Table II. Recovery of Ammonium Hydrogen Sulfate in Synthetic Acid Mixture
KH,HSO,, Grams
Added 1 0010 1.0010 1.0010
XHaHSOd, Gram Found 0.9961 0.9982 0 yotiti
XHaHSOd,
% Recovered 99 6 99.8 99 tj
formed ior each equivalent of aminonium salt present. -15 the proposed method depends on measui ement of the liberated acid, it was necessary first to neutralize the free acids already present in the sample. Seutralization of the sample to a slightly acid pH was also necessary to prevent possible loss of ammonia resulting from the presence of the alkali. The equivalence point for the acid niivture occurred a t pH 6.0, vdiereas after addition of formaldehyde it was a t p H S.4. When the acid was neutralized to a p H of 6.0 before addition
of the formaldehyde (pH 6.0) and then titrated to pH 8.4 after the formaldehyde addition, calculated recovery values were obtained for the ammonium salts as shoivn in Tables I and 11. Only a slight excess of formaldehyde vias necessary to drive the reaction to completion. As the reaction mas almost instantaneous, the approximate amount of formaldehyde necessary for samples containing varying amounts of ammonium salts could be found by adding small increments of the formaldehyde solution and then titrating the liberated acids. This procedure was continued until no more acid was liberated including completion of the reaction. Although no kinetic studies were undertaken and no final proof was developed for the course of the reaction, the following equations for the reactions involved with ammonium sulfate and ammonium acid sulfate (neutralized with alkali) appear feasible: (IjH4)zSOi f 4HCHO + (CHaSH2)2.HzSOi 2HCOOH (4)
+
+
2NH4SaSO4 4HCHO -+ ( C H I S H ~ ) ~ . H ~ ~Ka2S04 O,
+
+
SHCOOH (5)
The method is simple, convenient, and suitable for use in the control laboratory. LITERATURE CITED
(1) Baur, E., Reutschi, W.,Helv. C h i m Acta 24, 754 11941). ( 2 ) Boyd, 11.L., Winkler, C. A., Can. J . Research 2 5 , 387 (1947). (3) Dering, H. O., Kelly, bl. D. (to
Superfine Chemicals, Ltd.), Brit. Patent 396,467 (-4ug. 10: 1933). (4) Grissom, J. T., J . Ind. Eng. Chem. 12, l i 2 (1920). (5) Kolthoff, I. M., Pharna. Weekblad 58, 1463 (1921). 16) Knudsen, P., Ber. 47, 2694 (1914). (7) Marcali, K., Riemsn, W.,ANAL. CHEM.18, 709 11946). ( 8 ) Plochl, J., Ber. 21, 2117 (1888). (9) Polley, J. R., JTinkler, C. 4.,Kcholls, R. V. V., Can. J . Research 25B, 525 (1947). (10) Rusconi, A., Chimica(Milan) 5, 107 (1950). (11) Schieferwerke Ausdauer A-G, Brit. Patent 286,730 (March 10, 192i). for review December 15, 1956. RECEIVED Accepted April 11, 1957.
Theory of Gradient Elution through Ion Exchangers HELMUT SCHWAB’, WILLIAM RIEMAN 111, and PHILIP A. VAUGHAN Ralph
G. Wright
Chemical laboratory, Rufgers University, New Brunswick, N.
b Equations were developed to predict the position of the peak in the graph of a gradient elution. Elutions of chloride, bromide, and oxalate ions were performed with sodium nitrate as eluent, first with nongradient technique to evaluate the necessary parameters, then with gradient technique to test the equations. Agreement within the experimental error of locating the peak was obtained with both linear and exponential variation of the eluent concentration. The principles should be applicable to elutions with varying pH or varying concentration of a complexing agent.
A
gradient elution has been the subject of numerous recent investigations, both practical (1, 4, 7 , 9, 10) and theoretical (5, 6), no satisfactory equations have been available for calculating where the position of the peak will appear. This paper presents the derivation of such equations and experimental data to attest their validity. LTHOUGH
Present address, National Cash Register Co., Dayton, Ohio.
