Yasunori Nishiiima
Kyoto University. Japan and Gerald Oster Polytechnic Institute of Brooklyn, New York
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Diffusion Under the Microscope
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Diffusion processes are extremely imy ~ r t a nin t ehe~nistry(1) but are difficult to demonstrate ~ l r ~ r i nag t,ypic:d laboratory period. 111the eonvent.ional diffusion apparat,us, e.g., the Tiselius cell, measurements ofteu require several days especially if macromole~desare involved. I n the present paper a simple and inexpensive apparatus is described in which diffusion can he demonstrated in a matter of minutes and arcumte quantitative measurements ran be carried out during a single classroom period. Furthermore. our apparat,us is capable of uniquely studying systems whirh otherwise are impossible to examine by the ordinary methods; henre it is of genuine scirntific interest in it,s ow11 right.. Accordiog to the theory of Rro~vlria~r movement (2) the average of the square of t,he distance over which a particle is randomly wandering is proportional to the time during whirh it was travelling. Therefore, if the diffusion is observed over a small dist,anre the time required for the ohservation rau be reduced by the sqnare of t,he magnification factor. Thus if the diffusion measurement is carried out under a microscope wit,h a maguification factor of 50, the time scale is reduced by 2500 so that hours in the ronventional diffusion appamt,us herome sero~rdsin the micm-diffusion apparat,us. Another feature of the micro-diffusion apparatus is that diffusional processes mhirh normally take plare over microscopic distanres, e.g., those assoriat,ed with living rells and with synthetic fiber formation, can he readily ohser1-ed. Furthermnre, ill the apparatus to he described, only mirrogram amount,s of solut,iol~are required.
has heen successfully employed hy Berg ( 5 ) for the study of the roncentration gradient surrounding a crystal immersed in a liquid. hnhrosr (6) further improved I this apparatus hy adapting it to the conventional niirrmrope and by i ~ ~ t r ( ~ d u cai npinhole g aperture for illcreasing the slrarpnr~snf the iuterfcrence fringes. Iiobinson (7) has utilized this apparatus, ill slightly mcdifird furm, to study the difl'u~inn of solvents into plastics. Our appnratu?; differs from that of Amhrwe and Robinson in the wnstrurtion of t,he diffusimr cell. Whereas Rchiuson's apparatus r d l n.hr se used a sperially constructed i~~terferametrir adjustment. is delicate, curs r ~ ~ l ~ s i merely sts of tn-11 standard microscope slides, n~etalliacdto rwder them partially reflecting, that are held apart [in r m end with a microscope rover slip to fnrm all optiral n-edgr. Resides Ileiug very inexpensive, our crll is easy- tn set up for the diffusion measurrmmts. A diagrammatic sketrh of our original apparatus (8) is shown in l'igure 1. S is an -4Fl-4 IOO-~i-att merrury lamp. The light is rendered appn~ximately parallel ~ r i t ha Irns L, and heat withdrawn frcm the beam 17ith the water filter F,. A C o r ~ ~ i nglass g filter comhination (or suitable infrrcnrr filter) F2, 17-hirh isolates the green line (546 mp) of t h mcrrury ~ spectrum, iuterpuses the lieam. The light falls upon the miuc;srope mirror (flat side) d l , and the lens I.; (K.A. 0.5) faruses the light OII the aperture (a pi11h111e 0.1 mm in diameter) made in the opaque plate P. The light is the11 rendered parallel agniu I;? the le~is14
Interferometric Micro-Diffusion Apparatus
10order to observe and measure the diffusio~rproress, one must know the spatial dist,ribut,ion of the coneent,rat,ion as a function of t,ime. The relat,ive cmcentration can in the usual case be most convenient,Iy det,ermined hy optiral means. The micro-diffusim~ apparatus of Fiirt,h ( 3 ) is a colorimetric method and heme is not readily adaptable for colorless subst,ances. Even for colored solutes the conrentratio~igradient is difficult to ascertain. The t,ot,allv reflecting mirrodiffusio~rapparatus of Zuher (4)suffers from the dificulty of formation of t,he boundary bet,~n?mthe starting solution and solvent. To carry out precise diffusion measurements under the microscope one must employ accurate and sensitive methods to determine t,he concent,ration distribution around t,he boundary. Light interference mrt,hods are particularly suibhle for the measuremeut of refractive index and t,herefore of concentration. 4 mim-difi'u-ion apparatus using a Fnhry-Perot interferometer
MICROSCOPE h C A M E R A
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DIFFUSION CELL
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Journal of Chemical Educofion
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apparotur.
