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Electroosmosis of wet wool
JOURNAL OF COLLOInSCIENCE 19, 268-278 (1964)
ELECTROOSMOSIS OF WET WOOL D. Stigter Western Regional Research Laboratory ~, 800 Buchanan S~reel, Albany, California Received October 14, 1968
ABSTRACT Electroosmosis is measured of wool yarn and fabric in equilibrium with aqueous buffer solutions. The eleetroosmotic flow vs. pH curve shows a minimum ascribed to fiber conductance. Approximate equations are developed to account for this effebt. Transport of water through the fibers is estimated to be negligible. The surface of natural wool is isoelectric near pH 3. This is considerably lower than the IEP of any known wool protein fraction. The variability of surface IEP may result from mechanical damage to wool in processing. It is shown that in a recently developed practical process for shrinkproofing wool fabrics, a polyamide film is grafted onto the fiber surface. INTRODUCTION A study of the surface of wool fibers is of interest for several reasons. I n the first place, the fiber surface greatly influences technical processes such as dyeing, laundering, and felting. Furthermore, identification of reactive sites located at the fiber surface would be helpful and, indeed, necessary to design chemical modifications for improving wool. We have studied wool b y electroosmosis. This method gives information on the ~-potential of tile fiber. F r o m suitable data, one m a y evaluate the average charge density at the surface of shear of the wool fiber. Thus, from electroosmosis as a function of pH, one obtains a titration curve of the fiber surface. F r o m detailed experiments one m a y estimate the concentration of acid and basic groups at the fiber surface and tile relevant p K values. Also, the comparison of electroosmosis of natural and chemically modified wool m a y show which surface sites, if any, are chemically modified. Finally, one m a y study the interaction of the wool surface with adsorbants such as ionic detergents and dyes to help explain the effects of the p H and of other concentration variables in the wet processing of wool. With these applications in mind, a program of electroosmotic measurements on wool was started. I t was soon discovered t h a t in the interpreta' A laboratory of the Western Utilization Research and Development Division, Agricultural Research Service, U. S. Department.of Agriculture. 268
ELECTROOSMOSIS
OF
WET
WOOL
269
tion of the experiments one should allow for ionic conduction through the wool fibers. The next section is devoted to this complication. ELECTROOSMOSIS THROUGH A PLUG OF CONDUCTING FIBERS
We consider a model plug of parallel fibers immersed in a salt solution. The fiber diameter and the distance between the fibers is large compared with the thickness of the electric double layer. We apply an external electric field E parallel with the fibers. The relevant electroosmotic velocity of the liquid inside the plug is (1) -
41r~/'
[1]
where/" is the average electrostatic potential in the surface of shear of the fibers with respect to the solution far from the fiber surface, e is the dielectric constant, and ~ is the viscosity of the solution. When the cross section of the plug is A and that of the fibers is A0, we have for the total electroosmotic flow (volume per second) through the plug V = v(A
-
Ao).
[2]
The total electric current through the plug is i = (A - Ao)KE + Ao~sE,
[3]
K and Ks are the specific conductance of the solution and of the fibers, respectively. Eliminating v and E from Eq. [1] by means of Eqs. [2] and [3], the result for ~ is parallel
V4~r~Kf~
[4]
with f~ = 1 +
KsA0 K(A A0)" -
-
The factor fp corrects for fiber conductance. The correction is similar to the one for surface conductance (1). The present expression is exact for the assumed geometry of the plug. We now turn to the case of an external electric field which is perpendicular to the assembly of parallel fibers. The exact description of electroosmosis is difficult. Therefore, we use the approximate model of the plug introduced in the previous paper (2(a)). A cross section is shown in Fig. 1. It is assumed that the electroosmotic flow is uniform through the slits between successive layers of fibers and parallel to the applied field. Let the liquid between
270
STIGTER
~E
FIG. 1. Cross section of schematic model for wool plug in transverse electric field.
o
1
2
A
;3
4
A-A o
FIG. 2. Corrections for fiber conductance of the electroosmosis through fibrous
plugs for three values of the relative fiber conductance K//~. Broken curves: applied field parallel with fibers, fp from Eq. [4]. Solid curves: applied field transverse to fibers, ft from Eq. [5]. the fibers in each single layer be at rest. The liquid velocity in the slits is given by Eq. [1]. An elementary derivation yields _ V4~wft
ie
transverse
[5]
with Ky/K
ft = 1 q-
1 - v'G/A + (v%/a + v'-d/Ao - 2) In Fig. 2 we have plotted the correction factors of Eqs. [4] and [5] for some values of KffK.Even for relatively small values of the fiber conductance the correction factors f may be appreciably different from unity. We assume that a plug of randomly oriented fibers is equivalent to one in which one third of the fibers are parallel to the applied field and two thirds are perpendicular. The correction for fiber conductance in the expression for ~ is the relevant average of the correction factors in Eqs. [4] and [5]. dr = (fp -~ 2dr)~3
random.