J.
The equations n ere derived by means of the plate theory of exchange chromatography which has been used successfully to calculate the minimum column height required for a desired separation (Z), to calculate the positions of the peaks in elutions with stepwise changes in eluent concentration ( 8 ) , to elucidate the chromatographic behavior of condensed phosphates ( 2 ) and glycols ( I d ) , and to determine the best conditions for the separation of condensed phosphates (8, 11) and glycols (IS). Gradient Devices and Equations. T h e device with a constant-volume mixing chamber (3, 5 ) , sketched in Figure 1, delivers eluent whose concentration follows the equation [El] = M2- ( M 2-
Jfl)e-d/r7R
(1) where [El] denotes the concentration of eluent when C$ ml. have flowed from the mixing chamber, MI the initial concentration of eluent in the mixing chamber, TIR the volume of the mixing chamber, and M z the concentration of eluent in the reservoir. If MI is zero, as in all the work reported in this paper, Equation 1 becomes
[El] = J f 2 ( 1 -
e-$/VR)
(2)
Gradients that follow Equation 2 are hereinafter called exponential gradients. The simple device of Bock and Ling (3) with vessels of equal cross sections, Figure 2,B, is designed to deliver eluent according to the equation (‘If, - Jfl) (1 -
or
if M i is zero. LTnfortunately,this device does not deliver exactly linear gradients, unless the liquids in the two chambers have about the same density. Because this requirement was not fulfilled in the work described here, the device of Bock and Ling was not used. The device sketched in Figure 2 4 , delivers eluent whose concentration follo~vs( 1 ) the equation d
[El] = .Ila - (Ma - AI2) ---e-4/”x VR (;$fa- 11fl)e-4/vR VOL. 2 9 , NO. 9, SEPTEMBER 1957
1357
provided that both mixing chambers have the same volume, VB. If ill1 is zero and if M s = 2Mz, this equation becomes [El] = .$f,
2 - 2d -e-#/”R VR
(
- e-d/T‘R) (4)
If C$ V E / 2 ,the value of [El] by Equation 4 checks the value by Equation 3 within 3%. This restriction was observed, and gradients produced by the apparatus of Figure 2,A, are referred to as linear gradients. EXPERIMENTAL
Apparatus and Reagents, The automatic fraction collector has been described (2). The siphon pipet (12) n a s modified (16) by attaching a side arm below the bulb of the pipet (Figure 3, Ace Glass, Inc., Vineland, N. J.). The side arm led t o a U-tube containing some mercury. As the pipet was filled, the mercury was displaced toward the open end of the U-tube, coming in contact with two platinum wires and thus activating the relay that controls the fraction collector. Thus the balance (11) and mercury switch vere eliminated. The columns had a cross-sectional area of 3.8 sq. em. and were provided with a fritted-glass disk. They were filled to appropriate heights with resin AG l-XlO, 150 to 200 mesh, control number 1390B72, obtained from BioRad Laboratories, Berkeley, Calif. This resin is a purified form of Dowex 1-XlO (Dow Chemical Co.). The total capacities of the columns, WQ,and the interstitial volumes, V , were determined as previously described (12). The chemicals were of reagent grade. Nongradient Elutions. Elutions with eluents of sodium nitrate of constant concentration were performed by equilibrating the column with the eluent to be used, draining almost to the level of the resin, adding the sample dissolved in about 2 ml. of eluent, draining again almost t o the level of the resin, rinsing the upper part of the tube with a few milliliters of eluent, draining again almost to the resin level, connecting the reservoir to the column, and controlling the flow rate to 0.7 em. per minute (2.7 ml. per minute) by a stopcock a t the bottom of the column. Fractions, usually 6 ml., were collected with the automatic fraction collector and analyzed separately. Halides were determined by titration with silver nitrate and oxalate by titration with permanganate. Graphs of concentration of sample ion (halide or oxalate) us. U , the volume of efEIuent, were plotted. Values of U*, the volumes of effluent a t the peaks, were read from the graphs. The measurement of U was started a t the beginning of the addition of the sample. Nongradient elutions of sodium chloride, bromide, iodide, and oxalate were performed individually. The quantity of sample and concentration of eluent were varied from elution to elution. 1358
ANALYTICAL CHEMISTRY
Gradient Elutions. Gradient elutions of sodium chloride, bromide, and oxalate were performed with both the exponential and linear type of gradient. The column was washed with water to remove the eluent from the previous elution before starting a gradient elution. Except for the provision to vary the concentration of eluent during the course of the elution, the procedure was the same as for the nongradient elutions.