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schematic drawing of the micro-diffusion
(N.A. 0.10) and PASSRS t h r ~ u g h the diffusion cell. The interference friuge formed by the diffusion cell is observed with the objective lens Lp(N.A. 0.10) and the eye piece (10X) of the microscope, the latter being replaceable by a microscope camera (e.g., Leitz MicroIbso adapter with a 35 mm camera or a I'olaroid Land camera wit,h microscope adapter) for taking photographs. A later version of our apparatus (9)has a concentrated source 350-wat,t arc lamp which together with its lens and filter system is arnu~gedso that the parallel light. heam is directed upwards into t,he microscope with the mirror removed. With the iust,rument the light is suffiriently irlbense so that the iut,erferetire fringe image can be projrrted for clapsroom use on a scree11 when a prism is inserted above the eycpiecr (Fig. 2).
separated by d = 0.034 mm and hence are readily observahle under a low-powered microsrope. When some of the space between the slides is replared by a liquid of refractive index n then the optical distance differc~mis greater hy a fact,or of n , so one observes lines closer together. Thus for xater (n = 1.33) oue observcs four friuges in the water droplet to every three liues in the air gap. I n this case the liquid-air iuterfare is disrontinuous 11-ith regard t o refractive index. With a hiiundary hetween two interdiffusihle liquids, on t,he other hand, the refractive iudex across the boundary varies continur:usly so that, one obtains curved iuterferenre fringes (l'ig. 3). 111 the bulk of the two liquids the fringes are equally spaced straight lines corresponding to uniform refractive indices. Along any fringe, he it straight or wr\-ed,
Figure 3. Interference fringes for diffusion of 10% sucrote rolution agoinst distilled water 3 mi" ofter formation d boundary. AA' is a reference line. Figure 2 . Photograph of the micro-diffu!ion opporatur orronged for ciorrroom projection.
The Optical Wedge
There are many i~lterfcrumetric methods for thc determinatiou of refractive indices (10). The met,hod me have choseu, namely, the interferometric wedge, is perhaps the simplest to adjust and is easy to adapt for microscopir observation. The theory of the wedge is simple in outline hut coinplirated in its details (11). .I beam of inouochromatic light tra~rsversil~g an optical wedge will int,erfcre with that portion of t,he light which is partially reflm:ted. When the optical distance (the geometric dist,auce mult.iplied hy t,he refractive index of the medium) hetween the beams is s a n e odd integral number of half t,he wavelength of the light, then there is cancellation. If the refractive index of the medium in the wedge is constant throughout, the wedge then the optiral dist,ance hetween the two heams varies linearly along t,he length of the wedge so that complete cancellat,ion appears regularly along the wedge giving equally spaced interferenre fringe.?. As the spaciugs d of the fringes are larger, the smaller t,he angle 0 of t,he wedge and the lower t,he refractive index n,. The distance betweell fringes is given by the formula d = A/2nO where A is t,he wavelength of the light. Thus for green light (A = 546 mp) we used a wedge of 0 = 8 X lo-' mdiaus (made with two ordinary microscope slides using two 0.2-mm cover slips as spacers on one end). This wedge exhibits evenly spared fringes
the uptiral distance is constant, i.e., the friuges rrprewrt contour lines of constant optical distance. If a straight line is drawn parallel t,o the fringes in the co~istai~t. refractive index region (i.e., drann perpeiidicular tu the long axis of the wedge), then the refereure line represents a liue of constant thirkue.~sof the wcdgcs. The change of optical path along this referenre line depends only upon the change of refrartive index nlong the line. Hence, the closer the fringes are which cross the reference line the greater is the variatim cf refrartive index along this line. A plot of the density cf fringes against distance along the reference line is a refractive index gradient plot (Fig. 4).
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Figure 4. Refractive index gradient versus distance for Figure 3.
