Ratho, T

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LOW ANGLE X-RAY MEASUREMENTS ON DENSELY PACKED c o l l o id a l  SYSTEMS—WOOLT. RATHOR e OTONAL E n OINKERTHG CoLLKfJE, R oU K KELA (Recvived Majf 18, J9t>4; Resubmitferl July 17, 1984)ABSTRACT. Low miglf x-my methods hav(* bo(>n applituj to determiru^  the size of the seatteriii  ^ inhomogeneitit^ s in wool assuming it to belong to tiie densfdy packed colloidal system after Guinier m('thods of (^ valuation. The ab«enee of particle scattering in stich systoins is mad(' clear.I N T K (3 D IT C 3^ I O NBy using ilip low angl(‘ soattoring canitTa of Kratkv it lias been possible to deteniiine tlu‘ siz(‘ of tlu‘ largt' sized particles. The differemie between jiartiek  ^s(‘,attering as in the (*ase of dilute colloidal systems and scattering by matter in densely packed colloidal systems as considered by Jhirod (1951) and Kratky (1952) becomes elmxr. It bas btMm possibl(‘ to tletermine the thickness of the layers assuming wool to bt» distributed in layers Avitli free spaei s^ in between.K X P E R I M E N TA sample of wool of the type Greany Lincoln Ewes from England was the substance investigati‘d. In order to rtuuove any amount of impurity and fats the sample was washed with soap, cleaned in a stream of distilled water, cooked with 1:3 mixture of aether and alcohol for 25 hours, in cyclohexane for S hours and finally in lienzene for S hours to attain high degree of purity. Cooking the sample for longer pc'riods produced no effect on the x-ray diagram, as by tlu’> above process most of the fats were rmnoved and the substam*e arranged itself in layers with free spaces in between. It was then stretc-hed to avoid any curling, its density determined and an amount with a definite cross-section was introduced into a Mark capillary, the scattering due to the empty capillary container having been determined previously. The sample had the following constants :-Length 35 mm.Weight 31 mg.Density 0.32gm/e.c.Thickness 1.88 mm. (Thi.s was also the internal diameter of the Markcapillary.)475456476 T . RathoExposures were taken with the empty capillaries, exposure time in each case being 2J3 of that for tho corresponding sample. This is duo to the difference in absorption between the container glass and the sample^ , the latter being a strong absorber ox2)osure times were less tliercforo for om2)ty (jontainers. Tiio capillary containing the sample was so placed that the length of the j)rimary beam was parallel to the fibre axis. Therefore the diffraction pattern should correspond to the equator representation of the fibre diagram of “ 0 ” Kratky (1955) or Polanyi (1921).The apparatus userl is the well known small angle scattering camera of Kratky (1958) fitted with a photograjihic arrangement. As it is desired to photograjih the scattered intensity from very small angli‘s up to high angular values, in tho small angle region, it is not 2>ossible to obtain the complt>te picture in a single photograph. When the time of exposure is large, the scatt(u*ed intensity as regis­tered by the photographic film at very small angli\s is so strong that it cannot be measured by densitometer. For too sliort (^x]»osures, intensity eorros2)onding to larger angles being very weak, cannot be rogisten f^l by a phoiograpliic film at all. Therefore it w'as decided to photograph the Avhol(^  region in parts by keep­ing the primary beam shutter of the apjmratus at various heights following the procedure of Kratky outlined in this paper. A scries of photographs w'cre obtained with different times of exposure by adjusting the primary beam shutter at different heights. The highest of tlu^  j)rimary beam slmtter and tlu^  corres­ponding exj)osure timings are given below.H('ight of thojirimary beam Expo.suroshutter in in niirni1/100 mm.1S5 12105 24207 48221 96238 192260 384The time of exposure varied from 12 mins, to 384 mins., thus photographing a range corresponding to Bragg values of 800 A to 50 A for A ^  1.54 A  in stages. After this the corresponding densitometer curves were obtained under identical conditions. Each partial curve represents a particular angular range of dif­fraction. They are plotted in parts in Fig. I. After this the total curve can be obtained by multiplying the partial curve intensities with their rospcvjtive time factors. The experimental measurements and their relative transformations are given in Table L A Siemens apparatus fitted with a copper target was(.mployt,fl in the present investigation. Tlie balanced filter method due to Ktatky (1943) was utilized to obtain the above j)artial intensity curves duo to CuKa tadiation. The entrance slit of the low angle camera was 0.11 mm, and the film sample distance was 135 mm.Low Angle X -R a y  Measurements on Densely, etc. 477Kig. 1. ap-- 13.6 /25.4  D I S C U S S I O N  A N D  T H E O R YAs wool is an oriented substance one can proccHMl with the smcared-out curve and no slit eorrcMdion is necessary. Mon'over due to a very large difference in the scattt‘re<l intensity of tlic innermost and the outcTinost portions of the curve, it is only convenient to plot log / versus ytt to know the exact nature of the scattering curve (Fig. 2). H(u*e I  is tlu^  smeared-out intensity and m is the1? B TAFig. 