of the field. This replacement is allowed SEW I-ORK USIVERSITY KURTXISLO!T if the number of primary ions does not change apSET! TORK 53, S I ' Hon ARD D PERLUIUTTCR' preciably RECEIVED A 43 , 196% ~ ~ ~ ~ ~ due to reactions. The influence of the initial velocity distribution in the direction of the field will be found back in the upper limit of the inteNEGATIVE TEMPERATURE COEFFICIENTS FOR IONMOLECULE REACTIONS gral over the trajectories of the ions within the ioniSir: zation chamber. This influence will be neglected Stevenson and Schissler',? observed a "small but as the contribution to the reaction is very small real" negative temperature coefficient for the cross- when the velocity of the ion in the labor,itory refsection of reactions between hydrocarbon ions and erence system is much larger than gc. The sixfold integral which has to be evaluated bemolecules. The phenomenological cross-section is inversely proportional with the repeller field conies now strength in these cases. Gioumousis and Steveni. 'z,, = S J u ( g ) f , ~f,if,>f,zf.dv,ldz'\ ItlU,?dz8,-dt3,ds son2 calculated also the rela tion between the where . f x l is the Maxwell-Roltzmann distribution phenomenological cross-section Q and the microof the velocity L I ~ of , the ion in the x direcscopic cross-section u for reactions between molec- function tion, etc. The indices 1 and 2 are used to indicate, ular ions and molecules when the rate of reaction is determined only by the interaction between a charge respectively, the ion and the molecule; the homoand an induced dipole, i.~.,uhen u is inversely pro- geneous electric field is taken in the 2; direction; i, is are, respectively, the primary and secondary portional to the relative velocity g a t a large dis- and ion current; ds is an element of the relative path of tance between ion and molecules. In this case Q is found to be inversely proportional to the square an ion-molecule pairi) and _V the density of the root of the repeller field strength, and independent molecules. Taking ~ ( g )= C,/g, i t is easily derived t h a t of temperature. Q = r'./i,, X l / & T d ,= Cl(2iizI/eE&)'/Y I t has been pointed out by Hamill and Roelrijk3s48S,d t h a t a variation of Q inversely propor- which is equivalent to Gioumousis' expression (li).' tional to the repeller field strength occurs when the E is the electric field strength and do is the distance average value of u for velocities of the ion a t the between electron beam and exit slit. exit slit is practically zero. It also has been found Evaluation of the integral for ~ ( g )= (gc/g- 1 ) u ~ experimentally that u for ion-molecule reactions in vields cyclopropane4 and in neopentane"'; can be described adequately by functions of the form u ( c ) = ulc-1'2 - C H , for E E , and U ( E ) = 0 for c 3 E , , where thc dimensionless quantity zo is given by zo = where E is the kinetic energy of the ion, and cc, u1 ( p / % T ) ' / 2 g c . Tables of the value of the integral as and UH are constants. This suggests that u ( g ) = function of w have been published.s (&g - 1)UHfor g gc and ~ ( g = ) O for g 3 gc is a The temperature effect can be found by calculatsuitable model. The constant u1 is presumably ing Q a t different temperatures. The results of such equal to the cross-section for a collision in the ion calculations for eEdo = 2 eV. and for three reactions induced dipole model a t I e1'. relative kinetic en- are presented in the table. ergy multiplied by an efficiency factor for the reaca1 OH T 0 tion under consideration. The physical meaning of Reaction (ev.'/nK.?) (A,?) (OK.) (A.2) UH is not clear, though it may be related to nearly C?Ha+ 4- CzHa" 49.2 40.0 400 26.8 head-on collisions. 500 26.3 An examination of Gioumousis and Stevenson's GOO 25.6 derivation shows t h a t no temperature effect occurs, CHIOH+ + CH30Ha 42.8 49.1 400 14.8 if the product g.(g) is a constant. An example will 800 14.3 be given t h a t a negative temperature coefficient can 600 13.7 be found for the phenomenological cross-section CS2+ + neo-C,H12b 5.3 3.1 400 0.422 without introducing a temperature effect in the 500 0.420 microscopic cross-section when gu(g) is a decreasing 600 0.413 function of g. a Estimated, see p. 35 of ref. 6 ; no efficiency factor f
bonded interaction of carboxyl groups and benzene hydrogens in the transition state is likely to contribute significantly to the destabilization of the transition state. U'ork is in progress to settle this question by studies of the resolvability (and optical stability) of Id and of other dissymmetric cyclooctatetraenes.
