completely eluted before magnesiu-n started to elute. With 13' perchloric acid, magnesium also eluted immediately but tailed scmewhat and was not completely separa1,ed from calcium which started to elute slightly before two column volumes had passed. The calcium elution curve was very broad with 1M acid. When the acid concentration of the eluent was increased to 3 M J the calcium also broke through immediately. CONCLUSIONS
The three stationary phases investigated (TBP, TOPO, m d HDPPVI) are generally more powerful extractants in the order given. The high partition coefficients of most metal salts into H D P M make this compound particularly suitable for reversed-phase paper chromatography. Tht: small amount of H D P X needed on the paper (approx. 10-6 mole per sq. em.) and the fact it has a low melting p o n t and does not crystallize on the paper are definite advantages. The capillary flow of solvent over the paper does not seem to be affected by treating the paper with this amount of H D P M . A number of otherwise difficult separations can be achieved quickly and simply by means of reversed-phase partition paper chromatography. No sperial equipment or the use of noxious or volatile solvents is required. The problem sometimes encountered in solvent extraction of finding a suitable solvent for the adducts formed is avoided. LITERATURE CITED
(1) Cerrai, E., Testa, C., Energia Nucl. (Milan) 8 , 510 (1961). (2) Cerrai, E., Testa, C., J . Chromatog. 8, 232 (1962). (3) Ibid., 9, 216 (1962).
(4) Cerrai, E., Testa, C., Triulzi, C., Energiu h'ucl. (Milan) 9, 193 (1962).
I
I
I
I
I
I
I
pMOLES OF N o C W ON COLUMN
t;
2kl0 b
I
I
I
I
I
I
33% HDPM ON Kel-F(60-EOMESH),5g ELUTING AGENT- WATER COLUMN LENGTH- 5 0 crn I D - 0 4 crn FLOW RATE - 048rnl/rnin. TEMP 25'C
g 8
z
i 6
u $ w4
2 $ 2
a I
Figure 6.
2
3
4
5
6 7 8 MILLILITERS ELUTED
9
IO
II
!2
13
Elution curves of sodium perchlorate as a function of column load
(5) Ibid.,,p. 377. (6) Dietrich, W. C., Caylor, J. D., Johnson, E. E., U . S . At. Energy Comm. Rept. Y-1322 (1960). (7) Fidelis, I., Siekierski, S., J . Chromatog. 4. 60 ii96n). (8j'~&.', 5,-ibi (1961). (9) Fletcher, W., Franklin, R., Goodall, G. C., U . S . At. Energy Comm. Rept. TID-7629,276 (1961). (10) Fritz. J. S.. Hedrick. C. E.. ANAL. CHEM.34, 1411 (1962). ' (11) Gwbhdf, R., Siekierski, S., N u k leonzka 5 , 671 (1960). (12) Hamlin, A. G., Roberts, B. J., Loughlin, W., Walker, S. G., ANAL. CHEW33, 1547 (1961). (13) Hayes, T. J., Hamlin, A. G., Analyst 87. 770 f 1962). ~
(20) Mikulski, J., Strofiski, I., Nukleonika 6, 295 (1961). (21) Ibid., p. 775. (22) Naito, K., Suzuki, T., J . Phys. Chem. 66, 989 (1962). (23) Oshima, K., J . At. Energy Soc. Japan 4, 8 (1962). (24) Pierce, T. B., Peck, P. F., Nature 194, 84 (1962). (25) Ibid., 195, 597 (1962). (26), Richard, J. J., Burke, K. E., 0 Laughlin, J. W., Banks, C. V., J . Am. Chem. Soc. 83, 1722 (1961). (27) Siekierski, S., Sochaka, R. J., Polish Acad. Sci., Inst. Nucl. Res. Rept. 262-V, 1961. (28) Small, H., J . Znorg. Nucl. Chem. 18, 232 (1961). (29) Ibid., 19, 160 (1961). (30) Testa, C., J . Chromatog. 5 , 236 I 1 961 \. \ - - - -
(1959): (16) Ishimori, T., Kimora, K., Fujino, T., Murakami, H., J . At. Energy SOC. Japan 4, 117 (1962). (17) Ishimori, T., Watanabe, K., Nakamura, E., Bull. Chem. SOC.Japan 33, 636 (1960). (18) Katzin, L. I., J . Inorg. Nucl. Chem. 4,187 (1957). (19) Kuznetsov, V. I., Compt. Rend. Acad. Sn'. U.R.S.S. 31, 898 (1941).