2. -.^map 13.'>x 25.4478 T. Rathodistance from the centre of th(' primary beam measured along ihv dcuisitometer eurv(‘ and is thenddre a function of tlic scattering angle Tlie double logarith­mic plot log I versus log nt is a straight line of slope —2.Sb (Pig. 3).According to Porod (1953) the tail portion of the smeared-out scattering curve of a general two phase system decreases like where k is a measure of the interface of the two phases. As usual m is given by— 7nlapwhere 20 is the angle of scattering, ' a \ the film saniple <listance and is the transformation factor. The intensity I can thercTore be c^ xpresscrl as/  K/ni^log /  i:rr log (kjyn^). log I  — log k ~  3 log m d logTd log 7/?... 3, since log k is a constant.As tan a, the slope of the straight line in the double logarithmic plot is about - 3, (Fig. 3). this exactly represents thc‘ tail portion of such a sim‘ar<‘d-out curve For accessible scattering angles. Tt is not i)ossibl(‘ thcTcfore to determine the size of the scattering inhomogeneiti(\s as a whole. \V(‘ can estimates that it must only be larger than the largest measurable Bragg^valuc' of aboutI) A1 (fp Ai.e. D =  1.54x 13.5x25.4 -- 520A; for A -  1.54 A, r/_^13.5 and P--25.4.Assuming mi,.oil,-s of variable tluckness as mo.Jel for the sc attering system (Kratky an,l P.m.d, 194!i), vv,- ean hop,^  to obtain the m,-an tlnck,u>ss from the Guinier plot log Irn^  versus mK From such a eurv,> one ean easily get, on drawing two asymptotic tangents at tlie two extremities, two values of tl,e thickness factor of about OOA and 125 A respectively.Low Angle X-Ray Measurements on Densely, etc 479T,\BLE JMeasurements on wool, filt,‘r differenc,' methodJtn2/3F>1 / .1.1 9.3 293.01 2 7 3 :i2 229.01 0 . 8 ISl .01 . 4 8. 1 125.01 u b.i 10 93 01 s 8 4 03.22 1 (i 35 s 40.82 3 10 2 30 82 .-) 8.5 \ 30 02 U 10 0 28 02.S 12 0 20 0H (» 10 0 2 10 0:j.2 13 0 13 0:i.r> 10.7 10.74. 0 8.0 8,04. 0 0.2 1 0.2I — Tutonsity not coiTecttHl for time factor.F—‘Timo factor./ — Smcarc(l-out intensityX —Corrected for t)ie background intensity.A thorough thoorotical handling of the problem of low angle scattering is due to Porod (1049) which applies to fully oriented systems like regenerated cellulose. The scattering of such a systtuu treated after Babinet's reciprocal relation, after certain assumptions, leads to a s(*attoring function resulting out of interparti­cular intcrfereu(*e. This effect is very important where the distance between neighbouring particles is much smaller than the dimensions of the particles themselves. The function ^2 increases rapidly to very high values as the480 T . Eathoscattering angle 20 approaches zero. When 20 =  0 this intensity beconie.s infinite. That is why in the case of wool, irregular system not highly oriented, the scattering curve, (Fig. 2), is very steep and runs almost parallel to the Y axis for very small values of 20. In this case the particle scattering is practically absent due to the irregularity of the free space and the occupied space.While intcrpartieular effects are predominant. The scattered intensity speaks about the spread or extension of the micelle system.C O N C L U S I O NThe size of the scattering inhomogeneities in wool are larger than 520 A. Interparticular interference is predominent in the system.K E F 13 K E N C E SKratky, ()., 1942, Naturwii/Sf 80, 542.*’ (1955), Physik der Hochpolymeren, 8, 288.Kratky, O. and Hcala, Z., 1958, Z, Elelctrochemie, 62(1), 06. Kratky, 0. and Porod, G., 1949, J. Colloid Sd., 4, 36.Kratky, O. and 8ekora, A., 1943, NaturwissenschafteHf, 81, 46. Polanyi, M., 1921, Z* Physik, 7, 149.Porod, G.. 1951, Kolloid, Z, 124(2), S3.Porod, G., 1953, Kolfid-Z., 133, 16.Porod, G., 1949, .4c^ f; Physicn Avst., 3(1), 66.

Low Angle X-Ray Measurements on Densely Packed Colloidal Systems—Wool

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Low Angle X-Ray Measurements on Densely Packed Colloidal Systems—Wool

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