SEDIMEXTATION RATEOF SPHERICAL PARTICLES
Jan., 1961
51
Refinement of the projection on [OOlj is expected TABLEI11 to be less satisfactory, since the (hkO) zone shows POSITIONAL AND TEMPERATURE PARAMETERS FOR the faint reflections corresponding to the 36 8. ao. 1N(CHahltC~Clc Neglect of these faint reflections can therefore be -hOE ( R 0.119)7 h k O (R = 0.181)d a Z/C B dc. y/b B expected to lead to only approximate coordinates. 0.2281 0.4028 3 . 3 0.2281 0.250 5 . 9 Fixing the x coordinates at the values calculated Cu ,0495 .3700 6 . 5 ,0450 .250 6 . 1 from the projection on [OlO], it was found possible Clt .3100 .5320 6 . 5 ,3170 .250 8 . 5 to refine the projection on [OOl] only to R = 0.25. Clz .2750 .3490 9.9 ,2740 ,029 6 . 5 Allowing both x and y coordinates to vary, it was c1, ,1280 .0970 6 . 0 .1280 .250 8.0 found possible t o refine the projection on [OOl] to N1 .5050 .8330 6.0 .5280 .250 8 . 0 R = 0.18, with final x coordinates differing some- Nz ,2590 .1130 8.0 ,2220 .250 8.0 what from those obtained from the projection on C1 .1270 -.0010 8.0 .1270 .250 8 . 0 [OlO]. The final coordinates are given in Table 111. CZ .0770 .1320 9 . 0 .0600 ,121 7 . 0 The differences in x coordinates between the two CO .4210 ,7580 7 . 5 .4210 .250 8.0 projections range from 0 to 0.085 A.,with a mean C4 C S ,4500 .9150 7 . 5 .4500 .250 8.0 value of 0.023 for the heavy atoms, Cu and C1, .5710 .8280 9.0 .5920 .121 7 . 0 and from 0 to 0.45 A., with a mean value of 0.15 A., Ca for the light atoms. It therefore seems apparent angles of 128 and 101'; and in C U C ~ ~ in O~,~~ that the differences between the three sub-cells which the copper ion is surrounded by a set of are primarily in the y-coordinates of the N and C oxygen ions with 0-Cu-0 angles of 122 and 103". atoms. Since our main interest in [N(CH3)4I2CuCl4 The configuration has been quantitatively acis in the configuration of the CuC14--, no further counted for on the basis of ligand field theory for attempts have been made to refine the projection CuC14-- by Felsenfeld. l1 on [OOl] using the faint reflections. Some comment should be made with regard to Using y-coordinates from the projection on [OOl], the values obtained for the atomic temperature x coordinates from the projection on [OlO], and the factors in [N(CH&]ZCUC~~. The large value for two sets of x coordinates, two sets of bond distances Cu for the hkO zone is due to omission of the disand angles in CuC14-- have been calculated and are persion correction as discussed by Stewart, given in Table 11, along with the values from the Breazeale and Lingafelter.I2 The large values for CszCuCle. Beca,use of the uncertainty in the co- C1 may arise from either actual large thermal ordinates, no significance should be attached to the motion or a small randomness of position associated differences between the values from the two com- with the tripling of the small cell. pounds, but it is apparent that the CuC14-- is disThis work was supported in part by the Office of torted from tetra,hedral toward square configuration Ordnance Research (U. S. Army) under Contract No. DA-04-200-ORD-668 and in part by the U. S. as described by Helmholz and Kruh. This intermediate configuration for 4-coordinate Public Health Service under Grant A-2241. Cu(I1) has now been found in three cases: the (10) E. Prince, kbid., 10, 544 (1957). present CuC14---; the CuBrr-- in C S ~ C Uwith B ~ ~ ~ (11) G. Felsenfeld, Proc. Roy. SOC.(London), A236, 506 (1956). 3
w.,
(9) B. Morosin and E. C. Lingafelter, Acta cryst., 13, 807 (1960).
(12) J. M. Stewart, J. D. Breazeale and E. C. Lingafelter, Acta Cryst. (in press).