(31) White, J. C., Ross, W. J., U . S . At. Enerau _ _ Comm. Rept. NAS-NS-3102 (1961). (32) Winchester, J. W., U . S . At. Energy Comm. Rept. CF-58-12-43(1958). RECEIVEDfor review December 2, 1963. Accepted March 18, 1964. Division of Analytical Chemistry, 142nd Meeting, ACS, Atlantic City, N. J., September 1962. Work performed in the Ames Laboratory of the U. S. Atomic Energy Commission.
Mechanism of Electrophoretic Migration in Paper J. CALVIN GlDDlNGS and JAMES R. BOYACK Department o f Chemistry, University of Utah, Salt lake City 72, Utah The factors contro'lling the mobility of charged species in media composed of swelling fibers (especially in paper electrophoresis) have lbeen investigated theoretically. Mobility is influenced by three factors, none of which are negligible. First is the tortuosity as originally proposed by Kunkel and Tiselius. Second is the constrictive effect proposed by the present authors. Third is the ion retardation factor which has not previously been formulated. Using a cell model, theoretical expressions are derived for these effects which show their relative importance under various conditions.
The theoretical concepts developed here are used as a framework for the discussion of previous theories, particularly the tortuous path theory and the barrier theory.
P
REVIOUS THEORIES of
electrophoresis have centered around the tortuous path concept of Kunkel and Tiselius (7) and the barrier concept of McDonald (8). The present authors (3, 6 ) have recently extended these theories to include a number of important considerations heretofore neglected. I n regard to the tortuous path concept a constrictive factor, arising from the
variable cross section of a migration channel, affected the migration rate to approximately the same extent as tortuosity, and the two could be combined to yield very satisfactory values for the zone mobility (3). I n the case of the barrier concept, a quantitative theory was developed (6) to show the effect of diffusion in skirting barriers, and the mobility depends upon the applied potential providing the latter is sufficiently high. Synge (1.4) first suggested the concept that escape from barriers occurred by diffusion. The fundamental relationship of the tortuous path and the barrier concepts YOL. 36, NO. 7, JUNE 1964
1229
was discussed by Synge (f4). He showed that the former concept was applicable when the support particles or fibers were insulators, and the latter when the fibers were conductors. This criterion also applies to the later theoretical developments (3, 6). Since swelling fibers are generally not perfect insulators and since they do not conduct as well as the free solution, it would appear that most electrophoretic separations in stabilized media are made under circumstances where neither theory is entirely applicable. The object of this report is to explore the role of various factors affecting mobility in this intermediate case.
porosity is the same as for the medium as a whole, will show nearly the same electrical properties as the medium itself. This model is reasonably consistent with the random structure of porous materials since the calculated obstructive factors are independent of the location of the fiber within the cell. The agreement of theoretical obstructive factors obtained from this model with experimental values is excellent in view of the severe complications of electrical phenomenon in randomly packed materials. The conductance K of a cell containing solid material compared to the conductance K Oof the same cell without solid is
THEORY
Most polymer materials which are capable of swelling become electrical conductors in electrolyte solutions because of their permeability to small ions. Of specific interest in the theory of electrophoresis is the permeability of the cellulose fibers of filter paper to ions of the background electrolyte. If the migrant concentration is small, the conductivity of the solution is essentially the same as that of the background electrolyte alone, and the lines of force will be the same in the migrant zone as elsewhere. Providing the fibers of the filter paper are sufficiently permeable to ions of the background electrolyte, the fiber will have a significant conductivity and some of the lines of force will pass through them. The mobility of the migrant species will depend upon its ability to permeate the fibrous material. At one extreme the fiber may be completely impermeable to the migrant, and at the other extreme the permeability to the migrant may be as great as to the background electrolyte. In the latter case the obstructive factor 6 (defined as the mobility of the species divided by its free solution mobility) would be the same for migrant and background electrolyte. The calculation of 6 in this case can thus be made in terms of the background electrolyte alone. In the former case the forward motion of a migrant species is temporarily halted upon each collision with a fiber. The motion resumes after a time sufficient for the migrant to diffuse clear of the fiber. The obstructive factor will, in this case, be required to account for the sporadic motion of the migrant species. This matter was considered in a previous paper ( 6 ) . We shall first consider the case in which the permeability of fibers to the migrant and to background electrolyte is approximately the same. The theory will be developed in terms of the cell model, developed prevjously by the authors ( 3 ) . One assumes here that a particle or fiber enclosed within a cell, which is adjusted in size such that the 1230
ANALYTICAL CHEMISTRY
K/Ko
