Kinetics of fading of some triphenylmethane dyes: Effects of electric charge, substituent, and aqueous binary mixtures of dimethyl sulfoxide and 2-propanol

Article abstract of DOI:10.1002/kin.20831

The rate constants of alkaline fading of a number of triphenylmethane (TPM) dyes including methyl green (ME²⁺), brilliant green (BG ⁺), fuchsin acid (FA^2-), and bromophenol blue (BPB ^2-) were obtained in aqueous binary mixtures of 2-propanol (protic solvent) and dimethyl sulfoxide (DMSO) (aprotic solvent) at different temperatures. It was observed that the reaction rate constants of BG⁺ and ME²⁺ increased and those of FA^2- and BPB^2- decreased with an increase in weight percentages of aqueous 2-propanol and DMSO binary mixtures. 2-Propanol and DMSO interact with the used TPM molecules through hydrogen bonding and ion-dipole interaction, respectively, in addition to their hydrophobic interaction with TPM dyes. The fundamental rate constants of a fading reaction in these solutions were obtained by the SESMORTAC model. Also, the effect of electric charge and substituent groups of a number of TPM dyes on their alkaline fading rate was studied.

Full text of DOI:10.1002/kin.20831

Kinetics of Fading of Some
Triphenylmethane Dyes:
Effects of Electric Charge,
Substituent, and Aqueous
Binary Mixtures of Dimethyl
Sulfoxide and 2-Propanol
B. SAMIEY, Z. DALVAND
Department of Chemistry, Faculty of Science, Lorestan University, 68137-17133 Khoramabad, Iran
Received 22 December 2012; revised 29 August 2013; 21 September 2013; accepted 10 October 2013
DOI 10.1002/kin.20831
Published online 21 November 2013 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: The rate constants of alkaline fading of a number of triphenylmethane (TPM) dyes
2
+
+
2−
including methyl green (ME ), brilliant green (BG ), fuchsin acid (FA ), and bromophenol
blue (BPB2 ) were obtained in aqueous binary mixtures of 2-propanol (protic solvent) and
−
dimethyl sulfoxide (DMSO) (aprotic solvent) at different temperatures. It was observed that the
+
2+
2−
2−
reaction rate constants of BG and ME increased and those of FA and BPB decreased
with an increase in weight percentages of aqueous 2-propanol and DMSO binary mixtures.
2
-Propanol and DMSO interact with the used TPM molecules through hydrogen bonding and
ion–dipole interaction, respectively, in addition to their hydrophobic interaction with TPM
dyes. The fundamental rate constants of a fading reaction in these solutions were obtained by
the SESMORTAC model. Also, the effect of electric charge and substituent groups of a number
of TPM dyes on their alkaline fading rate was studied. ꢀC 2013 Wiley Periodicals, Inc. Int J Chem
Kinet 46: 60–70, 2014
brilliant blue FCF (BB2 ), bromophenol blue (BPB ),
−
2−
INTRODUCTION
2−
and bromophenol red (BPR ) are triphenylmethane
(TPM) dyes (Scheme 1). These dyes represent a class
of dyes of commercial and analytical importance [7,8].
TPM dyes are used to dye materials and can be used
as a pH indicator or as a bacteriological stain [9] or to
treat parasites and bacterial infections in fish and fish
eggs [10–13]. Also, some of them such as PB and
BB are food dyes [14,15]. In this work, we stud-
ied the BG , ME , FA , and BPB alkaline fad-
ing in binary mixtures of water with different weight
Solvent effects on reactivity may be very large. Or-
ganic solvents, as cosolvents, can change the rate of
2+
chemical reactions [1–6]. Methyl green (ME ), bril-
+
+
liant green (BG ), malachite green (MG ), crystal vi-
+
2−
2−
olet (CV ), fuchsin acid (FA ), patent blue V (PB ),
2
−
2−
Correspondence to: Babak Samiey; e-mail: babsamiey@
+
2+
2−
2–
yahoo.com.
ꢀ
C
2013 Wiley Periodicals, Inc.

KINETICS OF FADING OF SOME TRIPHENYLMETHANE DYES
61
-
SO3
+
+
(
CH ) N
(C H ) N
2 5 2
3
2
H C
N
3
+
-
(C H ) N
2 5 2
SO3
-
SO3
+
-
H C
N
SO
3
3
(
CH ) N
(C H ) N
2 5 2
3
2
-
O
+
+
MG
BG
(
C H ) N
-
2 5 2
SO3
2-
2-
BB
PB
+
+
(
CH ) N
(CH ) N
-
3
2
3 2
H N+
SO3
2
O
Br
Br
Br
Br
+
N(CH3)2
N (CH )
3
3
NH2
-
-
O
H C
3
SO3
-
SO3
(
CH ) N
(CH ) N
3 2
3
2
-
H N
SO3
2
+
2+
CV
ME
2-
FA
2-
BPB
O
Br
-
O
-
SO3
Br
2-
BPR
Scheme 1
chased from Merck. BB2 and PB were provided
by Acros.
−
2−
percentages of 2-propanol and dimethyl sulfoxide
DMSO), and their fundamental rate constants of a
(
fading reaction in these solutions were obtained using
the SESMORTAC (study of effect of solvent mixture
on the one-step reaction rates using the transition state
theory and cage effect) model [16]. Also, the effects of
Kinetic Procedure
2+
+
electric charge and substituent groups of ME , BG ,
The fading of TPM dyes was followed at their
maximum absorption wavelength (λmax) values in a
thermostated cell compartment of a Shimadzu UV–
+
+
2−
2−
2−
2−
MG , CV , FA , PB , BB , and BPB on their
alkaline fading rate were investigated.
