Oscillatory behavior during the oxygen oxidation of ascorbic acid

Oscillatory Behavior During the Oxygen Oxidation of Ascorbic Acid

JACK YOUNG, BORIS FRANZUS, and THOMAS T.-S. HUANG* Department of Chemistry, East Tennessee State University, Johnson Ci ty , Tennessee

37614

Abstract

The oscillatory phenomenon was observed in aqueous solution during the oxidation of ascorbic acid by oxygen. Even though the exact number and amplitude of the oscillations could not be exactly duplicated for each and every run, such factors as temperature, concentration of ascorbic acid, cupric ions, and pH affecting the oscillatory behavior were studied, and those regions where oscillations occurred were delineated. A mechanism consistent with the oscillatory behavior is proposed and discussed.

Introduction

In recent years there has been a great deal of interest in the reaction between ascorbic acid (AA) and oxygen in aqueous solutions [l-31. Many mechanisms have been proposed for this reaction, including the postulation of free-radical intermediates and copper(II1) ions [4]. The system is highly complex. There has been no consensus concerning a single reaction mechanism among the various literature reports. The oxidation is essentially catalytic, induced by micro amounts of transition metal ions. When these transition metal ions are complexed with a chelating agent such as ethylenediaminetetraacetate (EDTA), oxidation is inhibited [2,5,6]. Many transition metal ions have been used as catalysts. However, copper(I1) ions appear to be particularly effective. The kinetic order with respect to cupric ions, which has been reported, varied dramatically from 0.5 [7] to 0.9 [8] to 1.0 [9,10]. Oxidation rates are also affected drastically by a variation in pH. The kinetic order with respect to hydrogen ion concentration varied from 2 [8] to 1 121 to 0.5 [7]. Some of the experimental results were so complicated that simple kinetic expressions would not suffice to rationalize the data [ll]. The kinetic order with respect to oxygen concentration was also diverse and has been reported to be 0.4 [12], 0.5 [2,5], and 1.0 [4,9]. A redeeming feature in most of the studies is the fact that the reaction is first order with respect to AA concentration [7-lo]. How- ever, the situation may be further complicated by the fact that other oxi-

* To whom all correspondence should be addressed.

International Journal of Chemical Kinetics, Vol. 14,749-759 (1982) 0 1982 John Wiley & Sons, Inc. CCC 0538-8066/82/070749-11$02.10

750 YOUNG, FRANZUS, AND HUANG

dizing agents such as halogens and peroxides may provide alternative pathways for the oxidation of AA. We can summarize previous kinetic studies on the oxidation of ascorbic acid as follows:

(1) Rate -[AA], where AA is ascorbic acid concentration. (2) Rate -[02] n. Usually n = 1; in our own kinetic investigation n =

1. However, there have been some instances in which n z 1. (3) Rate -[H+] m , where m has not been clearly determined. (4) Rate --[metal ionlj. Again j has not been determined.at all con-

centrations, and the metal ion is now assumed to be C U + ~ . During one of our exploratory runs in our investigation of the oxidation

of AA by molecular oxygen we noted the rather remarkable phenomenon of AA concentration increasing rather than decreasing. Since we followed AA concentration by ultraviolet spectroscopy (A,,, = 265 nm), what we observed was an increase in absorption at 265 nm rather than the usual decrease in absorption due to the oxidation of the substrate. This was the first observation of an oscillatory oxidation (and reduction) of AA.

The oscillatory behavior of other oxidation reactions have been observed and discussed for many systems [13-151. However, as far as we know there has never been an observation or report concerning the oscillatory oxidation of AA by molecular oxygen. Herbert et al. [6] reported in 1933 that a t the end of the oxidation of AA there still remained 5% of AA. No explanation was given for this observation. For any oscillation to occur there must be one or more steps in a sequence of steps regenerating AA. In our laboratories we have found that oxidized ascorbic acid OXAA (this has also been termed dehydroascorbic acid) at pH - 7 undergoes an oxidation-reduction reaction to form AA (reduction) plus carbon dioxide and oxalic acid (oxidation products).l Although this oxidation-reduction will be the subject of another paper, it is very important to involve this regeneration step in the oscillatory behavior for the oxidation-reduction of AA.