[61
ELECTROOSMOSIS OF WET WOOL ON ELECTROOSMOTIC
WATER TRANSPORT [FIBERS
THROUGH
271 WOOL
In the previous section the total current through the plug was corrected for the fraction of the current shunted through the wool fibers. Now, with ionic conduction through the fibers, it is consistent to assume that the ions drag water along in their motion through the fibers. Such transport constitutes a correction to the electroosmotic flow V between the fibers. The transport in a representative case (see Fig. 5) was found to be V i i = 0.5 to 0.7 ml./Coul, or V i i = 2600 to 3700 mol/F = 2600 to 3700 water molecules per monovalent ion. The water transport through the fibers is difficult to evaluate exactly, and a definitive treatment is not presented. However, we advance three separate arguments suggesting that the correction for transport of water through the fibers is negligibly small under the conditions of our experiments. Transport through a Continuous Medium with Uniform Permeability As an approximate model for transport through wool fibers, we consider liquid motion through a permeable medium, represented by an assembly of identical, regularly spaced, stationary beads suspended in a viscous liquid. Let the friction factor of each bead be f and the number of beads per unit volmne be ~. In general, the boundary conditions for liquid motion past such an array of beads are hard to define and, consequently, exact solutions to the NavierStokes equation of viscous flow are intractable. However, if we consider the limit ~-~ ~ ;
f--~0
the finite product ,f suffices to characterize the medium. When v is the local liquid velocity, the term --,fv is a continuous volume force exerted by the beads on the liquid. This force enters into the flow equations, which now read v curl curl v ~- grad p -~ ,fv -- 0; div v = 0.
[7]
This set of equations has been used extensively to describe liquid motion inside coiled polymer molecules (3-6). It follows from Eq. [7] that the Darcy permeability constant of the medium is K = ~?/,f.
[81
Using standard mathematical techniques (4, 7), the force on a solid
272
S~mTEa
sphere with radius a moving through the medium with velocity v0 is found ¢o be
(
o
F = 6,.~avo I + ~ - ~ + ~
.
[9]
The volume of liquid transported by the sphere, W, is obtained by integrating the liquid velocity over the entire volume of the medium.
W=5
~ra3 3 +
--. a
[10]
In the limit K --~ ~ Eq. [9] yields the Stokes friction factor for a solid sphere moving through a viscous liquid. Furthermore, for K --~ ~ Eq. [10] shows that W -* ~. As has been discussed elsewhere (8), this limiting result is not directly applicable because Eq. [7] neglects inertia terms. Following Eq. [9], one may express the ratio of the mobility of a sphere in the permeable medium, us, to the mobility in pure liquid, u, as a function of a/x/K only us__ (1 + a u ~
a 2~-1 + 9-K] "
[11]
Also, Eq. [10] gives the ratio W/(4/3)~ra~ as a function of a/~/K only. Thus, one may plot W/(4/3)lra~ versus uffu as shown in Fig. 3. Experimental data on ion mobilities in wool may now be used to estimate the water transport through the wool. It was found (2(a)) that uffu ranges from 0.0031 to 0.0099. Thus we read from Fig. 3 that W is of the order 0.1 X (4/3)~ra3. This means that W is less than a few water molecules per (hydrated) ion transported through the wool. This result is to be compared with the previous estimates of V / i = 2600 to 3700 water molecules per ion transported between the fibers. The electric current between the fibers is of the same magnitude as the current through the fibers or larger. Hence, the electroosmotic flow through the fibers may be neglected.
Transport through Ion Exchange Resins The model used above is only approximate for wool. For example, it does not consider the fact that wool is a mixed ion exchanger with a nonhomogeneous distribution of the ion exchange sites (2(a)). It is likely that this feature of the wool structure depresses uffu more than it does W. So the theoretical estimate of W given above might well be low as is supported by data on water transport through synthetic membranes (9-11). It is found experimentally that W depends on the type of membrane, the water content of the membrane, and the type of ion. For wool fibers with about
ELECTROOSMOSIS OF W E T WOOL
273
100
W ' ' ' ,~-3/Ta I0
0.001
0.01
u_..A_f
0.1
U
FIG. 3. Volume of solvent W carried along by sphere wi~h radius a and moving through medium of uniform permeability with relative mobility uf/u. 33 % water at 100 % R.H., it seems reasonable to assume a transport of fewer than 20 water molecules per ion. So, in general, the resulting flow through the wool fibers is small compared with the electroosmotic flow between the fibers.