1650PC spectrophotometer. The experiments were
conducted in the temperature range of 283–323 K
within ± 0.1 K in a stoppered cell. All the kinetic runs
were carried out at least in triplicate. To perform each
EXPERIMENTAL
Materials
−4
+
kinetic run, a 100-μL aliquot of 4.46 × 10 M ME ,
−
4
+
−4
2−
3
.39 × 10 M BG , 8 × 10 M FA , or 3.17 ×
ME2 , MG , BG , CV , FA , BPB , 2-propanol
+
+
+
+
2−
2−
10 M BPB solutions was added by a microsyringe
into 2.9 mL of a solution containing 4.88 × 10
−4
2−
−4
(
>99.5%), DMSO (≥99%), and NaOH were pur-
,
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

6
2
SAMIEY AND DALVAND
N(CH3)2
electric charge and substituents on it. As seen in Table I,
reaction rate constants change as follows:
+
(
CH ) N
3 2
FA2 > ME > MG > BG > CV
−
2+
+
+
+
-
+
OH
OH
ꢁ
BPB2 > BB > PB
−
2−
2−
(1)
As reported before [17], the electron-releasing
inductive effect of the ethyl groups of BG is
(
CH ) N
+
3
2
N(CH3)2
+
greater than that of the methyl groups of MG . This
+
+
A TPM dye
carbinol base
makes (C2H5)2N = group of BG more stable than
+
+
(
CH3)2N = group of MG and results in an in-
Scheme 2 Typical fading reaction of a TPM dye.
+
crease in the fading rate constant of MG compared
+
to BG . Owing to symmetric localization of positive
electric charge on CV , its fading rate constant is
much less than BG and MG at similar temperatures.
+
.087 × 10− , 4.88 × 10 , and 0.2 M sodium hy-
3
−4
1
+
+
droxide, respectively, and certain weight percentages
of 2-propanol or DMSO. Also, in another series of ex-
2−
FA has three −NH2 groups and due to the electron-
−
withdrawing inductive effect of its three −SO groups
−
4
2−
3
periments, a 100-μL aliquot of 3.26 × 10 M PB or
+
which also reduces its symmetry compared to CV
−4
2−
3
.17 × 10 M BB solutions was added into 2.9 mL
2−
(
in spite of two negative electric charge FA ) its fad-
ing rate constant is much greater than those of ME
MG , BG , and CV . The presence of the (CH3)3N –
group in ME increases its positive electric charge
and thus increases its fading rate constant compared to
of an aqueous solution containing 0.2 M sodium hy-
2
+
,
−
4
+
droxide and a 100-μL aliquot of 2.01 × 10 M CV or
+
+
+
+
−4
+
1
.38 × 10 M MG solutions was added into 2.9 mL
2+
−4
of an aqueous solution containing 4.46 × 10 or 4.88
−
4
×
10 M sodium hydroxide, respectively, at differ-
+
+
+
MG , BG , and CV .
ent temperatures. TPM alkaline fading is a one-step
reaction and has been found to be bimolecular, first
order with respect to each reactant (Scheme 2), but in
these series of experiments, pseudo–first-order condi-
tions (excess alkali) were used in all cases.
2−
In alkaline solutions, –OH groups of BPB
BPR , and PB are deprotonated and change to
,
2−
2−
−
−
−
O groups. The presence of negative electric charge
2−
2−
−
O electron-releasing groups in BPB , BPR [18],
2
−
−
and PB and SO C6H5CH2− hydrophobic groups
3
2
−
in BB reduces drastically their fading rate con-
2−
2+
+
+
+
stant compared to FA , ME , MG , BG , and CV
RESULTS AND DISCUSSION
−
(
Table I). The presence of the −O electron-releasing
2−
2−
group in BPB and PB decreases their fading rate
Effects of Electric Charge and Substituents
on the Fading Reaction Rate
2−
constant than that of BB . But the presence of four
Br electron-withdrawing groups in BPB increases
its fading rate constant than that of PB . Also, BPB
has two −Br electron-withdrawing groups more than
2−
−
2−
2−
Here, we compare the reaction rate of a number of
TPM dyes with the hydroxide ion and effects of their
Table I kobs Values of Some TPM Dyes at Different Temperatures
−
1
−1
kobs (M min )
TPM
λmax(nm)
283 K
293 K
303 K
313 K
323 K
ME2
MG
+
623.1
617
624
589.9
544.6
630
103 ± 2
23 ± 2
14 ± 1
3 ± 0.1
272 ± 2
–
231 ± 8
59 ± 2
31 ± 2
7 ± 0.2
510 ± 2
–
514 ± 13
129 ± 4
–
–
–
–
–
–
–
–
+
+
BG
CV
85 ± 4
+
19 ± 1
2
−
FA
781 ± 2
–
–
2
−
BB
0.064 ± 0.003
0.065 ± 0.002
0.004 ± 0.001
0.150 ± 0.011
0.128 ± 0.013
0.011 ± 0.002
0.310 ± 0.019
0.252 ± 0.020
0.030 ± 0.009
2
−
BPB
591
630
–
–
–
–
2
−
PB
obs values of BPB2 and BPR in 308 K are 0.074 and 0.011 M min [18], respectively.