This paper describes certain limits of temperature, pH, C U + ~ concentration, and AA concentration, all at essentially constant 0 2 concentration, which will give rise to oscillatory behavior. A simple mechanistic model is proposed, and its implications are discussed.

Experimental

The observation of oscillatory behavior (under constant temperature) was performed using a Cary, Varian 14 CM ultraviolet spectrophotometer equipped with a Lauda-Brinkman K-2/R thermostated circulator. Ad- justment and maintenance of pH were accomplished with the use of a Fisher

Unpublished work in our laboratories has shown that a t a pH of about 7, dehydroascorbic acid [lS] (probably OXAA) undergoes a rapid and probably irreversible lactone ring opening followed by an oxidation-reduction reaction regenerating AA with the concomitant formation of oxalic acid and carbon dioxide.

OXYGEN OXIDATION OF ASCORBIC ACID 751

hbmbance 0. O.!:

0.2

Accument model 420 pH meter. AA (m.p. 190-192°C) was purchased from Matheson, Coleman and Bell, methanol (spectrophotometric quality) from Allied Chemical, oxygen (99.99%) and nitrogen (99.998%) from Air Prod- ucts, and all other chemicals were reagent grade obtained from Fisher Scientific Company.

All solutions (except the AA concentrate) were saturated with oxygen. This kept the 0 2 concentration essentially constant (1.26 X M in 0 2 )

[ 11 throughout each run, since 0 2 was on the order of 10-1000 times the concentration of the other reagents. All pH were kept constant by using a 1000-fold excess of buffer over that of the reagents.

Typically all solutions were placed in a constant-temperature bath (*O.l"C), which was the same circulator bath that was connected to the ultraviolet spectrophotometer. The cupric sulfate solution was prepared in a Na2HP04-NaH2P04 buffer. Fresh standardized AA solutions (0.1M) were prepared every 3 days. The buffered ( C U + ~ ) solution was added to a 1-cm quartz cell equipped with a Teflon lid. A precision syringe was then used to inject the proper amount of AA into the cell. Finally the cell was shaken vigorously to achieve homogeneity, and care was taken to exclude any additional air from the cell. Any air bubble in the cell seriously affected duplication of the results and tended to reduce any predilection toward oscillation. The oscillatory behavior was followed at 265 nm since A,,, for AA, at least in the pH range of 5.5-8.5, was 265 nm. Although the results observed could not be precisely duplicated for every run in terms of oscillation, amplitude, and frequency of oscillation, nevertheless duplication of oscillation was essentially observed for every run.

k 1

Results

The oscillatory behavior was observed by following the concentration of AA (or some complex of AA) in the ultraviolet at 265 nm. An oscillatory run is shown in Figure 1. The overall absorption is generally a decreasing


function with respect to time. We were unable to reproduce exactly the width and the amplitude of the oscillation. However, under identical conditions the frequency of oscillation (each peak in this irregular sinusoidal decay is called one oscillation) was generally quite consistent. In general the absorbance A decreases with time ( d A l d t < 0) in normal oxidation of AA. However, as shown in Figure 1, for regular oscillating behavior d A l d t < 0. Then in the “trough” d A l d t = 0, followed by an increase in AA concentration d A l d t > 0, culminating in a “crest” where d A / d t = 0, followed by a normal decay where d A l d t < 0. In the following we will be using the term “turning point,” which implies that we will have encountered a trough where d A l d t = 0, but instead of increasing ( d A l d t > 0), the absorbance starts to decrease again ( d A l d t < 0).

The data on the oscillatory oxidation of AA with oxygen under various conditions in aqueous solutions are shown in Tables 1-111. Integral num- bers in the tables indicate the total number (frequency) of damped oscil- TABLE I. acid and constant concentration of cupric sulfate [at pH = 8.09 (a), 6.98 (b), and 6.02 (c)].