nongradient elutions of small amounts of sample ion
U*=W+V
(5)
where C, the distribution ratio, is the quantity of sample ion (halide or oxalate) in the resin of any plate divided by the quantity of this ion in the interstitial solution of the same plate. Also ,
c=--WQE V [ElIz
DERIVATION OF THE EQUATIONS
General Equation for U* in Gradient Elution at Constant pH. In
where W is the weight of resin in the column, Q the exchange capacity in millequivalents of 1 gram of resin, and z the valence of the sample ion (sign always considered to be positive). E is the classical equilibrium constant of the exchange reaction X”*
+ zREl e R,X + zEl’ E = [ R X I [El*]* [REl]’[X”*]
The square brackets around ions in the aqueous phase denote molarities, and those around resin constituents denote mole fractions. From Equations 5 and 6 (7)
If V’ denotes the interstitial volume in the column above the plate where the maximum of the sample ion is located, then V’ = V when U = U*. If C#I denotes the volume that has passed through this maximum concentration of viniple ion, U - V’ = 4; C$* = C#I 11hen U = C.* Then
u* - v = b*
U
(8)
From Equations 7 and 8
Figure 1. Device with constant-volume mixing chamber for gradient elution
I n gradient elution when an increment of eluent solution, d U , moves through any horizontal plane of the
B
Figure 2.
Devices for gradient elution
column a smaller increment, d+, passes through the peak concentration of sample ion because this peak is moved down the column through dW' grams of resin. Therefore
molar with a weak base-e.g., sodium acetate-MIA molar with its conjugate acid, and [El] molar with the major constituent of the eluent. Let the solution in the upper reservoir be zero molar with the weak base, M S Amolar with the conjugate acid, and [El] molar with the major constituent. There are many other arrangements for varying the pH. By application of Equations 1 and 2, the concentration of the weak base, B, and its conjugate acid, A, in the solution in the mixing chamber after the efflux of + ml. are, respectively
The concentration of eluent a t the peak of the sample ion is a function of +, given by Equation 2 or 3.
[&A] = Al12A -
From Equations 9 and 10
=
m
Upon integrating this equation between the limits = 0 to C$ = +* and W' = 0 to W' = W , the value of C$* is obtained. The value of U* is obtained from Equation 8. Details of the integration are given for only one case, that of the elution of a halide (z = 1) with an exponential gradient. Elution of Univalent Ion with Exponential Gradient. By substitution of Equation 2 in Equation 11
[ B ]= MiB e - + / v R
Therefore, the concentration of hydrogen ion in the mixing chamber is
+
E is placed in front of the integral sign because the experimental work on nongradient elutions of chloride, bromide, and oxalate indicated that it was constant. Equations for the gradient elution of iodide ion, where E varied with changing [El], were not derived, because the integration becomes very unwieldy if the variable E is expressed as a function of + and put into the integral on the left side of the equation.