−
2−
−1
−1
k
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

KINETICS OF FADING OF SOME TRIPHENYLMETHANE DYES
63
+
Table II kobs and Ea Values of BG Fading in 2-Propanol–Water Solutions at 283–303 K
−
1
−1
kobs (M min )
Ea (kJ mol 1
−
)
W2-PrOH (%)
[2-PrOH](M2)
[H2O] (M)
283 K
293 K
303 K
0
9
1
2
3
4
5
5
.0
.7
0.000
1.568
3.053
4.455
5.793
7.065
7.672
8.269
55.556
49.166
43.174
37.986
32.498
27.164
24.588
21.735
14 ± 1
14 ± 1
15 ± 1
16 ± 1
20 ± 1
56 ± 1
73 ± 1
104 ± 3
31 ± 2
34 ± 1
37 ± 1
40 ± 1
71 ± 1
129 ± 1
170 ± 1
238 ± 1
85 ± 4
89 ± 2
65 ± 5
65 ± 4
64 ± 2
64 ± 1
64 ± 3
61 ± 2
61 ± 2
59 ± 2
9.3
9.0
8.7
8.3
3.2
8.0
93 ± 5
97 ± 2
176 ± 4
310 ± 3
398 ± 11
544 ± 5
k
mc1 values are shown in bold. Zones 1 and 2 are in the range of 0–29.0% and 29.0–58.0% 2-PrOH, respectively.
BPR2 and it increases fading rate constants of BPB
−
2−
where kMeOH, keg, kGl, kprd, k1−PrOH, kEtOH, k2−PrOH, and
2−
+
than BPR [18]. Finally, we investigated the effect
of negative electric charged groups on the TPM fad-
ing rate. As seen in Table I, the fading reaction rate
kw are the rate constants of the MG fading reaction in
aqueous mixtures of methanol, ethylene glycol, glyc-
erol, 1,2-propanediol, 1-propanol, ethanol, 2-propanol,
and in water, respectively. It shows the role of pre-
liminary hydrogen bonding between –OH group(s) of
2−
2−
of FA is too much greater than that of BPB . This
shows that negative electric charged substituent groups
−
2−
+
such as the −O group in BPB that share a pair of
electrons in the resonance structures of a TPM dye de-
crease drastically its fading reaction rate compared to
nonhydrophobic negative electric charged substituent
alcohols and MG , in addition to their hydrophobic
interaction.
As seen in Tables II–IX and Fig. 1, an increase in
2-propanol and DMSO concentration increases the fad-
−
2−
+ 2+
ing reaction rate of BG and ME and decreases the
groups such as −SO3 in FA that act through the
2−
2−
electron-withdrawing inductive effect.
fading reaction rate of FA and BPB . 2-Propanol
and DMSO interact with TPM dyes through a prelimi-
nary hydrogen bonding and ion–dipole interaction, re-
spectively, and then a hydrophobic interaction occurs
between TPM dyes and these cosolvent molecules.
When we carried out experiments with similar mo-
lar concentrations of these cosolvents, a decrease in
Effects of 2-Propanol and DMSO on the
Fading Rate of Some TPM Dyes
In continuation of earlier work [16,19,20], we com-
pared effects of different concentrations of 2-propanol
a protic solvent) and DMSO (an aprotic solvent) in
2−
2−
2+
the fading rate of FA and BPB and an increase
(
+
in the fading rate of BG and ME in 2-propanol–
water solutions were greater and less than those of
DMSO–water solutions, respectively (Tables VII–IX).
To interpret these observations, it must be said DMSO
is a polar molecule and forms strong hydrogen bond-
ing with water molecules through its oxygen atom [24]
but 2-propanol forms hydrogen bonding through its –
2+
+
2−
2−
water on the ME , BG , FA , and BPB alka-
line fading rate. These two organic solvents have a
lower dielectric constant than water and according to
Hughes–Ingold rules for solvent effects in nucleophilic
substitution reactions [21–23], formation of the neutral
or less charged carbinol base from two charged reac-
tants may be more favorable and formation of the more
charged carbinol base from them is not more favorable
in higher weight percentages of these solvents and in-
creases or decrease the reaction rate, respectively.
−
OH group. Thus, hydrogen bonding between −O and
−
2−
2−
−
3
−
SO groups of BPB or −SO and −NH2 groups
3
of FA with 2-propanol is stronger than the ion–dipole
2−
interaction between these substituent groups of BPB
and FA with DMSO molecules. A decrease in the
fading rate of BPB in the presence of DMSO shows
+
As reported before [20], the MG alkaline fad-
2−
ing rate in low molar ratios of a series mono- and
polyhydroxyl alcohols, which their viscosity has no
effect on the fading rate, is as follows:
2−
the important role of the hydrophobic interaction be-
tween the used dyes and DMSO molecules. As reported
before [25], the interaction between DMSO and oc-
tanol is most likely due to a hydrophobic association.
This results in changing the maximum wavelength val-
ues of each of these dyes in the presence of DMSO and
kw < k2−PrOH ≈ kEtOH < k1−PrOH
≈
kprd < kGl < keg ≤ kMeOH
(2)
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

6
4
SAMIEY AND DALVAND
+
Table III kobs and Ea Values of BG Fading in DMSO–Water Solutions at 283–303 K
−
1
−1
kobs (M min )
Ea (kJ mol 1
−
)
WDMSO(%)
[DMSO] (M)
[H2O] (M)
283 K
293 K
303 K
0
9
1
2
2
3
4
5
5
.0
.7
0.000
1.228
2.474
3.089
3.723
4.953
6.183
6.817
7.425
55.556
50.840
45.928
43.644
40.592
35.548
30.961
29.101
26.512
14 ± 1
16 ± 1
18 ± 1
19 ± 1
21 ± 2
36 ± 1
64 ± 1
87 ± 1
118 ± 1
31 ± 2
37 ± 2
44 ± 1
48 ± 1
53 ± 1
89 ± 1
156 ± 1
208 ± 6
289 ± 5
85 ± 4
98 ± 2
65 ± 5
65 ± 4
66 ± 6
65 ± 2
66 ± 1
65 ± 2
63 ± 1
61 ± 2
61 ± 1
9.3
4.2
9.0
8.7
8.3
3.2
8.0
113 ± 7
121 ± 5
130 ± 6
220 ± 2
369 ± 2
489 ± 5
645 ± 10
k
mc1 values are shown in bold. Zones 1 and 2 are in the range of 0–29.0% and 29.0–58.0% 2-PrOH, respectively.