Invariance of the I E P For small values of ~, the water transport through the fibers becomes relatively more important; consequently the question arises of how to interpret the isoelectric pH (IEP). In general, the IEP of the fiber surface may differ from that of the bulk of the fiber. Hence, from the condition that the total flow through a plug be zero, one determines an average IEP. In this average the IEP of the fiber surface and of the fiber bulk are weighted according to the flows between and through the fibers, respectively. Experimentally, the ratio of these flows can be regulated by changing the cross-sectionM area A of the plug. Hence, the significance of flow through the wool fibers can be tested by measuring the dependence of the (experimental) IEP on A. In our experiments no such dependence was found. We conclude, therefore, that water transport through the fibers was not significant. EXPERIMENTAL The electroosmosis cell and the wool plugs were described in the foregoing paper (2(a)). Measurements were made on properly equilibrated plugs. For small electroosmotic flows, near the IEP, a capillary was used (see reference 2(b). Otherwise, the capillary was closed off and the flow through the plug and a stopcock was measured under a small pressure head with the d.c. field in either direction. It was established that within the experi-
274
STmTEn
mental error, the electroosmotic flow was independent of the pressure head and proportional to the electric current. Readings were taken at different permeabilities of the plug. Also, the electric resistance of the plug was measured before and after d.c. was passed. Only in solutions of p i t > 6 did passage of d.c. change the plug resistance more than a few per cent. This effect is probably related to the increased ionic conductance through the fibers in this p H range (2). As a result, the determinations of V i i at high p H are subject to additional errors. RESULTS AND Discussion
Electroosmosis was measured for wool fabric as a function of p H at two different values of the ionic strength. The results are shown in Fig. 4. I t appears that the isoelectric pH does not depend significantly on the ionic strength. Moreover, the data for the nitric acid and the acetic acid buffer overlap satisfactorily. This suggests that the wool fiber surface does not specifically adsorb the small ions presently used (other than H+), at least not to any significant extent. The F-potentials, evaluated with the simple theory, fp = f t = 1 in Eqs. [4] and [5], show a peculiar minimum in the intermediate p H range. I t was the observation of this anomaly which led to the investigation of fiber conductance described in the preceding paper (2(a)). In order to test the amended electroosmosis theory, measurements were carried out as a function of cross section for a fabric plug at p H = 8.85 and ionic strength 0.002. Under such conditions the correction for fiber conductance is expected to be appreciable. The results are presented in Fig. 5. On the basis of Eqs. [4], [5], and [6], a fairly good approximation in the present range of experimental values is i V
_
+10 ~ 0
~mV -20
.....
4~v~fi ~ a
random
.c
b
' " "'o,.,,~.
,
~
pH
"" ..................... ....... A ............................ ~o %
-30
[12]
%
......• ,o ......
-40
FIG. 4. Electroosmotic ~--potential of wool fabric plug versus pH calculated without corrections for fiber conductance. Circles: ionic strength 0.002. Triangles: ionic strength 0.01. One half of the total ionic strength derives from NaNOa ; the rest from buffer as follows: a: HNOa/NaNO3 ; b: HAc/NaAc; c: NH4OtI/NIt4NO3.
ELECTROOSMOSIS OF WET WOOL
275
o 1.$
/
/
j~
/ 1.6
~.s o ~.,,/o
/"
o o
,,s o
0/4. ¢-~ 1,4
/
/
sS
o
o
1..2
A_~o A-Ao
FI~. 5. Electroosmosis t h r o u g h wool fabric as a f u n c t i o n of cross section of plug.
Open points: experiments a t p H = 8.85 a n d ionic s t r e n g t h 0.002. Broken curve: from Eq. [12] w i t h K]/K = 0.093 and i n t e r c e p t adjusted.
with fr = 1 +
2KfA0 K(A A0) " -
-
According to this approximate expression i / V varies linearly with Ao/(A -- Ao). The experimental data in Fig. 5 indeed show a definite trend. This trend agrees well with the slope of the theoretical line which is based on Eq. [12] with Kff~ -- 0.093 as reported previously (2(a)). It is unfortunate that the scatter of the experimental points is so large that the data cannot serve to adequately test any quantitative aspect of the present theory. We have applied Eqs. [4] and [12] to evaluate the ~-potential as a function of pH for yarn and fabric plugs, respectively. The results in Figs. 6 and 7 show that the corrections for fiber conductance are substantial. At high pH settling of the plugs affects the measurement of fiber conductance (2(a)). Therefore, the relevant corrections to ~" are uncertain, as indicated by the parentheses in Figs. 6 and 7. In addition, the theory oversimplifies the fiber orientation and disregards the anisotropy of the fiber conductance. Thus we must conclude that at present the anomalous eleetroosmosis of wool at high pH is not completely resolved, but that fiber conductance probably causes the apparent anomaly. We now discuss the IEP of wool. Taking amino acid compositions and pK values from the literature (12, 13), we find that a and 7 keratose have an IEP at 4.5 and 5.1, respectively, while from the overall composition
STIGTER
276 +10
pH
0
~;mVz ° ~v...
.... o
-%0 ..Oo • ..,
. .... ...,, .,,, , ..........
,,,,, ..........
• ...:,,,,:,.,,,~..,,.o. ................. :
-20
c.~
c.~
-30
FIG. 6. Electroosmotic i'-potential as a function of pH for wool yarn plug. Ionic strength 0.002, buffers as in Fig. 4. Open points: from Eq. [4] with K//~ = O. Filled points: from Eq. [4] with K//Kas reported earlier (2(a)). +10 ~'::~%
0
----~-%.
~.