JllA) ? - @ i v R
and
QEdW' dQ
-
[H+]= K , MZA- ( i i f 2 A - & f , * ) e - + / 1 . ' ~ .&flBe- 4 / V R
Figure 3. Automatic fraction collector A . Open side-arm tube; insert for two platinum electrodes B. Mercury pool C. Ball and socket joint, 12/5 D. Slot, ground open E . Glass tubing, 4 to 5 mm. ( i d . ) F . Glass tubing, 1 t o 2 mm. (Ld.) G. Glass tubing, 5 mm. (i.d.) H . Variable chamber size, depending upon pipet volume
where K , is the ionization constant of the weak acid. This gradient eluent can be used with an anion exchanger to elute a sample ion which is the anion of a weak monoprotic acid of ionization constant KI. For such an anion, C (6)is
Exponential gradient, tervalent ion. Q*
- 3 V ~ (l e-+*/VR)
VR (1 3
+
e-34*/vR)
=
W QE -
M2'
Linear gradient, univalent ion.
Linear gradient, bivalent ion. Although Equation 12 is implicit with respect to +*, it can be readily solved graphically. Other Specific Equations for Gradient Elution at Constant pH. B y substituting other values for [f(+)]" in Equation 11 and proceeding as above, the following equations are obtained: Exponential gradient, bivalent ion. d* -
vR(1
- e-+*/VR)
x
Linear gradient, tervalent ion.
Equation for a Gradient Change in pH. I n some gradient elutions the concentration of the major constituent of the eluent--e.g.,sodium nitrateis constant while the pH changes. More specifically, consider a n arrangement such as Figure 1 in which the solution in the mixing chamber is MiB
RESULTS AND DISCUSSION
Nongradient Elutions. Table I shows the effect of the quantity of sample on the values of U.* To eliminate the effect of sample size, all subsequent elutions %-ere done with 0.2 meq. of sample. VOL. 29, NO. 9, SEPTEMBER 1957
1359
Table 1.
Effect of Sample Size on in Nongradient Elutions"
U*
Sample, P, hll. Meq. Chlorideb Bromidec Iodidec 2.6 68 134 192 1.3 62 134 198 0.8 60 ... ... 0.6 .. 136 228 0.5 58 136 ... 0.4 55 ... 0 3 .. 136 235 0.2 50 135 244 TfrQ = 37.61 meq., V = 14 ml., column height = 6.6 cm. Eluent = 0.300M KaS03. c Eluent = 1.50M NaSOI.
Table I1 shows the effect of the concentration of the eluent on the classical equilibrium constant of the exchange reaction. Throughout the ranges of concentration studied for chloride and oxalate, the respective equilibrium constants are constant within the experimental error Gradient elutions of these ions are conveniently performed without applying values of [El] above the maxima of these respective ranges. Therefore Equations 12 and 14 can be applied to the gradient elutions of chloride, and Equations 13 and 15 to the gradient elutions of oxalate. Although bromide shoms a variation of E values a t large concentrations of the eluent, the equilibrium constant is constant within the experimental error a t concentrations of eluent below 0.6;M. Because this value of [El] is not ordinarily exceeded in gradient elutions of bromide, Equations 12 and 14 are applicable to bromide ion, On the other hand, the exchange constant of iodide varied over the entire range of [El] that i. useful in gradient elutions; the approximate constancy below 0.6-41is of very little value in gradient elutions of iodide because excessively large volumes of eluate must be collected before iodide is eluted by 0.6M sodium nitrate. Therefore Equations 12 and 14 cannot be successfully applied to iodide. Because E is a classical equilibrium constant, changes in its value n i t h changing concentration of eluent are due to variations in the activity coefficients of the various chemical species entering the equilibrium. The variations of these activity coefficients are such that they cancel each other and give a constant E for chloride, bromide, and oxalate (but not iodide) within the respective useful ranges of concentration. Good approximations to the Gaussian elution graph were obtained in all of the nongradient elutions except those of iodide which showed appreciable tailing. Gradient Elutions. The observed
1366
ANALYTICAL CHEMISTRY
values of U * in exponential gradient elutions are compared with the calculated values in Table 111. A similar comparison is made in Table IV for linear gradient elutions. For the 35 gradient elutions performed with chloride, bromide, and
Table
II.