Table IV kobs and Ea Values of ME2 Fading in 2-Propanol–Water Solutions at 283–303 K
+
−
1
−1
kobs (M min )
Ea (kJ mol 1
−
)
W2-PrOH(%)
[2-PrOH] (M)
[H2O] (M)
283 K
293 K
303 K
0
4
9
1
1
2
2
2
.0
.8
.7
6.5
9.3
1.8
4.2
9.0
0.000
0.799
1.574
2.321
3.051
3.425
3.770
4.456
55.556
51.864
49.126
45.827
43.493
41.888
39.954
37.460
104 ± 2
124 ± 2
142 ± 7
174 ± 9
199 ± 13
224 ± 5
252 ± 10
315 ± 8
231 ± 8
265 ± 4
315 ± 9
351 ± 16
406 ± 5
472 ± 10
569 ± 7
772 ± 11
514 ± 13
577 ± 4
57 ± 2
55 ± 2
55 ± 1
53 ± 3
54 ± 3
56 ± 3
57 ± 2
60 ± 2
669 ± 8
770 ± 5
907 ± 8
1062 ± 8
1259 ± 13
1700 ± 9
k
mc1 values are shown in bold. Zones 1 and 2 are in the range of 0–19.3% and 19.3–29.0% 2-PrOH, respectively.
Table V kobs and Ea Values of ME2 Fading in DMSO–Water Solutions at 283–303 K
+
−
1
−1
kobs (M min )
Ea (kJ mol 1
−
)
WDMSO(%)
[DMSO] (M)
[H2O] (M)
283 K
293 K
303 K
0
4
9
1
1
2
2
2
.0
.8
.7
4.5
9.3
1.8
4.2
9.0
0.000
0.621
1.241
1.859
2.481
2.783
3.099
3.719
55.556
52.812
50.557
48.096
45.675
44.656
43.053
40.749
104 ± 2
120 ± 3
133 ± 2
145 ± 2
160 ± 2
175 ± 2
190 ± 5
223 ± 3
231 ± 8
275 ± 10
307 ± 2
346 ± 6
396 ± 3
425 ± 5
473 ± 4
565 ± 11
514 ± 13
595 ± 10
682 ± 7
57 ± 2
57 ± 1
58 ± 1
59 ± 1
59 ± 2
59 ± 3
61 ± 2
61 ± 2
759 ± 16
846 ± 10
918 ± 11
1037 ± 14
1241 ± 19
k
mc1 values are shown in bold. Zones 1 and 2 are in the range of 0–19.3% and 19.3–29.0% 2-PrOH, respectively.
2
-propanol in a similar trend (Fig. 2). On the other
Proposed Reaction Mechanism. Data presented in
Tables VIII and IX were analyzed by the SESMORTAC
model. In SESMORTAC model [16], a range of sol-
vent composition in which the equation of logarithm
of the reaction rate constant, log k, versus reciprocal
of dielectric constant of the solution, D , is linear
[26–30], is called a “zone” and a solvent composition in
which a zone finishes and another zone starts, is called
2+
hand, an increase in the fading rate of ME (in the
most cases) and BG molecules in the presence of
+
DMSO is more than which was observed in the pres-
ence of 2-propanol (Tables VI, VIII, and IX). This is
due to a preliminary ion–dipole interaction between
−1
DMSO and ME2 and BG compared to preliminary
+
+
hydrogen bonding of 2-propanol with these two dyes.
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

KINETICS OF FADING OF SOME TRIPHENYLMETHANE DYES
65
Table VI kobs and Ea Values of FA2– Fading in 2-Propanol–Water Solutions at 283–303 K
−
1
−1
kobs (M min )
W2-PrOH (%)
[2-PrOH] (M)
[H2O] (M)
283 K
293 K
303 K
Ea (kJ mol 1
−
)
0
4
9
1
1
1
2
2
3
3
4
5
.0
.8
.7
0.000
0.805
1.568
2.322
2.723
3.054
3.763
4.458
5.133
5.791
6.437
7.675
55.556
52.334
49.073
46.068
45.156
43.308
40.490
37.387
34.809
31.900
28.704
23.891
272 ± 2
188 ± 3
130 ± 5
93 ± 4
75 ± 1
57 ± 3
50 ± 2
45 ± 1
39 ± 3
35 ± 1
32 ± 2
25 ± 3
510 ± 2
358 ± 3
255 ± 1
185 ± 2
159 ± 2
126 ± 2
109 ± 3
98 ± 2
89 ± 2
77 ± 2
68 ± 4
56 ± 3
781 ± 2
542 ± 5
417 ± 3
320 ± 2
269 ± 5
224 ± 1
208 ± 5
192 ± 4
178 ± 4
166 ± 4
150 ± 2
130 ± 7
38 ± 4
38 ± 4
42 ± 3
44 ± 2
45 ± 4
49 ± 4
51 ± 2
52 ± 2
54 ± 2
56 ± 6
55 ± 2
58 ± 3
4.5
6.9
9.3
4.2
9.0
3.8
8.7
3.5
3.2
k
mc1 and kmc2 values are shown in bold. Zones 1 and 2 are in the range of 53.2–19.3% and 19.3–0.0% 2-PrOH, respectively.