ON THE VARIATION OF THE SEDIMENTATION RATE OF SPHERICAL PARTICLES WITH COSCENTRATIOX BY A. G. OG.STOX Department of Phg.rica1 Biochemistry, John Curtin School of Medical Research, Australian National University, Canberra A.C.T. Received May 3, 1960
The resulk of Cheng and Schachman' on dynamic properties of suspensions of uniform polystyrene latex particles are used to test the theory for the concentration dependence of sedimentation rate, based by Fessler and Ogston2 and Ogstona on the treatment of Sullivan and Herte14 of the flow of fluid through a porous plug.
Fessler and Ogston2 and Ogston3 showed that, obtained by this treatment for a variety of types with certain assumptions, Sullivan and Hertel's4 of solute particles were in reasonable agreement with treatment of the flow of fluid through alporous plug what were believed to be the weights, shapes and can be applied to the sedimentation of solute parti- hydrodynamic volumes of these particles. Howcles a t finite concentration through a fluid medium. ever, it has not so far been possible to apply this Ogston3 showed that the particle characteristics treatment to any material whose particle characteristics are certainly and accurately known from (1) P. T. Cheng and H. K. Schachman, J . Polymer Sci., 16, 19 (1955). independent evidence. (2) J. H. Fessler and A. G. Ogston, Trans. Faraday Soc., 47, 667 The measurements of Cheng and Schachmanl on (1951). a suspension of polystyrene latex particles make (3) A. G. Ogston, ;bid., 49, 1481 (1953). (4) R. R. Sullivan and K. L. Hertel, Adv. ColZoid Sei., 1, 37 (1942). such a test possible. These particles are known by
A. G. OGSTON
52
electron microscopy to be spherical and closely homogeneous, and their radius has been accurately measured. Cheng and Schachmanl showed that the equation of Einstein for the intrinsic viscosity of a suspension of spheres is obeyed strictly, taking the hydrodynamic volume as equal to the geometric volume of these particles; that is, solvation is negligible. They showed also that the sedimentation coefficient at zero concentration is very close to the value expected for spheres of that size and density; and, finally, that the variation of sedimentation coefficient over the volume fraction (4) is expressed by range 0-7.5 X
Vol. 65
namic volume fraction of solute, is equal to rp, since V’ = 8, and l/e = pp the density of the solute particles; accordingly
Expanding this to the second power of rp
Discussion The forms of equations 1 and 3b are the same and the experimental ratio of the coefficients of 42 1 1 = - (1 + 4.060 + 15.9&*) and of rp is 3.92 in good agreement with the theoretis 80 cal value of 4. If the theory is correct there where s, SO are the sedimentation coefficients at should be complete correspondence between these volume fraction 4 and zero volume fraction of equations, but comparison is made difEcult by uncertainty about the proper values of p and 1;[ is solute. Theory.-In the expressions given by Fessler and probably close to 2/3, but the value of k is rather Ogston2and by Ogstonathere is an error in the con- uncertain. Ogston3 chose IC = 1.8 in preference to version of the sedimentation rate relative to solvent the value of 3 used by Fessler and Ogston, on the (which is the quantity given directly by their treat- grounds that this gave better agreement with ment) to that relative to the cell (which is that what were believed to be the molecular characterisdirectly observed) ; the former quantity was divided tics of a number of different types of macromoinstead of multiplied by the volume