Extraction by Immiscible Solvents THEODORE W. EVANS,The Shell Development Company, Emeryville, Calif.
S
EVERAL excellent articles ( 2 ) h a v e a p p e a r e d re-
In the extraction of a solute by immiscible solrents such that the partition law holds, the degree of solute removal is conditioned mainly by the relatiae volumes of the solvents. Vt7hile use of several small portions is preferable to one combined portion, excessive subdivision is unjusiiJied, since a limiting percentage removal exists for every ratio of solvent volumes. At least 94 per cent of this maximum remota1 of which a given volume of solvent is capable is achieaed by division into Jive portions, so that in practice it is scarcely worth while to divide the extracting solvent into more than Jive portions.
cently dealing with the extraction of a solute from a solution by means of a second immiscible solvent. For the laboratory worker the case of greatest interest is that ordinarily encountered-i. e., repeated shaking of the solution with fresh portions of solvent in a separatory funnel. Ordinarily a predetermined total volume of extracting solvent is taken, and this solvent used in several successive portions, the portions being of equal size for greatest efficiency. (For a proof that equal subdivision is superior to unequal, see citation 3.) While it is generally recognized that the larger the number of portions used (keeping the total volume constant) the better the extraction, no particular attention seems to have been given to the maximum extraction obtainable in this way, although the impression is given that by sufficiently increasing the number of subdivisions any required percentage of the solute may be recovered with a given total volume of extracting solvent (1, 2 ) . In the following, this last conception will be shown to be erroneous, the limits of extraction determined, and a practical value set upon the number of portions into which the solvent should be divided. Suppose a solvent of volume L liters contains m grams of solute. This solute is to be extracted by a total volume U liters of an immiscible solvent, the solutions being such that the partition coefficient is a constant. Assume U to be divided into n equal portions and L extracted successively with these n portions. Let xi be the amount of solute remaining in the i t h portion of the second solvent, and yi similarly the amount of solute left in the first solvent a t the end of the ith extraction:
where
lA
x1
Hence
+ y, = m; x1 = m - y,
Yn
m
=
(1
+E)‘
KO\\-let n approach infinity; i. e., let the solvent be divided into an infinite number of Fortions, thus securing the greatest possible extraction:
Consequently, once the relative volumes of the two solvents are fixed, the maximum percentage of the solute which can
be removed is also fixed; it is given by: (1
- e-K)
100 per cent
This formula leads to several i n t e r e s t i n g results. Suppose the original solution is extracted in a perfect’ c o u n t e r c u r r e n t tower. Then, since the solution leaving the tower is in equilibrium m-ith that entering (once the steady state is r e a c h e d ) , f o r a v o l u m e L of s o l u t i o n there is required a volume U = L / k of solvent to extract completely tlie entering volume L. S o w , if instead of employing the ideal countercurrent extraction, the same L / k liters were used in consecutive small I; L’ amounts, K = = - = 1, the percentage removal
L
k(yk)
would be (1 - e-1) 100 per cent, or 63 per cent as contrasted with 100 per cent in the tower. It should be remembered, of course, that in the infinite tower we assume the steady state to be already established. I t is of particular interest to examine the effect of increasing n on the total percentage extracted, since this effect should determine the practical choice of the number of extractions made. Table I s h o m the percentage of the solute removed for various values of n and K . The value of K is fixed by the value of k and the relative volumes of the t x o liquids. It is increased by increasing the amount of extracting solvent used, doubling this amount doubles K , etc. The figures show clearly that, in order to achieve an extraction of 80 per cent, or better, sufficient solvent must be used to give a value of K of from 2 to 10, depending on the recovery desired. Thus, if k = 1-4. e., the two liquids are equal solvents for the solute-then a t least two volumes of extracting solvent should be used for each volume of solution. As to the number of portions into which the solvent should be subdivided, it seems that 5 is generally sufficient, the labor of further subdivision being scarcely justified by the additional amount of solute recovered. To investigate this choice of five subdivisions as a practical maximum, the ratio of the recovery for n = 5 to n = should be considered, since this ratio gives the relative efficiency of the process for five subdivisions. These values have been tabulated as the final column in Table I. This ratio passes through a minimum of approximately 0.94, indicating that by five subdivisions one always secures a t least 94 per cent of the maximum solute removal, of which the given volume of solvent is capable, xhen used in the batch extraction. To fix this figure more definitely, the minimum of this function (n = 5)/(n = m ) may be approximated as follows: 1 By this expression is meant a tower consisting of a n infinite number of perfect plates. I n the present case t h e choice of volumes makea K = 1. lOOn For this value of K. n perfect plates will achieve a removal of par cent n + l of t h e solute.