Table VII kobs and Ea Values of FA2– Fading in DMSO–Water Solutions at 283–303 K
−
1
−1
kobs (M min )
Ea (kJ mol 1
−
)
WDMSO (%)
[DMSO] (M)
[H2O] (M)
283 K
293 K
303 K
0
3
4
7
9
1
2
3
.0
.4
.8
.3
0.000
0.443
0.619
0.933
1.248
2.476
3.732
4.954
55.556
53.672
53.143
51.844
50.476
45.646
40.309
36.283
272 ± 2
256 ± 4
245 ± 6
230 ± 3
218 ± 2
210 ± 3
204 ± 2
198 ± 1
510 ± 2
469 ± 11
459 ± 3
438 ± 3
419 ± 6
413 ± 2
407 ± 1
400 ± 2
781 ± 2
757 ± 5
753 ± 5
684 ± 7
652 ± 14
645 ± 1
640 ± 1
632 ± 2
38 ± 4
39 ± 2
40 ± 2
39 ± 3
39 ± 4
40 ± 4
41 ± 4
42 ± 4
.7
9.3
9.0
8.7
k
mc1 and kmc2 values are shown in bold. Zones 1 and 2 are in the range of 38.7–9.7% and 9.7–0.0% 2-PrOH, respectively.
Table VIII kobs and Ea Values of BPB2– Fading in 2-Propanol–Water Solutions at 313–333 K
−
1
−1
kobs (M min )
Ea (kJ mol 1)
−
W2-PrOH(%)
[2-PrOH] (M)
[H2O] (M)
313 K
323 K
333 K
0
4
9
1
1
2
.0
.8
.7
4.5
9.3
9.0
0.000
0.790
0.547
2.362
3.005
4.388
55.556
52.386
50.150
47.468
44.840
40.578
0.128 ± 0.013
0.068 ± 0.014
0.037 ± 0.005
0.018 ± 0.003
0.010 ± 0.002
0.003 ± 0.001
0.252 ± 0.009
0.135 ± 0.022
0.072 ± 0.004
0.036 ± 0.005
0.021 ± 0.004
0.006 ± 0.001
0.418 ± 0.017
0.228 ± 0.013
0.126 ± 0.007
0.064 ± 0.011
0.038 ± 0.003
0.010 ± 0.002
51 ± 4
52 ± 6
53 ± 3
55 ± 2
58 ± 4
52 ± 4
k
mc1 values are shown in bold. Zone is in the range of 29.0–0.0% 2-PrOH.
“
mechanism change point” (or a mc point). Consid-
[30,31]. In such cases, the differential solvation of the
initial and transition states is the controlling factor for
changes in the rate constant with the solvent compo-
sition. In the SESMORTAC model, variation in the
mechanism is followed through the study of changes
in microenvironment (or solvent cage) of the activated
complex. Dielectric constants of DMSO–water and
ering a mechanism on the basis of point charge on a
dielectric continuum suggests that the plots of log k
against D should be linear. The failure of the sim-
ple electrostatic interpretation shows the importance of
hydrogen bonding and other nonelectrostatic medium
effects in controlling the reactivity of the substrates
−1
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

6
6
SAMIEY AND DALVAND
Table IX kobs and Ea Values of BPB2– Fading in DMSO–Water Solutions at 313–333 K
−
1
−1
kobs (M min )
Ea (kJ mol 1
−
)
WDMSO (%)
[DMSO] (M)
[H2O] (M)
313 K
323 K
333 K
0
4
9
1
2
.0
.8
.5
9.0
8.6
0.000
0.613
1.221
2.447
3.664
55.556
52.386
49.613
44.425
38.937
0.128 ± 0.013
0.108 ± 0.008
0.090 ± 0.003
0.065 ± 0.015
0.043 ± 0.006
0.252 ± 0.009
0.213 ± 0.011
0.178 ± 0.015
0.125 ± 0.006
0.087 ± 0.010
0.418 ± 0.017
0.358 ± 0.020
0.306 ± 0.021
0.231 ± 0.013
0.170 ± 0.020
51 ± 4
52 ± 2
53 ± 4
55 ± 3
60 ± 3
k
mc1 values are shown in bold. Zone is in the range of 28.6–0.0% 2-PrOH.
1
000
8
6
4
2
00
00
00
00
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Mole fraction of cosolvent
+
2+
2−
Figure 1 kobs values of BG in 2-propanol (♦) and DMSO (ꢀ), ME in 2-propanol (ꢁ) and DMSO (ꢂ), FA in 2-propanol
2−
+
2+
,
(
ꢀ) and DMSO (+), and BPB in 2-propanol (×) and DMSO (ꢃ) vs. mole fraction of cosolvents. kobs values of BG , ME
2−
2−
and FA were measured at 293 K, and those of BPB were measured at 323 K.
6
6
6
6
5
5
5
5
60
40
20
00
80
60
40
20
0
0.05
0.1
0.15
0.2
0.25
Mole fraction of cosolvent
+
2+
2−
Figure 2 λmax values of BG in 2-propanol (♦) and DMSO (ꢀ), ME in 2-propanol (ꢁ) and DMSO (ꢂ), FA in 2-propanol
2−
(
ꢀ) and DMSO (+), and BPB in 2-propanol (×) and DMSO (ꢃ) vs. mole fraction of cosolvents.
2
-propanol–water solutions are obtained from the lit- of 2-propanol and DMSO was two zone and those of
2−
erature, [32,33].
It is found that the fading reaction rate of BG ,
BPB was one zone (Tables VIII and IX).
+
In aqueous solutions of DMSO and 2-propanol,
ME2 , and FA in the studied concentration range
+
2–
ꢀS and ꢀH values of the fading reaction are
ꢂ
ꢂ=
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

KINETICS OF FADING OF SOME TRIPHENYLMETHANE DYES
67
8
6
4
2
0
0
0
0
0
0
10
20
30
40
50
60
70
-
-
20
40
Weight percentage of cosolvent
ꢂ
+
2+
2−
Figure 3 ꢀH values of BG in 2-propanol (♦) and DMSO (ꢀ), ME in 2-propanol (ꢁ) and DMSO (ꢂ), FA in 2-propanol
2
−
(
ꢀ) and DMSO (+), and BPB in 2-propanol (×) and DMSO (ꢃ) versus weight percentage of cosolvents.