,
pH
~
,
-10
~mV -~'0
~N
~,,.::,.~
,,,,,,-".o"
(,
-30
FIG. 7. Electroosmotic i--potential as a function of pH for wool fabric plug. Ionic strength 0.002, buffers as in Fig. 4. Open points: from Eq. [12] with ~I/~ = O. Filled points: from Eq. [12] with ~y/Kas reported earlier (2(a)). of Merino wool, one calculates 4.8 as the I E P . On the other hand, from eleetroosmosis of several samples of natural wool (Figs. 4, 6, and 7), the I E P of the fiber surface was found to vary between 2.5 and 3.5. A trend among the data suggests t h a t mechanical processing of wool tends to increase the I E P of the fiber surface. This might link the change of I E P with damage to the fiber surface. Increased surface damage might expose more of the interior of the fiber with higher I E P and thus increase the average I E P of the fiber surface. Similarly, surface damage might account partly for the different potential levels to which ~ decreases for y a r n and fabric plugs; compare Figs. 6 and 7. These tentative suggestions require further study. Another puzzling feature is the low p H part of the electroosmotie curve for wool yarn in Fig. 6. Judging from the shape of the corrected curve, the acid groups at the fiber surface have an average p K around 3.3 or lower. Even if allowance is made for interactions in the fiber surface, this low p K is difficult to ascribe solely to the carboxylie acid groups known to be present in wool, glutamic, and aspartic acid with p K 4.6. Ruptured and oxidized sulfur-sulfur bonds in the fiber surface suggest themselves as a possible origin of strongly acidic sites. Further study is needed at this point. We now discuss experiments on chemically modified wool. In this laboratory, a technique has been developed (14) for forming polyamides on the
ELECTROOSMOSIS OF WET WOOL
277
+10
0
.__...p
3
°~ 4
~5.
~mV -10
-20
FIG. 8. Electroosmotic ~-potential of wool fabric at ionic strength 0.002, uncorrected for fiber conduction. Buffers as in Fig. 4. Curve a: fabric with 2 weight % polyamide. Curve b: treated with sebacoyl chloride. Curve c: treated with 1-6-hexamethylene diamine. Curve d: natural wool.
surface of wool fibers by interracial polymerization. Wool fabric is padded consecutively through an aqueous solution of a diamine and through a water-immiscible solution of a diacid chloride. The polymer film formed at the fiber surface makes the fabric shrink-resistant through many washing cycles. One is curious to know whether or not the polyamide film is grafted onto the wool fiber surface. In order to answer this question, samples of the same wool fabric were subjected to (a) the complete technical treatment, or (b) omitting the dinmine, (c) omitting the diacid chloride, or (d) omitting both monomers. After the treatment, the fabrics were washed to remove excess chemicals. Electroosmotic results for the four samples are shown in Fig. 8. Curve d refers to natural wool, the blank. After treatment with sebacoyl chloride (curve b), the fiber surface had become more acidic. Evidently, the sebacoyl chloride reacted with amine groups at the fiber surface and, after hydrolysis of the remaining acid chloride group, surface amine groups were converted into surface carboxylie acid groups. The chance of one sebacoyl chloride molecule reacting with two surface amine groups is very small, of course. Treatment of wool with 1-6-hexamethylene diamine produced the reverse effect. In this case the diamine converted a surface carboxylic acid into a surface amine group, thus increasing the average IEP of the fiber surface as shown by curve c. It is not known whether the diamine is held at the fiber surface by an amide bond or by a salt linkage. ~[ore elaborate experiments are required to settle this point. In summary, the present results provide evidence that some polymer chains originate at amines, and perhaps also at carboxylic acids, located at the fiber surface. Thus, we may regard the polyamide as a true graft polymer. Finally, we discuss electroosmosis of polymer treated fabric. Electronmicroscopy (15) has shown that 2 % polyamide is sufficient to substantially cover the wool fibers. Therefore, curve a in Fig. 8 refers to polyamide
278
STIGTE'R
surface rather than to wool surface. It is interesting that the polyamide surface has an intermediate, and not an extreme, IEP. It shows that in this sample carboxylic acids and amines both occur as polymer end groups, and in comparable amounts. I:~EFERENCES 1. See, e.g., 0VERSEEK, J. TH. G., in H. R. Kruyt, ed., "Colloid Science," Vol. 1, Chapter 5. Elsevier, New York, 1952. 2(a). STIGTER,D., J. Colloid Sci., 19, 252 (1964); (b) ibid., Fig. 1. 3. BRINKMAN,H. C., Proe. Koninkl. Ned. Akad. Wetenschap. 50,618, 821 (1947). 4. DEBYE, P., AND BUECIIE, A. M., J. Chem. Phys. 16,573 (1948). 5. HERMANS,J. J., ANDFUJITA, H., Koninl~l. Ned. Akad. Wetenschap. Proc. B58, 182 (1955). 6. 0¥ERBEEK, J. TH. G., AND STIGTER,D., Rec. tray. chim. 75, 543 (1956). 7. BUECHE, A. M., Thesis, Cornell University, Ithaca, New York. 8. STIGTER,D., Rec. tray. chim. 73, 771 (1954). 9. MCKELVEY, J. G., SPIEGLER,K. S., AND WYLLIE, M. R. J., J. Electrochem. Soc. 104, 387 (1957). 10. SPIEGLER,K. S., Trans. Faraday Soc. 54, 1408 (1958). 11. CARR, C. W., McCLINTOCK,R., AND SOLLNER,K., J. Electrochem. Soc. 109, 251 (1962). 12. LUNDGREN,I~. P., ANDWARD,W. i . , "Ultrastructure of Protein Fibers," pp. 49, 53. Academic Press, New York, 1963. 13. TANFOnD, C., "Physical Chemistry of Macromolecules," p. 556. Wiley, New York, 1961. 14. WmTFIELD, R. E., MILLER, L. A., AND WASLEY, W. L., Textile Research J. 31, 704 (1961). 15. Unpublished results by Dr. 1%. S. Thomas of this laboratory.