-
439
INDUSTRIAL AND ENGINEERING
440
n = n
n =
w
( 8 9 ,
= f(K,
n)
=
- n(*K) 1-
CHEMISTRY
Vol. 26, N o . 4
to a t least 94 per cent of the maximum of which the given volume of solvent is capable. I n passing, it should be noted that the value K = 1 corresponds to the amount of solvent required for 100 per cent extraction in a perfect countercurrent tower, which is roughly one-fifth that demanded for substantial recovery by ordinary laboratory extraction. Unfortunately countercurrent extraction is impractical on a laboratory scale, and hence the above conditions must be met for the ordinary extractions encountered in regular work.
li
e-K
=
TABLE I. EFFECTOF n
($)
For a minimum, = 0. The values of this funct>ion for different values of K with n = 5, are:
K ON PERCENTAGE OF SOLUTE REMOVED
AND
n = 5
K
n - 1
%
%
%
%
%
‘lo
0.I 1 2 3 5
9.09 50.00 66.67 75.00 83.33 90 91
9.30 55.56 75.00 84.00 91.84 97.22
9.43 59.81 81.40 90.46 96.87 99.59
9.47 61.44 83.85 92.75 9s.27 99.90
9.52 63.21 86.47 95.02 99.33 99.99
0.99 0.947 0.941 0.953 0.97 0.99
10
n - 2
n = 5
n o 1 0
n - m
LITERATURE CITED Consequently K = 1.6 corresponds very nearly to a minimum for (n = 5)/(n = m ) . Using n = 5, K = 1.6, it is found that 75.05 per cent of the solute is removed, while n = w corresponds to a 79.81 per cent removal. The ratio 0.7505/0.7981 = 0.9403, so that in any case the use of five subdivisions is certain to achieve a removal of solute equal
(1) E’ischer, Z . tech. Physik, 5, 153 (1929); da Costa, Rev. quitn. pura aplicada, 5 , 34 (1930) ; Gatterman, “Practical Methods of Organic Chemistry,” 3rd Am. ed., p. 46, Macmillan, 1914. (2) Hunter and Nash, Ind. Chemist, 9,245 (1933) ; J. SOC.Cham. Ind., 51, 285T (1932). The latter contains copious referenres to the literature. (3) Underwood, Ihid., 47, 805 (1928). RECEIVED October 13. 1933.
Surgical Catgut Ligatures X-Ray Diffraction Studies GEORGEL. CLARK,University of Illinois, Urbana, Ill., K. K. FLEGE,AND P. Ir’. ZIEGLER, Curity Suture Laboratories, Chicago, 111.
R
ESEARCH in the field of surgical ligatures has been steadily progressing for many years. Processing technics, sterilizing technics, and exact tests on produvts have been rather thoroughly covered by the better ligature manufacturers. I n addition, there have been sponsored research programs a t universities and medical schools. All of this research, however, has dealt with the macro aspects of the ligature. After reaching a certain point, further knowledge of the products had to await the development of tools and technics that permitted examination of the ultimate structural characteristics of these protein fibers. Such a tool is x-ray diffraction equipment. X-RAY METHODOF STRUCTURAL STUDYOF LIGATURES Knowledge of the chemistry of proteins has been decidedly fragmentary, and definite information as to how protein molecules build themselves into solid animal tissues so as to account for complex behavior is almost entirely lacking. The microscope has been useful in disclosing gross structural features. By splitting up collagen fibers, such as those which constitute catgut sutures, by means of swelling experiments, it has been demonstrated that there are fiber bundles built up from five to ten fibers; each fiber is built up from about a hundred fibrils. These tiny fibrils are the real collagen units, and yet the microscope is able to say nothing as to the still smaller and more fundamental units which comprise the fibril. The experimental technic for x-ray diffraction analysis of ligatures is comparatively simple. A monochromatic beam of x-rays defined by small pinholes (about 0.025 inch, or
0.635 mm., in diameter) is passed through a ligature specimen perpendicular to the fiber axis. A photographic plate is adjusted a t a fixed distance (usually 5 cm.) behind the specimen. After development of the film the characteristic pattern appears and, in accordance with straightforwsrd principles, is measured and interpreted in terms of ultimate constitution and structure so that a model can be constructed.