fraction of sol- lecular materials. vent. Equation 9 of Ogstona (omitting the factor However, for none of these materials were the “4,” p.v.) should therefore read molecular characteristics known with certainty. Use of k = 1.8 gives the values for polystyrene latex particles shown in Table I. These are calculated from the data of Cheng and Schachman by the where s, so are sedimentation coefficients at con- method of Ogston3 using so = 2410 X 10-ls; 1 = centration C g./lOO ml. and zero; 8 is the surface 0.86 X [ q ] = 0.025; S for spheres = 3/r and area/unit hydrodynamic volume and V’ is the T , the particle radius = 1300 A.; pp = 1.052 and p hydrodynamic volume/g. of solute particles; k and = 0.997; d(l/s)/d+ = 4.06 X 1013/2410 (from { are constants; fj is the partial specific volume of equation 1). Evidently the axial ratio is oversolute and p is the density of solvent and 17 its estimated and the hydrodynamic specific volume is viscosity. For comparison with equation 1 it is underestimated. Alternatively, the data may be convenient to convert equation 2 into the same used to show that k = 1.35 gives agreement with terms. In this case rp’ (= CV’/lOO), the hydrody- the known dimensionsof the polystyrene latex particles, and this value may be used to calculate the TABLE I molecular characteristics of the substances discussed VALUES FOR THE AXIAL RATIOJ , THE HYDRODYNAMIC by O g ~ t o n . ~The results are given in Table 11, SPECIFIC VOLUMEV’ AND THE MOLECULAR WEIGHTM OF compared with those obtained with k = 1.8. PARTICLES OF POLYSTYRENE CALCULATED BY THE METHOD While the lower value of k gives perhaps more reaOF OGSTON* sonable values for the globular proteins, the axial Value knqwn Value estimated ratios of the chain polymeric substances are as a priora with k = 1.8 much less than 1 (the expected value) as they are 5.55 10M 5.87 greater than 1with k = 1.8. 1 4 J The present comparison theref ore gives only 0.54 V‘ 0.95 TABLE I1 PARTICLE DIMENSIONS CALCULATED BY THE METHOD OF OGSTON’ M Ovalbumin Serum albumin Carboxyhemoglobin Southern bean mosaic virus Myosin Tobacco mosaic virus Polysarcosine viii-75 Polyisobutylene F5 F4 LA2 LC2 LD3
4 . 9 x 104 6 . 4 x 104 6 . 2 x 104 6 . 9 X l@ 7 . 1 X lo6 4 . 0 x 107 1 . 9 x 104 l . 6 j X l@ 7 . 9 x 10‘ 2 . 2 x 106 1 . 2 x 10‘ 4.0 x 104
k
-
1.8 J
V’
M
2.5 5.2 5.6 7.8 16 7.8 3.2 3.4 3.2 3.5 3.1 3.9
1.35 0.69 0.61 0.67 8.4 2.9 7.5 120 74 27 19 7.4
4 . 9 x 104 6 . 7 x 104 6 . 4 x 104 7 . 5 x 1w 7 . 4 x 10’ 4 . 2 x 107 2.0 x 10‘ 1.7 X 1W 8 . 2 X los 2 . 3 X 10’ 1 . 2 x 106 4 . 2 x 104
k
-
1.35 J
1/8 3.2 3.7 3.9 12 5.6 115 1/3.9 1/5.1 112.5 1/5.4 112.4
V’ 0.64 1.1 0.91
0.96 12 4.2 6.1 123 59 35 15 11
Jan., 1961
DECOMPOSITION OF SOLIDH4NzBY CHARGED PARTICLE BOMBARDMENT
53
general support .to the treatment and estimates k that different values of IC are appropriate to different only for the case of spherical particles. It may be types of particle.
THE DECOMPOSITION OF SOLID H4Nz INDUCED BY CHARGED PARTICLE BOMBARDMENT BY HAROLD A. PAPAZIAN Cmvair Scientific Research Laboratory, San Diego, California Rec&ed Mow 4, 1080
The decomposition of solid hydrazine induced by ion and electron bombardment has been studied. The decomposition waa found to proceed throu h several steps. The stepwise evolution of NI, H3 and NH, during warmu of the bombarded solid waa meaaured. The %sorption spectrum of the bombarded solid showed the absence of .2" $he results indicate the formation of nitrogen compounds such as triazene which are stabilized at low temperatures and which decompose during warmup of the solid.