ELECTROOSMOSIS OF WET WOOL D. Stigter Western Regional Research Laboratory ~, 800 Buchanan S~reel, Albany, California Received October 14, 1968
ABSTRACT Electroosmosis is measured of wool yarn and fabric in equilibrium with aqueous buffer solutions. The eleetroosmotic flow vs. pH curve shows a minimum ascribed to fiber conductance. Approximate equations are developed to account for this effebt. Transport of water through the fibers is estimated to be negligible. The surface of natural wool is isoelectric near pH 3. This is considerably lower than the IEP of any known wool protein fraction. The variability of surface IEP may result from mechanical damage to wool in processing. It is shown that in a recently developed practical process for shrinkproofing wool fabrics, a polyamide film is grafted onto the fiber surface. INTRODUCTION A study of the surface of wool fibers is of interest for several reasons. I n the first place, the fiber surface greatly influences technical processes such as dyeing, laundering, and felting. Furthermore, identification of reactive sites located at the fiber surface would be helpful and, indeed, necessary to design chemical modifications for improving wool. We have studied wool b y electroosmosis. This method gives information on the ~-potential of tile fiber. F r o m suitable data, one m a y evaluate the average charge density at the surface of shear of the wool fiber. Thus, from electroosmosis as a function of pH, one obtains a titration curve of the fiber surface. F r o m detailed experiments one m a y estimate the concentration of acid and basic groups at the fiber surface and tile relevant p K values. Also, the comparison of electroosmosis of natural and chemically modified wool m a y show which surface sites, if any, are chemically modified. Finally, one m a y study the interaction of the wool surface with adsorbants such as ionic detergents and dyes to help explain the effects of the p H and of other concentration variables in the wet processing of wool. With these applications in mind, a program of electroosmotic measurements on wool was started. I t was soon discovered t h a t in the interpreta' A laboratory of the Western Utilization Research and Development Division, Agricultural Research Service, U. S. Department.of Agriculture. 268
ELECTROOSMOSIS
OF
WET
WOOL
269
tion of the experiments one should allow for ionic conduction through the wool fibers. The next section is devoted to this complication. ELECTROOSMOSIS THROUGH A PLUG OF CONDUCTING FIBERS
We consider a model plug of parallel fibers immersed in a salt solution. The fiber diameter and the distance between the fibers is large compared with the thickness of the electric double layer. We apply an external electric field E parallel with the fibers. The relevant electroosmotic velocity of the liquid inside the plug is (1) -
41r~/'
[1]
where/" is the average electrostatic potential in the surface of shear of the fibers with respect to the solution far from the fiber surface, e is the dielectric constant, and ~ is the viscosity of the solution. When the cross section of the plug is A and that of the fibers is A0, we have for the total electroosmotic flow (volume per second) through the plug V = v(A
-
Ao).
[2]
The total electric current through the plug is i = (A - Ao)KE + Ao~sE,
[3]
K and Ks are the specific conductance of the solution and of the fibers, respectively. Eliminating v and E from Eq. [1] by means of Eqs. [2] and [3], the result for ~ is parallel
V4~r~Kf~
[4]
with f~ = 1 +
KsA0 K(A A0)" -
-
The factor fp corrects for fiber conductance. The correction is similar to the one for surface conductance (1). The present expression is exact for the assumed geometry of the plug. We now turn to the case of an external electric field which is perpendicular to the assembly of parallel fibers. The exact description of electroosmosis is difficult. Therefore, we use the approximate model of the plug introduced in the previous paper (2(a)). A cross section is shown in Fig. 1. It is assumed that the electroosmotic flow is uniform through the slits between successive layers of fibers and parallel to the applied field. Let the liquid between
270
STIGTER
~E
FIG. 1. Cross section of schematic model for wool plug in transverse electric field.
o
1
2
A
;3
4
A-A o
FIG. 2. Corrections for fiber conductance of the electroosmosis through fibrous
plugs for three values of the relative fiber conductance K//~. Broken curves: applied field parallel with fibers, fp from Eq. [4]. Solid curves: applied field transverse to fibers, ft from Eq. [5]. the fibers in each single layer be at rest. The liquid velocity in the slits is given by Eq. [1]. An elementary derivation yields _ V4~wft
ie
transverse
[5]
with Ky/K
ft = 1 q-
1 - v'G/A + (v%/a + v'-d/Ao - 2) In Fig. 2 we have plotted the correction factors of Eqs. [4] and [5] for some values of KffK.Even for relatively small values of the fiber conductance the correction factors f may be appreciably different from unity. We assume that a plug of randomly oriented fibers is equivalent to one in which one third of the fibers are parallel to the applied field and two thirds are perpendicular. The correction for fiber conductance in the expression for ~ is the relevant average of the correction factors in Eqs. [4] and [5]. dr = (fp -~ 2dr)~3
random.