Number of Oscillations

Frequency of oscillation at different temperatures and concentrations of ascorbic

(i) [CUSO~] = 2 . 2 7 x lo-‘ M

Temp. (OC)

(ii) ICUSO~] = 1 . 3 6 x l o w 6 El 1 0 0 0 0 1 ; 1 0 0 1 5 0 1 1 1 0 1”

4 0 1 35 2 2 2 : 4 2 3 1 2 0 2 : 3 0 3 j 4 0 3

(iii) [ C U S O ~ ~ = 4 . 5 x t o - ’ t1


40

3 5

30

2 5

20

TABLE 11. sulfate at constant ascorbic acid concentration [at pH = 6.02 (h), 6.98 (i), and 8.09 (j)].

Frequency of oscillation at different temperatures and concentrations of cupric

Number of O s c i l l a t i o n s

(i) [ A . A . ] = 3 . 3 x M

Temp. (OC) ( i i ) [ A . A . ] = 6 . 6 x M

4 0 1 2hoi4j! o o Ij 2 o 2 ;; 1 2 o 3 : 1 o 0, 2 n 1

3 5 3 0 2 1 2 2 2 : 3 0 1 0 2 2 ; 3 2 4 ; 1“l l*

30 o o o : o o 4 j o o o 30 n i * 2 j 2 i 5 i o o i

25 0 0 1 ~ 1 0 1 ~ 0 1 1 25 0 1 2 ; 0 0 2 j 0 0 2

20 1 3 1 : 3 1 0 : 3 0 0 20 2 3 1 : 2 2 2 1 3 0 1

15 i ~ ~ : i ~ i ; 3 t o 15 2 3 ~ : 3 1 2 : 3 n ~

8 I

I

( i i i ) [ A . A . ] - 9 . 9 x M ( i v ) [ A . A . ] = 1 . 3 2 x M

0 0 3 j 1 ” O l j 0 0 0

o o 3 i 3 n 4 3 4 o 1”

~ 0 4 j n n i j i 0 4

I

1*0 2 : 1 1 4 : 3 1 3 I

0 0 1 j 0 * 0 1 ~ 0 0 1

lations. For example, 0 means that there were no oscillations under the specific conditions, 1 means that one peak was observed in the spectrum, and so on. The asterisk * indicates that there was no peak in the spectrum, but alternatively a turning point. For instance, 1* means one turning point in the spectrum and is regarded as one peak. In contrast to 1*, O* is regarded as no oscillation under this condition. The infinity symbol is used to represent very high frequencies of oscillation (usually over 15) with small amplitudes. Since we have four variables (our oxygen concentration at 1.26 X 10-3M is essentially constant), namely, temperature, C U + ~ concentration, AA concentration, and pH, we have kept one of the above variables constant and have varied the other three in order to generate Tables 1-111. Rather than attempting to plot the results in three dimen- sions, we felt it was as easy and informative to generate the tables in order to ascertain those limits required for oscillatory behavior.


TABLE 111. acid concentration (at [CUSO~] = 4.5 X

Frequency of oscillation at different temperatures and pH at constant ascorbic (k), 1.36 X lou6 (l), and 2.27 X 10-6M (m)).

Number of Oscillations

(i) [ A . A . ] = 3.3 x LO-' M

Temp. (OC) (ii) ( A . A . 1 = h . 6 x N

(iii) [ A . A . ) = 9.9 x lo- ' El (iv) [ A . A . ] = 1 . 3 2 x lo- ' M

(v) [ A . A . ] = 1 . 6 5 x 10-" E l

Table I shows the frequency of oscillation at different temperatures and concentrations of AA. The subtables in Table I are at three different concentrations of cupric sulfate (2.27 X 1OP6M, 1.36 X 10-6M, and 4.5 X lO-7M). The columns with superscripts a, b, and c indicate three different pH (a = 8.09, b = 6.98, and c = 6.02). The dashed lines separate five different AA concentrations (3.3 X 10-5M to 1.65 X 10-4M). In all of the tables it is to be understood that the superscripts (such as a, b, c) apply to all the other columns separated by dashed lines.