4
0
0
0
10
20
30
40
50
60
70
-
-
40
80
-
-
120
160
Weight percentage of cosolvent
ꢂ
=
+
2+
2−
Figure 4 ꢀS values of BG in 2-propanol (♦) and DMSO (ꢀ), ME in 2-propanol (ꢁ) and DMSO (ꢂ), FA in 2-propanol
2
−
(
ꢀ) and DMSO (+), and BPB in 2-propanol (×) and DMSO (ꢃ) versus weight percentage of cosolvents.
negative and positive, respectively (Figs. 3 and 4).
These may be due to the dissolution of cosolvent
molecules in the solvent cage and hydrogen bonding
[28]. Therefore, with an increase in 2-propanol or
ꢂ
ꢂ=
DMSO concentrations, ꢀS and ꢀH values become
less negative and more positive, respectively (Figs. 3
and 4).
(as previously reported for the interaction of dyes with
δ−
protic solvents) [34], ion–dipole interaction, and non-
electrostatic, especially hydrophobic interactions [35]
between TPM and cosolvent molecules when an ac-
tivated complex formed in the second mechanism
A solvent cage is microenvironment of TPM–OH
contact pair and, in spite of the first solvation shell,
includes many water and cosolvent molecules, and its
dielectric constant value is an intensive property. Thus,
in each region, n molecules of water can be replaced by
n molecules of cosolvent. Here, two processes occur
simultaneously, a chemical reaction between TPM and
(ACSM) is formed. ACSM will be explained later.
As shown experimentally, dissolution of hydrocarbons
in water is exothermic and results in more ordered
structure of water around the dissolved hydrocarbon
molecules [36]. Owing to the hydrophobic interaction
between hydrocarbon molecules which is endother-
mic, fewer water molecules are in direct contact with
them. Thus, the ordering influence of the hydrophobic
molecules will be decreased and the entropy decreases
and thermal energy is required for the destructuring
the hydration shells around hydrocarbon molecules
−
OH (first order in the contact ion) and replacement
of n water molecules of ACSM microenvironment by
n cosolvent molecules of its surrounding (n order in
cosolvent molecules).
As mentioned in the theory of the SESMORTAC
model, the values of n are different from each region
to next one and it produces a break in a plot of log k
−
1
versus D at each mc point.
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

6
8
SAMIEY AND DALVAND
In this reaction, a solvent is not a reactant. Thus,
The effect of cosolvent molecules on the reaction
owing to the SESMORTAC model, this reaction is
of type I [16]. In a TPM fading reaction, in the
presence of cosolvents the reaction rate changes
and the proposed mechanism for the TPM fading
reaction in these solutions involves two kinds of
mechanism.
The first mechanism occurs in a pure solvent. Start-
ing from the first zone, this mechanism can be written
as follows:
rate equation in the first zone (v2) as follows:
1
1
−
n
k k [TPM][OH ][S]
1
2
1 2
v2 = k [ACSM] =
(7)
1
−
n
1
2
k
(55.556 − [H2O]) + k
1
and the equation of the reaction rate in binary mixtures
v) is
(
−
ꢃ
k
1
v = v1 + v2 = kobs[TPM][OH ]
−
δ−
ꢂ
ꢀ
ꢁ
[
(TPM + OH )]cage ꢄ [(TPM − OH )] cage
1
1
n
ꢃ
k k [S]
1 2
k
AC
−
1
=
k + k1
ꢃ
n
1
2
k
2
(55.556 − [H O]) + k
−1
2
→
Product
(3)
ꢃ
ꢃ
ꢃ
× [TPM][OH−]
(8)
(9)
where AC is an activated complex and k , k , and k
1
−1
2
are the fundamental rate constants of the TPM fading
reaction and we cannot determine them. The related
rate equation, v1, is written as follows:
where
1
1
n
k k [S]
1
2
kobs = k +
1
−1
n
1
2
v1 = k[TPM][OH−]
(4)
k
(55.556 − [H2O]) + k
where kobs and k are the second-order rate constants in
where k is the observed rate constant in water.
1
1
a binary mixture and water, respectively, and k , k
,
Adding a cosolvent to a reaction medium results in
formation of ACSM and changes in the reaction rate.
The second mechanism is written as follows:
1
−1
1
and k are the fundamental rate constants of the TPM
2
fading reaction in the first zone. In the second zone,
Eq. (9) is replaced by
ꢃ
k
1
−
[
(TPM + OH ).nH2O]cage + nS ꢄ
n
ꢃ
2
2
k
k k ([S] − [S]mc1)
−
1
1 2
kobs = kmc1 +
(10)
(11)
2
−1
n
2
2
ꢃ
k
([H2O]mc1 − [H2O]) + k
k
δ−
ACSM
ꢂ
2
[
(TPM − OH ).nS] cage +nH2O → Product
where
(5)
1
1
n
k k [S]
1
2
mc1
+ k21
where cosolvent molecules are shown by S and k1, k−1,
and k2 are the fundamental rate constants of the TPM
fading reaction in cosolvent–water binary mixtures. In
each binary mixture, the structure of ACSM depends on
the structure of the solvent cage. Dielectric constants of
cosolvents are less than that of water, and when ACSM
forms in each zone n molecules of water existing in the
solvent cage are replaced by n molecules of cosolvent
from its surrounding. This decreases the dielectric con-
kmc1 = k +
1
−1
n
k
[H2O]
mc1
where [S]mc1 and [H O]
2
mc1
are the concentrations of
cosolvent and water at the mc point, respectively, and
1
2
1
2
2
2
k , k , and k are the fundamental rate constants of
−1
the TPM fading reaction in the second zone. The sec-
ond term in Eq. (10) shows the effect of cosolvent
molecules on the rate equation in the second zone.