[61
ELECTROOSMOSIS OF WET WOOL ON ELECTROOSMOTIC
WATER TRANSPORT [FIBERS
THROUGH
271 WOOL
In the previous section the total current through the plug was corrected for the fraction of the current shunted through the wool fibers. Now, with ionic conduction through the fibers, it is consistent to assume that the ions drag water along in their motion through the fibers. Such transport constitutes a correction to the electroosmotic flow V between the fibers. The transport in a representative case (see Fig. 5) was found to be V i i = 0.5 to 0.7 ml./Coul, or V i i = 2600 to 3700 mol/F = 2600 to 3700 water molecules per monovalent ion. The water transport through the fibers is difficult to evaluate exactly, and a definitive treatment is not presented. However, we advance three separate arguments suggesting that the correction for transport of water through the fibers is negligibly small under the conditions of our experiments. Transport through a Continuous Medium with Uniform Permeability As an approximate model for transport through wool fibers, we consider liquid motion through a permeable medium, represented by an assembly of identical, regularly spaced, stationary beads suspended in a viscous liquid. Let the friction factor of each bead be f and the number of beads per unit volmne be ~. In general, the boundary conditions for liquid motion past such an array of beads are hard to define and, consequently, exact solutions to the NavierStokes equation of viscous flow are intractable. However, if we consider the limit ~-~ ~ ;
f--~0
the finite product ,f suffices to characterize the medium. When v is the local liquid velocity, the term --,fv is a continuous volume force exerted by the beads on the liquid. This force enters into the flow equations, which now read v curl curl v ~- grad p -~ ,fv -- 0; div v = 0.
[7]
This set of equations has been used extensively to describe liquid motion inside coiled polymer molecules (3-6). It follows from Eq. [7] that the Darcy permeability constant of the medium is K = ~?/,f.
[81
Using standard mathematical techniques (4, 7), the force on a solid
272
S~mTEa
sphere with radius a moving through the medium with velocity v0 is found ¢o be
(
o
F = 6,.~avo I + ~ - ~ + ~
.
[9]
The volume of liquid transported by the sphere, W, is obtained by integrating the liquid velocity over the entire volume of the medium.
W=5
~ra3 3 +
--. a
[10]
In the limit K --~ ~ Eq. [9] yields the Stokes friction factor for a solid sphere moving through a viscous liquid. Furthermore, for K --~ ~ Eq. [10] shows that W -* ~. As has been discussed elsewhere (8), this limiting result is not directly applicable because Eq. [7] neglects inertia terms. Following Eq. [9], one may express the ratio of the mobility of a sphere in the permeable medium, us, to the mobility in pure liquid, u, as a function of a/x/K only us__ (1 + a u ~
a 2~-1 + 9-K] "
[11]
Also, Eq. [10] gives the ratio W/(4/3)~ra~ as a function of a/~/K only. Thus, one may plot W/(4/3)lra~ versus uffu as shown in Fig. 3. Experimental data on ion mobilities in wool may now be used to estimate the water transport through the wool. It was found (2(a)) that uffu ranges from 0.0031 to 0.0099. Thus we read from Fig. 3 that W is of the order 0.1 X (4/3)~ra3. This means that W is less than a few water molecules per (hydrated) ion transported through the wool. This result is to be compared with the previous estimates of V / i = 2600 to 3700 water molecules per ion transported between the fibers. The electric current between the fibers is of the same magnitude as the current through the fibers or larger. Hence, the electroosmotic flow through the fibers may be neglected.
Transport through Ion Exchange Resins The model used above is only approximate for wool. For example, it does not consider the fact that wool is a mixed ion exchanger with a nonhomogeneous distribution of the ion exchange sites (2(a)). It is likely that this feature of the wool structure depresses uffu more than it does W. So the theoretical estimate of W given above might well be low as is supported by data on water transport through synthetic membranes (9-11). It is found experimentally that W depends on the type of membrane, the water content of the membrane, and the type of ion. For wool fibers with about
ELECTROOSMOSIS OF W E T WOOL
273
100
W ' ' ' ,~-3/Ta I0
0.001
0.01
u_..A_f
0.1
U
FIG. 3. Volume of solvent W carried along by sphere wi~h radius a and moving through medium of uniform permeability with relative mobility uf/u. 33 % water at 100 % R.H., it seems reasonable to assume a transport of fewer than 20 water molecules per ion. So, in general, the resulting flow through the wool fibers is small compared with the electroosmotic flow between the fibers.