Frequencies of oscillation at different temperatures and concentrations of cupric sulfate are shown in Table 11. The AA concentration is constant at each subtable, and three different concentrations of cupric sulfate are divided by dashed lines. The columns with superscripts h, i, and j indicate a pH of 6.02,6.98, and 8.09, respectively.


Table I11 shows frequencies of oscillation at different temperatures and pH. The subtables in Table 111 are at five different AA concentrations, which are the same as those in Table 11. Three pH are separated by the dashed lines, and k, 1, and m indicate three different concentrations of cupric sulfate, which are 4.5 X.lOP7M, 1.36 X 10+M, and 2.27 X 10-6M.

In order to see how to read the tables consider Table I part i, where we have fixed the CuSO4 concentration at 2.27 X lO+M and we therefore have temperature, AA concentration, and pH as the other three variables. If one looks in the second column, that is, the second group of entries between the dotted lines, we can see that the AA concentration for this whole group is 2 X 3.3 X 10-5M, the pH in the three internal columns is 8.09,6.98, and 6.02, respectively, and in the vertical direction we can see that the temperature varies from 15 to 40’C.

Discussion It is obvious that no simple unique trend can be ascertained at the present

time as to the results obtained for the oscillatory behavior of this system. The variables are intertwined in a very complicated manner, and no trivial boundary conditions can be drawn. Generally speaking, the best condition for oscillation to occur can be described in two regions.

(1) In the temperature range of 15-20°C, with pH - 6, and with [CUSO~] = 2.27 X 10+M, the concentration of AA varies in the region between 6.6 X 10-5M and 1.32 X 10-4M.

(2) In the temperature range of 3&35”C, with pH - 7, and with [CUSO~] = 1.36 X 1OW6M, the concentration of AA varies in the region between 3.3 X lOP5M and 1.65 X 10-4M.

More experimental data are needed if possible in order to sort out the functions necessary to interpret the detailed oscillation behavior. From the work done in our laboratory,2 the “feedback” step (that is, some step regenerating AA) is provided in the mechanism for the necessary condition for oscillation behavior. At 265 nm, what we observed was the characteristic absorption of the conjugated double bond in AA and the complexes of AA with copper ions. The oxidized ascorbic acid OXAA does not absorb at this wavelength. When the results described above are applied in es- tablishing the mechanism of the oxidation of AA, a logical sequence of steps involving only first- and second-order terms has been deduced:

k i

k 2 C U + ~ + AA +CU+~AA

k3 (2) CU+~AA + 0 2 +OXAA

k q

2 OXAA 2 AA + products

(3) AA + H+ +products

(4) 2 See footnote 1.


I / (X.,Yo)

x = + [Cu-AA] = tdal &IS.

Figure 2. Phase space diagram for the oscillating oxidation of AA.

k6 (5) OXAA +products

From eqs. (1)-(5) and, especially, eqs. (l), (a ) , and (4), it will be noted that there is a condition generated wherein OXAA, which does not absorb at 265 nm, decreases as AA plus CU+~AA increases, and conversely, as OXAA increases, AA plus CU+~AA decreases. These results can readily be represented as an inward spiral, as shown in Figure 2. However, since one cannot, in reality, get negative concentrations of any of our species, the coordinates must be in the first quadrant in order to correspond to concentrations of AA and OXAA greater than zero. The above spiral can be expressed mathematically as a pair of linear differential equations in x , y, and t (time), such that under certain mathematical constrictions (as will be shown later) it can give rise to oscillation for a plot of AA plus CU+~AA versus t (time). The exponential decay of AA and the eventual loss of oscillation arises from eqs. (3)-(5). It is a well established fact that copper forms complexes with AA reversibly [as presented in step (l)]. In step (2), formation of OXAA (whose structure has been under a great deal of discussion r e ~ e n t l y ) ~ is formed from the copper complex by reaction with oxygen. Step (3) may be slow, but the lactone ring opening and the sub- sequent decomposition are definitely a possible irreversible pathway to the various products of the reaction. Step (4) represents the feedback step which was discussed previously. Finally, other pathways to products are represented in step (5). This scheme demonstrates many of the main steps in the oxidation of AA. We will show that it also generates a characteristic oscillation behavior. Let x’ = [AA], I” = [CU+~AA], andy = [ O W ] . The differential rate equations can now be written as

dx’ - = - ~ ~ [ C U + ~ ] X ’ + k 2 ~ ” - k4[H+]~’ + k5y2 dt (6)