Effect of Concentration of Eluent on E" in Nongradient Elutions
E
Concn. of
~~
Chlorideb
SaX03. -11
3.000 2.000 1.500 1.000
.
0,600
0.30 0.27 0 27
0.500 n 4on 0,300 0 200
n
28
0 ii
0.175 0 150
0.125 0.100 Mean Std. dev.
Bromideb
Iodideb
Oualatec
1 . 6gd
13.87 10.88 Y,28
. . . . . . .
8.17 7.IO
..
1 , 42d 1 .3gd 1 ,14d 1.074 1.00 1.03 1 03 0 99 0 99
.
. . ...
0,800
b
oxalate, the mean rxtio of calculated U* to observed I;*is 1.01, with a standard deviation of 0.022. This discrepancy is within the experimental error of locating CT" It is concluded, therefore, that the equations for gradient elution are reliable, provided that
6.46 6.64 G 85
... ...
0.20
.If*
Test of Elution Equations for Exponential Gradients'
Chloride*, U*, hfl. Obsd. Ca1cd.d
Bromide*, U * , 1211. Obsd. Ca1cd.d
n 7.5
4.00 5 00 6.00 7.00
c
d 6
64
60 55 54
67 61
57 54
114 101
05 93
LlfZ
0.75 1 .00
1.50
2.00 2.50
3.00 3.50
0
104
06 02
138
138
...
... ...
... ...
...
Test of Elution Equations for Linear Elutions"
Chloride*, 17*,M1. Obsd. Caldd . .
112 102
88 70
73 60
...
118 99 88
80 74
70
Bromideb, U * , h11. Obsd Calcd.d 173
137
...
209
152 137 127 118
152
iii
Oxalater, U * , hI1. Obsd. Calcd: 129 107 85
210
VR = 500. Same column as used for Table I. Same column as used for oxalate, Table 11. d By Equations 14 and 5. e By Equations 15 and 5. a
115
Oxalatec, U * , RI1. Obsd. Calcd.'
V R = 500. Same as in Table I. Coliimn same as used for oxalate in Table I1 By Equations 12 and 5. By Equations 13 and 5.
Table IV.
b
0 032 0 033 0 033 0.033 0.034 0.033 0 0007
Calculated by Equations 5 and 6. Same column as used for Table I. Column height = 6.7 cm., V = 13.4 ml., W Q = 37.02 meq Excluded from mean.
Table 111.
a
. . .
.. ... ... ...
1:oi. 0.020
0 010
...
127 118
57
...
132
111 88
60
...
E remains constant throughout the range of concentrations of eluent entering the column in the gradient elution. ACKNOWLEDGMENT
The authors express their gratitude to the Colgate-Palmolive Co. for financial assistance in this investigation. LITERATURE CITED
( 1 ) Alm, R. S., Williams, R. J. P., Tiselius, A., Acta Chem. Scand. 6, 826 (1952).
(2) Beukenkamp, J., Rieman, W., Lindenbaum. S.. ANAL. CHEM. 26. 505 (1954). ' (3) Bock, R. M., Ling, N. S., Zbid., 26, 1543 (1954). (4) Busch, H., Hurlbert. R. B.. Potter. V. R., J. Biol. Chem. 196, 717 (1952). (5) Drake, B., Arkiv. Kemi 8 , l (1955). (6) Freiling, E. G., J . Am. Chem. SOC. 77, 2067 (1955). (7) Gradde, T.' A.,' Beukenkamp, J,, ANAL.CHEM.28, 1497 (1956). (8) Lindenbaum, S., Peters, T. V., Rieman, W., Anal. Chim. Acta 11, 530 (1954).
Nervik, W. E., J . Phys. Chem. 59,690 (1955).
Palmer, J. K., Conn. Agr. Exptl. Sta., New Haven, Bull. 589, 1955. Peters, T. V., Rieman, W., Anal. Chim. Acta 14, 131 (1956).