Invariance of the I E P For small values of ~, the water transport through the fibers becomes relatively more important; consequently the question arises of how to interpret the isoelectric pH (IEP). In general, the IEP of the fiber surface may differ from that of the bulk of the fiber. Hence, from the condition that the total flow through a plug be zero, one determines an average IEP. In this average the IEP of the fiber surface and of the fiber bulk are weighted according to the flows between and through the fibers, respectively. Experimentally, the ratio of these flows can be regulated by changing the cross-sectionM area A of the plug. Hence, the significance of flow through the wool fibers can be tested by measuring the dependence of the (experimental) IEP on A. In our experiments no such dependence was found. We conclude, therefore, that water transport through the fibers was not significant. EXPERIMENTAL The electroosmosis cell and the wool plugs were described in the foregoing paper (2(a)). Measurements were made on properly equilibrated plugs. For small electroosmotic flows, near the IEP, a capillary was used (see reference 2(b). Otherwise, the capillary was closed off and the flow through the plug and a stopcock was measured under a small pressure head with the d.c. field in either direction. It was established that within the experi-
274
STmTEn
mental error, the electroosmotic flow was independent of the pressure head and proportional to the electric current. Readings were taken at different permeabilities of the plug. Also, the electric resistance of the plug was measured before and after d.c. was passed. Only in solutions of p i t > 6 did passage of d.c. change the plug resistance more than a few per cent. This effect is probably related to the increased ionic conductance through the fibers in this p H range (2). As a result, the determinations of V i i at high p H are subject to additional errors. RESULTS AND Discussion
Electroosmosis was measured for wool fabric as a function of p H at two different values of the ionic strength. The results are shown in Fig. 4. I t appears that the isoelectric pH does not depend significantly on the ionic strength. Moreover, the data for the nitric acid and the acetic acid buffer overlap satisfactorily. This suggests that the wool fiber surface does not specifically adsorb the small ions presently used (other than H+), at least not to any significant extent. The F-potentials, evaluated with the simple theory, fp = f t = 1 in Eqs. [4] and [5], show a peculiar minimum in the intermediate p H range. I t was the observation of this anomaly which led to the investigation of fiber conductance described in the preceding paper (2(a)). In order to test the amended electroosmosis theory, measurements were carried out as a function of cross section for a fabric plug at p H = 8.85 and ionic strength 0.002. Under such conditions the correction for fiber conductance is expected to be appreciable. The results are presented in Fig. 5. On the basis of Eqs. [4], [5], and [6], a fairly good approximation in the present range of experimental values is i V
_
+10 ~ 0
~mV -20
.....
4~v~fi ~ a
random
.c
b
' " "'o,.,,~.
,
~
pH
"" ..................... ....... A ............................ ~o %
-30
[12]
%
......• ,o ......
-40
FIG. 4. Electroosmotic ~--potential of wool fabric plug versus pH calculated without corrections for fiber conductance. Circles: ionic strength 0.002. Triangles: ionic strength 0.01. One half of the total ionic strength derives from NaNOa ; the rest from buffer as follows: a: HNOa/NaNO3 ; b: HAc/NaAc; c: NH4OtI/NIt4NO3.
ELECTROOSMOSIS OF WET WOOL
275
o 1.$
/
/
j~
/ 1.6
~.s o ~.,,/o
/"
o o
,,s o
0/4. ¢-~ 1,4
/
/
sS
o
o
1..2
A_~o A-Ao
FI~. 5. Electroosmosis t h r o u g h wool fabric as a f u n c t i o n of cross section of plug.
Open points: experiments a t p H = 8.85 a n d ionic s t r e n g t h 0.002. Broken curve: from Eq. [12] w i t h K]/K = 0.093 and i n t e r c e p t adjusted.
with fr = 1 +
2KfA0 K(A A0) " -
-
According to this approximate expression i / V varies linearly with Ao/(A -- Ao). The experimental data in Fig. 5 indeed show a definite trend. This trend agrees well with the slope of the theoretical line which is based on Eq. [12] with Kff~ -- 0.093 as reported previously (2(a)). It is unfortunate that the scatter of the experimental points is so large that the data cannot serve to adequately test any quantitative aspect of the present theory. We have applied Eqs. [4] and [12] to evaluate the ~-potential as a function of pH for yarn and fabric plugs, respectively. The results in Figs. 6 and 7 show that the corrections for fiber conductance are substantial. At high pH settling of the plugs affects the measurement of fiber conductance (2(a)). Therefore, the relevant corrections to ~" are uncertain, as indicated by the parentheses in Figs. 6 and 7. In addition, the theory oversimplifies the fiber orientation and disregards the anisotropy of the fiber conductance. Thus we must conclude that at present the anomalous eleetroosmosis of wool at high pH is not completely resolved, but that fiber conductance probably causes the apparent anomaly. We now discuss the IEP of wool. Taking amino acid compositions and pK values from the literature (12, 13), we find that a and 7 keratose have an IEP at 4.5 and 5.1, respectively, while from the overall composition
STIGTER
276 +10
pH
0
~;mVz ° ~v...
.... o
-%0 ..Oo • ..,
. .... ...,, .,,, , ..........
,,,,, ..........
• ...:,,,,:,.,,,~..,,.o. ................. :
-20
c.~
c.~
-30
FIG. 6. Electroosmotic i'-potential as a function of pH for wool yarn plug. Ionic strength 0.002, buffers as in Fig. 4. Open points: from Eq. [4] with K//~ = O. Filled points: from Eq. [4] with K//Kas reported earlier (2(a)). +10 ~'::~%
0
----~-%.
~.