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The optical wedge is a multiple-beam interferometer and hence the sharpness of the fringes depends on reflect,ivity of the partially transmitting metallized microscope slides (18). Highly reflecting surfares will give very sharp fringes which will also he weak, however, and hence a compromise must he reached. Ideally one would like high reflection with low absorption. A carefully prepared (13) met,allized glass slide wit.h a reflectivity of 85% and an absorption of about, 5% proved satisfactory. For this purpose either aluminum, silver, gold, or platinum can be used, the last named being especially useful when corrosive solutions are heing st,ndied. The more detailed theory of t,he wedge ( I f , 13) shows that the fringes appear sharpest when t,he angle of the incident beam is adjusted for optimal conditions. In practice we can sharpen the fringes by slightly adjusting the optical axis of the collimating lens system (LTP-LI) of the microsenpe and/or by t,ilting the microscope stage. Bot,h adjustments are provided for in the newer version of t,he apparatus (9). Measurements of Diffusion
The actual procedure for making a diffusion run is as follows: one drop each of t,wo liquids are placed near each other on one of the partially reflecting slides with t,he metallized surface upward; the slide is set on the mirrosrope &age. The t,wo cover slips are placed on one end of the slide and the second metallized slide, with it,s metal surface facing downward, is placed over them to make the wedge. The liquid droplets are now in physical cont,act. A field is chosen in the microscope where t,he sharp boundary between the liquids is a t right angles to the fringes and the ohservat,ions are made a t regular intervals (every minute). A feature of t,his simple wedge diffusion cell is that t,he houndary is formed very easily. This is the case even if the liquids are extremely viscous, where boundary formation in conventional cells is practically impossible. Sinre the thickness of the wedge is very small convert.ion current,s are practically non-existent,; the method involves short durations of observation and microscope proximity of the diffusing elements, t,herefore, no constant tmnperature control is required. LJor photographing the fringes, a high-speed film such as ICodak Tri-X is useful. The exposures should he of the order of '/so sec in order to obtain a sharp pirt,ure around the boundary and the film should he developed wit,h high cont,rast developer. The picture can be enlarged and examined as described above. Alt,ernat,ively, t,he original image can he projected on a screen for direct observation of the fringes. In this case the direct evaluat,ion of the refractive index gradient can he attained by using the so-called Moire pattern t,echnique. Moire pat,t,erns are those images obtained when one screen is placed over another screen in a nearly superposed position (IS). In our case when the original image of the fringes is project,ed on a sheet of paper containing parallel lines nearly a t right angles t,o the straight line fringes, one sees directly an image of a. series of parallel lines whose spacings represent the refrartive index gradient. This arrangement provides a dmmat,ic demonstration for classroom use of the hro:rdening of the gradient curve as the diffusion proceeds. 116
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Figure 5. Interference fringes for diffusion of pure glycerol ogoinst distilled water 5 min after formation of boundary.
When the refractive index gradient has a Gaussian form t,he diffusion constant is easily oht,ained by either the area-height method or the second moment. method ( I ) , sinre in the micro met,hod t,he duration of observat,ion is so short that the time a t which t,he starting houndary was formed is determined by extrapolation. For a highly concentrated solution the gradient will often be skewed toward the solution due to the increase in diffusion constant. with increasing concentrat,ion. If the solution is highly viscous the skewness may be in t,he other direction (i.e., t,oward the solvent) as in Figures 5 and 6, because the diffusion is retarded by the high visrosity of the medium (14). For t,he skewed diffusion curve t,he diffusion coefficient is obtained from Boltzmann's equation (15). The linear dependence of the diffnsion roeffirient on concentration can simply he obtained from the skewness of the curve (16).
Figure 6. Refractive index gradient verrvr dirtonce for Figure 5.
Miscellaneous Applications
A number of diffusion-rontrolled processes such as those encountered in synthetic fiber formation ran be conveniently studied hy the mirro method. For example, t,he diffusion of small molecules in highly conrentrated polymer solutions has been measured using our apparatus (8). The results show t,hat small moleculesmay move easily in a polymer solut,ion whose marrosropic viscosity is very high hut whose mirro
Literature Cited
Figure 7.
DiRulion of water into polymrylomide Rlm.
or local visrosity is ~icarlythat uf the pure solvent.
Other examples are of the swelling of plastirs hy solvents (I3g. 7), and the roagulation of a polymer solution hy non-solvents.
(1) See for example, NEIIRATH, H., Chert. Revs., 3 0 , 3 5 i (194'2); BaRRER, R. M., "Difiusion In and Through Solids," Cambridge University Press., Cambridge, 1951; JUST, W., "l)iKusion in Solids, Liquidn and Gases," Aradelnir Press, Inc., New York, 1952. (2) EINSTEIN, A,, ,472n. Phy.qik, 17, 54!l (11105); see also EINSTEIN, A,, " I n ~ e ~ t i g a t i o non s the Theory of the Brownian Movement," R. Fiirth, ed., Methuen and Co., Lid., I,ondon, 1926. (3) Fijm~,R., Z.physik., 26, il!) (1925). (4) ZOBER,R., Z . physik, 79, 280 (19.12). Roy. Soe. (Lmdon), AIM, ill (11138). (5) BERG,W. F., PTOC. , 134 (1948). (6) A~enosE,E. J., J. Sci. I n l ~ . 25, ( 7 ) Rosnvso~,C., Proc. Roy. Soc. ( L o n d m ) , AZ04, 330 (1950). Y., A N D OSTER, (?., J. Polymer Sri., 19, 337 ( 8 ) NI~HIJIMA, (1956). (9) 1)er;igned h,y Y. Sishijima and ro~nrnrrriallgnvail:lhle from t,he Tokyo I