(7)

3 See footnote 1.


Let x = x’ + x”,4 where x represents the total concentration of all species of AA observed at 265 nm using a ultraviolet spectrometer. Adding eqs. (6) + (7) gives

d x dx’ dx” (9) - = ~ + __ = -(h4[H+] + k 3 [ 0 2 ] ) ~

d t d t d t + h5y2 + h4[H+]x” + k3[02]x’

Since none of the concentrations can assume negative values, the critical point (xo, yo) of the spiral in the xy phase plane must be in the first quadrant [17], that is, xo > 0 and yo > 0. A change of variables, u = x - xo and L! = y - yo, leads to the following equations:

(10) d u - = -(k*[H+] + h3[02])u + 2h5you + k5u2 + k4[H+]x” d t

+ hs [02]~’ - (h4[H+] + h3[02] )xo + h5y02

If this shift makes the critical point (XO, yo) of the spiral move to the origin, the constant term should vanish, that is,

Solving for x o and yo, we have

(13) h 4 [ H + ] ( ~ ” - XO)

k6 Yo =

where XO, yo are constants, but will depend on the values of x‘ and x”, which are functions of time. This explains the difficulty one encounters in du- plicating a particular experimental run. From Eq. (12) x~ is always greater than zero. However, when x ” - xo < 0, then yo is less than zero in eq. (13). This is of course not realistic.

Mathematically when a system is written as follows:

Theoretically x = x’ + ax”, where a is the absorption of x” relative to x ’ . Since the molar absorption coefficient of total AA was found experimentally, independent of the Cu++ concentration used in this paper, we concluded that a = 1. The authors are grateful to the referee who pointed out the ambiguous description in this paragraph.


dx _ - - ax + by + F(x,Y) dt dY - = cx + dy + G(x,y) dt

the characteristic equation for the system can be written as

S 2 - ( a + d)S + (ad - bc) = 0

where S is a dummy variable. A spiral will form in the phase plane only when (ad - bc) # 0 and the roots of S are complex, that is,

[ (a + d)2 -4(ad - be)] < 0

Also if (a + d ) < 0, the trajectory goes inward. Comparing eqs. (10) and (1 1) with this model, we have

a = -(h4[H+] + h3[0z])

c = h3[02] b = 2h5yo

d = -(hs + 2hsYo)

The three necessary conditions for a spiral to occur in the phase plane with a trajectory going inward are as follows:

(A) a d - bc = (k4[H+I + h3[02I)(hs + 2k5Yo) - 2h~Yoh3[02I = h&6[H+] + 2h4hs[H+]yo + h3h~[O2] # 0

(B) u + d = -(k4[H+] + h3[02] + hfj + 2h5yo) < 0

(C) (a + d)' - 4(ad - bc) = (h4[H+] + h3[02])2

+ (h6 + 2h5Y0)2 - 2h4h6[H+1 - 4h4h5[Hf]Y0

- 2h3hS[O2l + 4h3h5[021~o < 0

(A) and (B) are naturally fulfilled. Condition (C) plays a very decisive role. If the spiral occurs, it should be less than zero. A t the present time, no further knowledge about the rate constants can be given to support or to disprove this simple model. However, we are in the process of evaluating some of the constants experimentally and modeling the other rate constants by computer simulation.

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Received March 16,1981 Accepted December 28,1981

Oscillatory behavior during the oxygen oxidation of ascorbic acid

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Transcript of Oscillatory behavior during the oxygen oxidation of ascorbic acid