Rieman, W., Lindenbaum, S., ANAL. CHEM.24, 1199 (1952). Sargent, R., Rieman, W., Anal. Chim. Acta 16, 144 (1957).
Sargent, R., Rieman, W., J . Phys. Chem. 60, 1370 (1956).
Schwab, H., doctor's thesis, Rutgers University, 1956. RECEIVED for review January 24, 1957. Accepted hlarch 4, 1957.
Determination of Melamine-FormaIde hyde Resins in Coatings M. H. SWANN and G. G. ESPOSITO Coating and Chemical laboratory, Aberdeen Proving Ground, Md.
b The insolubility of acid hydrolyzed melamine resins in dioxane provides a rapid gravimetric method for their determination in modified alkyds, epoxy and other coating resins.
A
resins used for baking finishes are frequently modified with 10 to 20% of a nitrogen resin such as urea- or For some melamine-formaldehyde. time, the extent of this modification was calculated from the value obtained by determining total nitrogen. An infrared spectrophotometric method ($), developed for determining relatire amounts of urea- and melamine-formaldehyde resins in alkyd blends, is rapid and applicable to mixtures of these two nitrogen resins, but has limited accuracy and is subject to interference from some other resins. Recently, urea resins (4) were determined from a calculation based on the measurement of ammonia evolved on high temperature saponification of the sample. The latter method appears to be applicable to coatings in general. The acid hydrolysis of the urea- and melamine-formaldehyde resins has been used by a number of investigators to measure the combined formaldehyde content of these resins. Hirt, King, and Schmitt ( 1 ) applied this hydrolysis to the determination of melamine resin content of certain wrapping papers, measuring the melamine by ultraviolet spectroscopy; this method is applicable to the analysis of the melamine-formaldehyde resin solutions b u t not to modified alkyds. I n recent investigations, the authors found that the products of acid hydrolysis of the urea and melamine LICYD
resins were insoluble in dioxane, which is a good solvent for coating resins in general. On this basis, a simple and
Table 1. Determination of Melamine in Melamine-Formaldehyde Solutions
Melamine - Present _ _ UV Total analy- nitrosis, gen, Resin Uformite hIhl-46 Undesignated Uformite 3.111-55 Melmac 243-3
Table
II.
7 0 %
19 19 17 20
hlelamine Found ~ (Acid Hydrolysis),
1 19 5 2 20 1 5 16 2 0 19 1
70
19 19 16 18
5 7 6 8
rapid method of analyzing modified alkyds for melamine-formaldehyde resin was developed. Urea resins, which may appear separately or in mixture with the melamine resins, also give quantitative yields, but a specific method for determining the urea resins (4) provides a means of correction, thus allowing analysis of mixtures for both resins. Polyamide and triazine resins interfere and the method for melamine is not specific, but it is considered useful for the rapid analysis of coating resina known to be modified with melamine, or which can be qualitatively identified. The procedure can also be applied t o the analysis of coatings known to be modified only with triazine or urea
Analysis of Some Modified Alkyds and Epoxy Resins
Melamine. 9% Present Found I
Coating Type Alkyd, medium oil length (linseed)
Alkyd, long oil length (soybean) .4lkyd, short oil length (coconut) Alkyd, medium oil length, with urea-formaldehyde blended in amounts equal to melamine content
3.72 7.04 4.06 6.71 6.19 3.91 7.84 4.99
I
"
3.72 7.17 4 16 6 71 6.20 3.82 7.64
Calculated as Melamine-Formaldehvde Resin., 41, Present Found I -
11.1 21.0 12.1 20.0
11.1 21.4 12.4 20.0
5.05
3.54 2.07 12.00 11.67
3 66a 2 22a Epon 1004, melamine-formaldehyde blend 1 1 71 35 8 34 9 Epon 1007, melamine-formaldehyde blend 11 64 34.8 34 7 a Corrected for urea-formaldehyde present by analysis via saponification method (4).
VOL. 2 9 , NO. 9, SEPTEMBER 1957
1361