,
pH
~
,
-10
~mV -~'0
~N
~,,.::,.~
,,,,,,-".o"
(,
-30
FIG. 7. Electroosmotic i--potential as a function of pH for wool fabric plug. Ionic strength 0.002, buffers as in Fig. 4. Open points: from Eq. [12] with ~I/~ = O. Filled points: from Eq. [12] with ~y/Kas reported earlier (2(a)). of Merino wool, one calculates 4.8 as the I E P . On the other hand, from eleetroosmosis of several samples of natural wool (Figs. 4, 6, and 7), the I E P of the fiber surface was found to vary between 2.5 and 3.5. A trend among the data suggests t h a t mechanical processing of wool tends to increase the I E P of the fiber surface. This might link the change of I E P with damage to the fiber surface. Increased surface damage might expose more of the interior of the fiber with higher I E P and thus increase the average I E P of the fiber surface. Similarly, surface damage might account partly for the different potential levels to which ~ decreases for y a r n and fabric plugs; compare Figs. 6 and 7. These tentative suggestions require further study. Another puzzling feature is the low p H part of the electroosmotie curve for wool yarn in Fig. 6. Judging from the shape of the corrected curve, the acid groups at the fiber surface have an average p K around 3.3 or lower. Even if allowance is made for interactions in the fiber surface, this low p K is difficult to ascribe solely to the carboxylie acid groups known to be present in wool, glutamic, and aspartic acid with p K 4.6. Ruptured and oxidized sulfur-sulfur bonds in the fiber surface suggest themselves as a possible origin of strongly acidic sites. Further study is needed at this point. We now discuss experiments on chemically modified wool. In this laboratory, a technique has been developed (14) for forming polyamides on the
ELECTROOSMOSIS OF WET WOOL
277
+10
0
.__...p
3
°~ 4
~5.
~mV -10
-20
FIG. 8. Electroosmotic ~-potential of wool fabric at ionic strength 0.002, uncorrected for fiber conduction. Buffers as in Fig. 4. Curve a: fabric with 2 weight % polyamide. Curve b: treated with sebacoyl chloride. Curve c: treated with 1-6-hexamethylene diamine. Curve d: natural wool.
surface of wool fibers by interracial polymerization. Wool fabric is padded consecutively through an aqueous solution of a diamine and through a water-immiscible solution of a diacid chloride. The polymer film formed at the fiber surface makes the fabric shrink-resistant through many washing cycles. One is curious to know whether or not the polyamide film is grafted onto the wool fiber surface. In order to answer this question, samples of the same wool fabric were subjected to (a) the complete technical treatment, or (b) omitting the dinmine, (c) omitting the diacid chloride, or (d) omitting both monomers. After the treatment, the fabrics were washed to remove excess chemicals. Electroosmotic results for the four samples are shown in Fig. 8. Curve d refers to natural wool, the blank. After treatment with sebacoyl chloride (curve b), the fiber surface had become more acidic. Evidently, the sebacoyl chloride reacted with amine groups at the fiber surface and, after hydrolysis of the remaining acid chloride group, surface amine groups were converted into surface carboxylie acid groups. The chance of one sebacoyl chloride molecule reacting with two surface amine groups is very small, of course. Treatment of wool with 1-6-hexamethylene diamine produced the reverse effect. In this case the diamine converted a surface carboxylic acid into a surface amine group, thus increasing the average IEP of the fiber surface as shown by curve c. It is not known whether the diamine is held at the fiber surface by an amide bond or by a salt linkage. ~[ore elaborate experiments are required to settle this point. In summary, the present results provide evidence that some polymer chains originate at amines, and perhaps also at carboxylic acids, located at the fiber surface. Thus, we may regard the polyamide as a true graft polymer. Finally, we discuss electroosmosis of polymer treated fabric. Electronmicroscopy (15) has shown that 2 % polyamide is sufficient to substantially cover the wool fibers. Therefore, curve a in Fig. 8 refers to polyamide
278
STIGTE'R
surface rather than to wool surface. It is interesting that the polyamide surface has an intermediate, and not an extreme, IEP. It shows that in this sample carboxylic acids and amines both occur as polymer end groups, and in comparable amounts. I:~EFERENCES 1. See, e.g., 0VERSEEK, J. TH. G., in H. R. Kruyt, ed., "Colloid Science," Vol. 1, Chapter 5. Elsevier, New York, 1952. 2(a). STIGTER,D., J. Colloid Sci., 19, 252 (1964); (b) ibid., Fig. 1. 3. BRINKMAN,H. C., Proe. Koninkl. Ned. Akad. Wetenschap. 50,618, 821 (1947). 4. DEBYE, P., AND BUECIIE, A. M., J. Chem. Phys. 16,573 (1948). 5. HERMANS,J. J., ANDFUJITA, H., Koninl~l. Ned. Akad. Wetenschap. Proc. B58, 182 (1955). 6. 0¥ERBEEK, J. TH. G., AND STIGTER,D., Rec. tray. chim. 75, 543 (1956). 7. BUECHE, A. M., Thesis, Cornell University, Ithaca, New York. 8. STIGTER,D., Rec. tray. chim. 73, 771 (1954). 9. MCKELVEY, J. G., SPIEGLER,K. S., AND WYLLIE, M. R. J., J. Electrochem. Soc. 104, 387 (1957). 10. SPIEGLER,K. S., Trans. Faraday Soc. 54, 1408 (1958). 11. CARR, C. W., McCLINTOCK,R., AND SOLLNER,K., J. Electrochem. Soc. 109, 251 (1962). 12. LUNDGREN,I~. P., ANDWARD,W. i . , "Ultrastructure of Protein Fibers," pp. 49, 53. Academic Press, New York, 1963. 13. TANFOnD, C., "Physical Chemistry of Macromolecules," p. 556. Wiley, New York, 1961. 14. WmTFIELD, R. E., MILLER, L. A., AND WASLEY, W. L., Textile Research J. 31, 704 (1961). 15. Unpublished results by Dr. 1%. S. Thomas of this laboratory.