On the other hand, the used cosolvents (DMSO and
δ−
stant of microenvironment of (TPM–OH ) in ACSM
2−
and changes the rate of the fading reaction. The used
cosolvents (DMSO and 2-propanol) increase the fading
2-propanol) decrease the fading reaction of FA and
2−
BPB . In this case, we studied an increase in the re-
action rate with an increase in the water concentration.
Thus, in Eqs. (6)–(11) water and cosolvent concen-
trations are transferred to numerator and denominator,
respectively. In the first zone, we have
+
2+
reaction of BG and ME . For this kind of reactions,
in the first zone, assuming that a steady-state concen-
tration of ACSM is reached in the used binary mixtures,
we have
1
−
n
1
1
n
k [TPM][OH ][S]
k k ([H O] − [H O]mc1)
1
1
2
2
2
[
ACSM] = k1
(6)
k
= kmc1
+
(12)
n
(55.556 − [H2O]) + k21
obs
1
n
1
2
k
([S] − [S]) + k
−1
mc1
−1
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

KINETICS OF FADING OF SOME TRIPHENYLMETHANE DYES
69
+
2+
2–
2–
Table X n, k1, k−1, k2, and Ea (k1) Values of Different Zones for the BG , ME , FA , and BPB Fading Reaction in
2
-Propanol–Water Binary Mixtures Obtained from the SESMORTAC Model at Different Temperatures
Ea(k1)
(kJ mol
−(n + 1)
−1
−n
−1
−1
−1
n
k1 (M
min
)
k−1 (M min
)
k2(min
)
)
T (K)
1st
2nd
1st
2nd
1st
2nd
1st
2nd
1st
2nd
+
BG
2
2
3
83
93
03
RC
RC
RC
2.04
2.04
1.86
–
–
–
5.61
12.58
36.09
–
–
–
1.67E-5
1.04E-5
1.28E-5
–
–
–
6.73E5
4.99E5
3.39E5
–
–
–
29
73
60
–
2
+
ME
1.30E-4
590.33
283
293
303
1.20
1.14
1.41
1.16
1.76
1.34
25.28
50.97
80.44
78.52
411.26
596.81
6.46E-6
5.81E3
1.99E3
3.97E5
3.05E5
2.54E5
3.35E5
1.32E5
1.19E5
41
47
53
2.50E-5
2
–
FA
2
2
3
83
93
03
1.38
1.41
1.17
1.33
1.32
1.12
6.58
11.15
24.90
0.62
1.38
3.35
9.74E-4
7.26E-4
3.24E-4
1.20E-3
5.27E-4
2.20E-4
6.45E5
5.31E5
3.91E5
1.56E6
1.16E6
8.29E5
2
–
BPB
3
3
3
13
23
33
2.67
2.80
2.65
–
–
–
9.29E-5
1.26E-4
3.14E-4
–
–
–
5.42E-4
8.88E-4
8.33E-4
–
–
–
1.21E7
1.39E7
1.87E7
–
–
–
RC refers that a rate constant is approximately constant. E
a
(k
1
) values are activation energy of k
1
values.
+
2+
2–
2–
Table XI n, k1, k−1, k2, and Ea (k1) Values of Different Zones for the BG , ME , FA , and BPB Fading Reaction in
DMSO–Water Binary Mixtures Obtained from the SESMORTAC Model at Different Temperatures
Ea(k1)
(kJ mol− )
−(n + 1)
−1
−n
−1
−1
1
n
k1 (M
min
)
k−1 (M min
)
k2 (min
)
T (K)
1st
2nd
1st
2nd
1st
2nd
1st
2nd
1st
2nd
29
+
BG
2
2
3
83
93
03
1.06
1.20
1.20
1.91
1.95
1.76
1.70
4.33
9.72
7.87
17.99
50.29
1.16E-4
7.61E-5
1.11E3
1.73E-5
1.69E-5
1.44E-5
1.05E6
7.43E5
5.51E5
5.95E5
4.38E5
2.99E5
27
2+
ME
2
2
3
83
93
03
0.92
1.04
1.01
1.05
1.67
1.81
24.33
62.84
133.30
50.04
229.13
683.46
3.23E-4
2.15E-4
169.58
2.66E-4
1.15E4
8.44E3
4.13E5
2.81E5
2.11E5
4.31E5
1.78E5
9.76E4
61
20
66
93
15
–
2–
FA
2
2
3
83
93
03
1.56
1.25
2.99
0.98
0.81
0.82
8.71
11.96
15.35
1.48
2.16
2.22
3.67E5
1.49E-3
1.70E6
2.26E-3
1.96E-3
3.29E-3
5.27E5
5.09E5
2.31E5
1.16E6
9.43E5
9.33E5
2–
BPB
3
3
3
13
23
33
1.56
1.27
1.30
–
–
–
1.46E-3
4.42E-3
6.53E-3
–
–
–
4.84E5
0.01
1.03E-3
–
–
–
1.19E7
9.72E6
8.42E6
–
–
–
a 1 1
E (k ) values are activation energy of k values.
In the second zone. we have
where the symbols and indices used in Eqs. (12) and
13) are similar to those used in Eqs. (9) and (10).
(
Here, mc1 in Tables VIII and IX is the highest used
concentrations of the cosolvents and zones start from
the highest concentrations of cosolvents.