= ZFipi/Z~iopio
(1)
where ci and c i 0 are the cell average electrolyte concentrations of species i with the solid matter present and absent, respectively, and pi and pio are the respective mobilities, properly averaged to account for any factor which may either slow the species down or temporarily halt it. This equation is based on the assumption that conduction takes place only through ionic migration. The obstructive factor, 5 = pi/pio, may be used to change this equation to
K/Ko = EZFi~io/Zciofiio
(2)
the average cell concentration E,, appearing in Equation 2, is given by ~i
=
(1- e)cSo
+
eci.iiber
(3)
where 8 is the filled fraction (fraction of cell occupied by the solid, in this case the swollen fiber) and Ci.flber is the concentration of the species which is absorbed into the fiber. We now assume that the electrolyte-wat'er ratio is the same inside the swollen fiber as outside. The data of O'Sullivan (10) show that this assumption is very nearly true for various electrolytes in cellophane. This assumption makes it possible to express the intra-fiber concentration as Ci.fiber
=
ciOX/(1
+ x)
(4)
where x is the fract'ional swelling of the fiber-Le., A O/e,, where A0 is the increase in e due to swelling, and 6, is the initial value of e (before swelling). The substitution of Equation 4 into 3 gives When this is used in Equation 2, the result is
K / K ~= ~ ( -i e,)
feasible only when it is assumed that the effects of tortuosity and other factors on conductance are mathematically separable- Le.,
K/Ko
=
fT-2
where T is the tortuosity (the tortuous length of path followed in the porous material divided by the straight-line length) and f is a quantity describing the change of conductance in a cell for which there is no electrical resistance to lateral ionic transport. (The only necessity for lateral transport, away from the overall field direction, arises in an ion's attempt to avoid the obstacles in its path. Since this is accounted for by tortuosity, the remaining factors may be calculated under the assumption that lateral conductance is infinity--.e., lateral transport, where required, is instantaneous.) The quantity f may be easily formulated, without approximation, as
where z is the coordinate in the overall field direction and the integration extends from the entering side (x = o) to the exit side (z = 28) of the cell. The constant cell area normal to the x direction is Ao. The variable cell area, excluding solid, is A . The area A, is the effective area normal to x which is conducting ions. If the solid particles were nonconductors, then A , would equal A , while if the solid conducted as well as the interstitial fluid, A , = -io. In intermediate cases
A,
=
-4
+
(U/60)
(A0
- A)
(9)
where u is the intra fiber conductivity and go is the free solution conductivity. Since A. is constant, the numerator of Equation 8 can be integrated to give
This can be broken into two physically meaningful quantities, C and R, such that
f = CR(1 - 0,)
(11)
where constrictive factor
c = 281 and
ion
(6)
The quantity can now be evaluated using the cell model for a n approximation to K / K o . The calculation of cell conductance, short of lengthy numerical techniques, is
(7)
Upon substituting Equations 7 and 11 into 6, we obtain [ =
CRTP2
(14)
which demonstrates the three factors contribut'ing to the decrease in mobility found in porous materials. The constrictive factor C was discussed earlier, ( 3 ) ,and its effect showri to be the same order of magnitude as 9"+. The physical significance of the terms in Equation 11 can be st,ated as follows. The constrict,ive factor is due to the variation in the conductivity found as one proceeds through tlie cell (or along a migration channel). This factor is analogous to the increased resistance one would find in goi-ng from a conducting wire of uniform cross section to a wire of the same length and mass with a larger cross-sectional area at one end t,han the other. The increased resistance of the restricted parts of t'he wire are responsible for a large potential drop which is not compensated for by the larger sections. The ion retardatior. factor is due entirely to the presence of a second phase or solid phase. If the second phase is inert (no absorption or adsorption), R = 1 . This can be shown since, under these circx.mstances, A, = A from Equation 9 ( U = 0), and since A also equals A o ( l - 0 1 ) for a nonabsorbing and tk,us nonswelling material. If by some (aircumstance the mobility of ions within the fiber were greater than without, R > 1. The typical role of absorption and adsorption, however, is to retard the ionic species, and thus, newly always, we may expect R < 1 (If one allows for adsorption, it, must he in an amount consistent with Equation 4). Even when no adsorption is (occurring, a case that, will be treated in 3ome detail here, a typical ion within the fiber is slowed down by virtue of the complicated network through which it must pass. This network is itself ,a miniature version of a porous material, a viewpoint that serves a very useful purpose a t a later point. The equations derive44 up to this point are applicable to swelling particles of any simple geometry including fibers. For the specific case of fibrous materials, a cell of length w with a square cross section of area 4tz will contain a fiber, also of length w, with re,dius r . The axis of the cell will be aligned perpendicular to the field direction, The effective area for this case, if the fiber is centered within the cell, will be
A, o
A,
=
2Lw
< z < L - r, L + T < z < 28
(15)
=
2w[f
-
b(r2 - [
e--
x ] ~ ) ~ ' ~ ] (16)
L-r