Introduction I n a recent study' of the photolysis of HNs we presented evidenlce for the existence of the inorganic nitrogen chain compounds. The photolysis of solid HN, was shown to proceed through the formation and subsequent decomposition of triazene, tetrazene and perhaps even longer chained compounds. I n an attempt to find evidence for these compounds in another system we have studied the decomposition OF solid H4N, induced by electron and ion bombardment. The decomposition of the irradiated solid H4N2 was found to be exceedingly complicated, proceeding through several steps. Although it is not possible to state with certainty, the evidence does indicate the existence of the compounds found in HN3 and also other kinds of nitrogen compounds which are stabilized a t low temperatures. Experimental Two methods of' purifying solid hydrazine were used. Anh drous hydrazine (95+%) waa vacuum distilled from KOA, onto a cold finger containing liquid Nt. The solid waa then allowed to warm up by removing the liquid Ns. During this warmyp, lower boiling impurities were pumped away. When the whte deposit started to disappear from the preparation cold finger, li uid NI was reintroduced; a fraction of the remaining H& waa then sublimed over to the reaction cold finger. The second method of purification waa the generation of HlNz from hydrazine bisulfate. There waa no difference in the results. The hydrazine waa deposited aa a transparent glaas on the reaction cold finger by careful sublimation of the hydrazine from the preparation cold finger. Approximately 2 mg. of hydrazine was deposited on 2 cm.* of surface yielding solid films on the order of lo-* 111111. thickness. After the deposition on the reaction cold finger, and with the apparatus under continuous umping, the solid waa subjected to ion and electron bomtardment by discharging a laboratory Tesla coil against the outer wall of the cold finger for various lengths of time. It has been shown* that this procedure subjects the solid to bombardment with 20 Kev. electrons and ions of undetermined energy. After the bombardment the liquid N1 waa removed from the cold finger, allowing the solid to warm up. During this warmup simultaneous mass 8 ectrometer and temperature measurements were made. &e temperature was memured by a thermocouple leoldered on to the glaas cold finger a t the depoaition surface with a s ot of glaas-to-metal "Cerroseal35" polder. A CEG modefB20 m u spectrometer was used to analyze the gases evolved from the solid during the warmup. (1) H. A. Pspssian, 1.Chem. Phys., 32, 456 (1960). (2) H. A. Papadan, ibid, 29, 448 (1958).
By adjusting the pumping speed of the system the presU pulses ~ that occurred durin warmup could be discriminated into definite peaks. %he umping speed waa controlled by means of a capillary placedietween the reaction cold finger and the stopcock leading to the vacuum pump. The inlet to the m a s spectrometer waa placed between the capillary and the reaction cold finger. A universal model Perkin-Elmer 112U spectrophotometer was ueed to study the spectrum of the solid between 3300 and 6300 A. The sample was depoeited on a specially constructed cold finger which consisted of a small flat plate whose edges were in contact with a surrounding volume of liquid Nz; the nitrogen was thus excluded from the light path. After depoeition of the hydrazine the absorption was measured. The sample then was bombarded and the difference in abporption caused by the bombardment was measured. R
Results The final products found after warmup of the bombarded solid hydrazine were H,, N2 and NH3. Figures 1, 2 and 3 show the stepwise evolution of these gases during the warmup of the solid, for three different bombardment times. I n these figures the ordinates are proportional to the quantity of gas evolved. Some comparison can be made between the Nz and Hz since these are pumped out of the system a t roughly the same rate but no comparison can be made with NH, since it was found to be pumped much more slowly. In Fig. 1 we also show the temperature vs. time warmup curve of the cold finger during the course of gas evolution. A warmup blank also was run with unbombarded hydrazine on the cold finger. The two curves were experimentally identical. It is apparent that the pressure pulses are not rate changes from sudden temperature rises of the cold finger, but that the gas evolution pulses result from stepwise reactions beginning a t different temperatures. Figure 1 shows the evolution of HZduring warmup from a solid which was bombarded for two seconds. Considerable structure is quite evident. We did not investigate Nz nor NH3 evolution for two second bombardment times. Figure 2 shows the evolution of HI, N2and "3, each from separate samples. Different samples had to be used because the mass spectrometer could analyze continuously only one gas a t a time. This, however, was no problem because of the excellent reproducibility in the gas evolution from the solid. It should be noted that even though the bombarding