2
2
n
k k ([H2O] − [H2O]mc2)
1
2
kobs = kmc2 +
(13)
2
n
2
2
k
([S]mc2 − [S]) + k
−1
International Journal of Chemical Kinetics DOI 10.1002/kin.20831

7
0
SAMIEY AND DALVAND
Also, as shown in Tables VIII and IX, in binary
3. Brinchi, L.; Di Profio, P.; Germani, R.; Salvelli, G.;
Spreti, N. J Colloid Interface Sci 2002, 247, 429.
solutions of DMSO and 2-propanol, k1 values in each
zone obey the Arrhenius equation [16] and the related
activation energy,Ea(k1), values are given in Tables
X-and-XI. At each certain temperature k1 values of
4
. Yesin, T. R.; Sinem, G.; Melda, T. Colloids Surf A 2005,
70–271, 72.
2
5. Xu, B. Q.; Aamundstad, T. A.; Lillekjendlie, B.;
Bj
ø´ rneboe, A.; Christophersen, A. S. Pharmacol Tox-
+
2+
the fading reaction of BG and ME increase and
icol 1997, 80, 171.
2−
those of FA decrease with an increase in the cosol-
vent concentration from zone 1 to zone 2 according
to trend of kobs variation. At each certain temperature,
6. Gao, Z. H., Gu, J. Y.; Bai, X. D. Pigm Resin Technol
2007, 36, 90.
7
. Gregory, P. Encyclopedia of Chemical Technology;
Kroschwitz, J. I., Ed.; Wiley: New York, 1993; vol. 8,
p 544.
2+
+
the trend of variation of k1 values is as ME > BG
2−
>
FA , which is similar to the trend of a decrease in
their positive electric charge. In each zone, k2 values
8. Duxbury, D. F. Chem Rev 1993, 93, 381.
9. Available at http://en.wikipedia.org/wiki/malachite
green. Accessed 2013.
+
2+
2−
of the fading reaction of BG , ME , and FA de-
crease with an increase in temperature. With changes in
temperature or cosolvent concentrations, k−1 values of
10. Culp, S. J.; Beland, F. A. Int J Toxicol 1996, 15, 219.
+
2+
2−
2−
11. Alderman, D. J. J Fish Dis 1982, 5, 113.
the fading reaction of BG , ME , BPB , and FA
change in disorderly manner.
1
1
1
1
2. Alderman, D. J. J Fish Dis 1985, 8, 289.
3. Chen, T. C.; Day E. J. Poultry Sci 1974, 53, 1791.
4. Flury M.; Fluhler H. Soil Sci Soc Am J 1995, 59, 22.
5. German-Heins J.; Flury M. Geoderma 2000, 97, 87.
CONCLUSIONS
16. Samiey, B.; Alizadeh, K.; Mousavi, M. F.; Alizadeh, N.
Bull Korean Chem Soc 2005, 26, 384.
+
2+
17. Samiey, B.; Rafi Dargahi, M. React Kinet Mech Catal
2010, 101, 25.
The rate constant of the BG and ME fading reac-
tion increase and those of FA2 and BPB decrease
with an increase in the weight percentages of aqueous
solutions of DMSO and 2-propanol. 2-Propanol and
DMSO interact with TPM molecules through hydro-
gen bonding and ion–dipole interaction, respectively,
in addition to their hydrophobic interaction with TPM
dyes. The fundamental rate constants of the fading re-
action in the binary solvent systems are obtained by
the SESMORTAC model. It was observed that in each
zone with an increase in temperature, k1 values of all
of the used dyes increase and k2 values of the fading re-
−
2−
18. Rudra, L.; Das, M. N. J Chem Soc A 1967, 630.
19. Samiey, B.; Zafari, M. J Chin Chem Soc 2011, 58, 1.
20. Samiey, B.; Raoof Toosi, A. Int J Chem Kinet 2010, 42,
508.
2
2
1. Hughes, E. D. Trans Faraday Soc 1941, 37, 603.
2. Ingold, C. K. Structure and Mechanism in Organic
Chemistry; Bell: London, 1953.
23. Bunton, C. A. Nucleophilic Substitution at a Saturated
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2
2
4. Borin, I. A.; Skaf, M. S. J Chem Phys 1999, 110, 6412.
5. Anchordoguy, T. J.; Carpenter, J. F.; Crowe, J. H.;
Crowe, L. M. Biochim Biophys Acta 1992, 1104, 117.
6. Reichardt, C. Solvents and Solvent Effects in Organic
Chemistry, 2nd Ed.; VCH: Weinheim, Germany, 1998;
pp. 189–207.
+
2+
2−
action of BG , ME , and FA decrease. As referred
in the SESMORTAC model, k−1 and k2 are not pure
rate constants.
2
On the other hand, the effect of electric charge and
substituent groups of a number of TPM dyes includ-
27. Meretoja, A. Acta Chem Scand 1948, 2, 352.
28. Zaghloul, A. A. Int J Chem Kinet 1997, 29, 431.
29. Ismail, A. M.; Zaghloul, A. A. Int J Chem Kinet 1998,
30, 463.
2+
+
+
+
2−
2−
2−
ing ME , BG , MG , CV , FA , PB , BB , and
2−
BPB on their alkaline fading rate was as follows:
3
0. El-Subruiti, G. M. Int J Chem Kinet 2002, 34, 495.
FA2 > ME > MG > BG > CV
−
2+
+
+
+
31. Laidler, K. J.; Landskroener, P. A. Trans Faraday Soc
956, 52, 200.
1
ꢁ
BPB2 > BB > PB
−
2−
2−
32. Akhadov, Y. Y. Dielectric Properties of Binary Solu-
tions; Pergamon Press: Oxford, UK, 1981; p. 462.
˚
33. Akerlof, G. J Am Chem Soc 1932, 54, 4125.
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International Journal of Chemical Kinetics DOI 10.1002/kin.20831