DIFFRACTION PATTERNS FOR CATGUT LIGATURES Upon the basis of typical diffraction patterns for cellulose, silk fibroin, and keratin fibers which have been extensively studied and interpreted, it is possible to approach intelligently the interpretation of patterns for ligatures which have not been subjected to any appreciable amount of study. An average diffraction pattern for a commercial catgut ligature is reproduced in Figure 1A and a graphical representation which may be somewhat more easily described in Figure 2A. The principal features of the ligature patterns, proceeding from the center out, are as follows: 1. The amor hous scattering or fogging near the undifkacted beam which in&ates truly amorphous matter may vary from ractically zero intensity t o a very martred blackening of the b m , showing an almost continuous variation between specimens containing little or no amorphous matter t o those which are almost completely broken down-for example, by heating or by digestive processes. 2. uThe innermost shar ring, corresponding to a spacing of 11.9 A. of all features of tKe pattern, is most sensitive to variations in specimens which appear to be very similar. The arcs which appear ordinarily on the equator of this inner ring may be so long actually as to form a continuous ring as in Figure 1B. In this case the molecular organized units responsible for this
interference would be drbtnbuted Cellophane. On t h e OnDOSite txtreme these arcs m y d,ualIy be.80 sharp and shoi%that they rippear simply as spots lying on the equator of the Dattcrn ai8 in FixI& IC. 2 8 . i n t h i s oase thk
I he
strucluriil clruruclerisfics 14 si~rgiciilcutgut ligulures arid sutures us reiwded 6y the mono/ /
chromatic lia-ruy of copper urid lhe eflecl of condiliom of process on thnl structure (ire discussed. Cutgut reuderedploslic by imniersion iu cerlairi smUing ageuts gives an x-ruy ~iullrrnindicating /hat it is almosl wholly aniorphous. Pcl1tern.s 06luiried from the same specimen tiffer uppliculion of tensiori, or dryiug ul corislunl leugth, show the presence of a d&i/ely orgunized or cryslullirie substance, indicutirr,g lhat tension has caused a parallel arrangemenl of rnicelles irilo long chains. Quality in calgul, lo u Iurge ealeril, Is shozrm to reside in slruclural unils. Tension-dried ruin cutgul hus u mure preferred orientalion than any specimen following further processing. Eletaled temperulures required for sterilization and cerlain tubiug fluids employed tend lo lower lhe degree 1tf orienlulion of the originul patleru nrore or less. The formnlu of lClark which relules tensile slreriglh uiter slrekhing with micellur dimensions is shown to be upplicu6le in the case of culgnl ligulures; new [orntulus ure deduced for lerrsile streuglh and niicellur dimmsions.
Between the two extreines dercribed, every possible arc length might easily be observed in different specimens. It isevident, therefore, that the length of these a,rcsi.; definitely a measwc of the degree of the preferred orientation of the crystalline particles or colloidal micelles which build up the protein collagen fibril. Different ligature specimons c:m be compared, therefore, b y relative measurement of are length. This comparison may be made strict,ly qurantitative bv a new method worked out b y Clark iind Sisson (6). A microdensitometer with rutsting stage is employed. The film is adjust,ed so ttlat it may be rotated with this inner circle in locus, and successive readings can be made of the actual density of the photographic emulsion which is plotted RS a function of nn nngle. A curve can thus be drni~nwhose width is B qu;u,titativr I I I Q ~ U E of the length of the arc. Figure 3 illtistrates thc eorrrcted curves rhtained lor the linnt,irre natterns. These curves may treated mathemxticully to give definite numerical values, expresiing the perlection of orientation of the micelles. These numerical values arc highly significant in that l,hey run parallel with measured physical properties 8uch &Y tensile strength. (&e last section of paper.) Other things being equd, the shorter and sharper these arcs. indicating high degree rd preferred orientation, t,he greater is the tensile strength of the fibril. The fact that it is possible with any given ligature spoeimien to change them arc lengths by suitable ohemieal and mochanical methods hrs given to this x-ray research method an even greater pFactical significance. 3. Running somewhat parallel with the inner area, the hub, due to a part of the collagen ivhich is ==nti:rily amorphous, may vary from a continuous band of uniform width, representing random distribution, to B high degree of even for this imperfectly organized material. In this latter m 4 p
re
A.
Awrage commercial produet FIGURE
B.
1.
the cqwrtur of the baud becomes very broad in marked bulges while the polar parts of the band become I I R ~ T O and W quite faint. 4. The lengths of the arcs 081 t,hc outer sharp ring sp aring at the poles may also vary a toritinuoua circle to short lengths. as preferred orientation i m p r o ve s .
t&
The spacing is 2.8 A. 5. I t is significmt that vaxiutiuirs in t.ho widths of the two principd sharp rhxs and the hslu may also be observed, as well as
variirtioiis in lengths. The widths of tho interferences tire conditioned by tho size nf th? crystalline par^ ticks or rnice1li.s. The broader these muxima, tfie smaller both in leiigth tirid cross section itre thest, coiioidnl jiarticlei;. If collagen is built u p in some fashion from long chains similar to the construction of cellulose. then it fuliuwv that any rupturing of $.hear ohains, or breaking down into shorter m o b
d e s and smaller colloidal particles, would be manifested by increase in width of the lines or spols which appear upon the pattern. 6. A significant varlntion iri patterns is the apparnircr or now appearmice of an additional diffraction ring wliieh apgoars simply as four sharp ares between the inner ring of inmil diameter which is nlrmys prewnt and the broad hdo. The a1,pearance of these new spots is alrvrrys Rssoeiated with t,he shortest, and sharpest arc lengths for the other interference-in other words. with the highest degree 01 fiberiiig (Figures IC, 2B). Ib generat, the appemmce of these new interfarenoes would indieate suture8 of unusunl quality, espeoiitlly as regards tensile strength. They appear only oac&onalIy in ordinary commercial s ecimcns of m w Catgut or of finished sutures, but it is significant tgat the car) bo made to appear by stretching a specimen while in 8 p&stic eonditiori. This process will he considered in a later section of tlir paper. 1'A,I"mxNS To I ~ s u L T S O N COLLAGEN AND GELATIN
lL1.;LAnOs OX' LloATUlrE DIFPi
