Densities, conductivities, and aggregation numbers of aqueous solutions of quaternary ammonium surfactants with hydroxyethyl substituents in the headgroups

Article abstract of DOI:10.1021/je400463n

The aggregation behaviors of two cationic surfactants, namely, N-dodecyl-N-2-hydroxyethyl-N,N-dimethyl ammonium bromide (C₁₂HDAB) and N-dodecyl-N,N-2-dihydroxyethyl-N-methyl ammonium bromide (C ₁₂DHAB), were studied by measurements of density, conductivity, and steady-state fluorescence quenching. The aggregation number, the volumetric properties, and the standard Gibbs energy (ΔGmic⁰) of micellization were obtained, and the surface area (A_mic) of the surfactant headgroups and the radius (r) of the micelles were estimated. It was found that substituting the methyl group with the hydroxyethyl group in the head of the surfactant led to the increase of the volume change of micellization and the decreases of the critical micelle concentration, association degree of the counterion, and the value of ΔGmic⁰, while the aggregation number of those surfactants in aqueous solutions was little affected by introducing the hydroxyethyl group. It was also found that the values of A _mic and r increase with the hydroxyethyl group.

Full text of DOI:10.1021/je400463n

Article
pubs.acs.org/jced
Densities, Conductivities, and Aggregation Numbers of Aqueous
Solutions of Quaternary Ammonium Surfactants with Hydroxyethyl
Substituents in the Headgroups
†
†
,†,‡
Zhiguo Zhang, Huanhuan Wang, and Weiguo Shen*
†School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
‡Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China
ABSTRACT: The aggregation behaviors of two cationic surfactants, namely, N-dodecyl-N-
2
-hydroxyethyl-N,N-dimethyl ammonium bromide (C HDAB) and N-dodecyl-N,N-2-
12
dihydroxyethyl-N-methyl ammonium bromide (C DHAB), were studied by measurements
12
of density, conductivity, and steady-state fluorescence quenching. The aggregation number,
0
mic
the volumetric properties, and the standard Gibbs energy (ΔG ) of micellization were
obtained, and the surface area (A ) of the surfactant headgroups and the radius (r) of the
mic
micelles were estimated. It was found that substituting the methyl group with the
hydroxyethyl group in the head of the surfactant led to the increase of the volume change of
micellization and the decreases of the critical micelle concentration, association degree of
0
mic
the counterion, and the value of ΔG , while the aggregation number of those surfactants in
aqueous solutions was little affected by introducing the hydroxyethyl group. It was also found that the values of Amic and r
increase with the hydroxyethyl group.
INTRODUCTION
■
Alkyltrimethylammonium bromide surfactants such as dodecyl-
trimethylammonium bromide (DTAB) and cetyltrimethyl-
ammonium bromide (CTAB) are widely applied in practical
fields as antimicrobial agents, fabric softeners, corrosion
1
−4
inhibitors, and catalysts.
Recently, it was found that by
substituting the methyl group with the hydroxylalkyl group in the
head of those surfactants can greatly enhance their efficiency of
catalysis, which was attributed to the formation of the hydrogen
4,5
bonds duo to introduction of the hydroxylalkyl groups. The
micellization of the hydroethyl group substituted surfactants ha6s
been studied using isothermal titration calorimetry (ITC);
however more experimental measurements are required for
understanding the role of the hydroxylalkyl groups in the
physicochemical properties and aggregation behaviors of these
surfactants in aqueous solutions.
In this paper, the micellization properties of two DTAB
derivatives, namely, N-dodecyl-N-2-hydroxyethyl-N,N-dimethyl
ammonium bromide (C HDAB) and N-dodecyl-N,N-2-dihy-
1
2
droxyethyl-N-methyl ammonium bromide (C DHAB), which
1
2
have the same tails with DTAB but one or two hydroxyethyl
substituent groups in the head, respectively, as shown in Figure 1,
are studied by measurements of density, conductivity, and
steady-state fluorescence. The critical micelle concentration
CMC, the volumetric property, the dissociation degree of the
counterions at the micellar state, and the aggregation number of
the micelle are determined. The results are analyzed to obtain the
Gibbs free energy of the micellization and to investigate the role
of the hydroxylethyl group in the self-aggregation of the
surfactants.
Figure 1. Chemical structures of the surfactants studied: a: DTAB, b:
C HDAB, c: C DHAB.
12
12
Received: May 14, 2013
Accepted: July 16, 2013
Published: July 30, 2013
©
2013 American Chemical Society
2326
dx.doi.org/10.1021/je400463n | J. Chem. Eng. Data 2013, 58, 2326−2338

Journal of Chemical & Engineering Data
Article
Table 1. Sources and Purities of the Chemicals
initial mass fraction
purity
purification
method
final mass fraction
analysis
method
chemicals
source
purity
dodecyltrimethylammonium bromide
cetylpyridinium bromide
J&K Chemical Ltd.
0.99
0.98
none
Sinopharm Chemical
Reagent Co.
none
1
-bromododecane
Sinopharm Chemical
Reagent Co.
0.98
0.98
0.98
none
N,N-dimethylethanolamine
N-methyldiethanolamine
Aladdin Chemistry Reagent
Co.
none
Aladdin Chemistry Reagent
Co.
none
N-dodecyl-N-2-hydroxyethyl-N,N-
synthesis
recrystallization
recrystallization
0.998
0.998
element
dimethylammonium bromide
analysis
N-dodecyl-N,N-2-dihydroxyethyl-N-
methylammonium bromide
synthesis
element
analysis
−1
8
EXPERIMENTAL SECTION
cm . The conductivities of surfactant solutions at various
concentrations were determined using a titration method. A
certain amount of water was weighed into the dip-type cell, which
was placed in a water bath where the temperature was controlled
within ± 0.1 K. A surfactant solution with the concentration
■
Chemicals. The chemicals used in this work as well as their
purities and suppliers are listed in Table 1, all of which were used
without further purification; double-distilled water was used in
preparation of all of the surfactant solutions.
Synthesis of N-Dodecyl-N-2-hydroxyethyl-N,N-di-
methyl Ammonium Bromide (C HDAB). C HDAB was
synthesized using the method reported by Tong et al. A sample
of 7.5 g of 1-bromododecane and 3.2 g of N,N-dimethylethanol-
amine were refluxed with 60 mL of acetone at 70 °C for 8 h. After
the reaction was completed, the mixture was cooled to −20 °C,
and a white crystal appeared which was recrystallized in acetone
at least four times; the product was then dried in an evacuated
1
−
being about 210.0 mmol·kg was prepared by weighing and
titrated into cell using a microsyringe; after each titration, the cell
was shaken and then kept undisturbed for thermal equilibrium
before the conductivity measurement. The relative standard
uncertainties in determinations of the conductivity and the
concentration were about ± 0.5 % and 2 %, respectively.
Steady-State Fluorescence Quenching. The steady-state
fluorescence measurements were taken using a fluorimetry
(model FLS 920) supplied by Edinburge Instrument. The
fluorimetry was equipped with a 450 mW Xe arc lamp and a
R928P Hamamatsu PMT detector. The temperature of the
sample for the fluorescence measurement was controlled within
1
2
12
6
1
desiccator for 24 h. A white solid was obtained in 80 % yield. H
NMR (CDCl , 400 MHz) δ: 0.89 (t, J = 6.8 Hz, 3H), 1.27−1.37
3
(
2
m, 18H), 1.73−1.79 (m, 2H), 3.38 (s, 6H), 3.54 (t, J = 8.4 Hz,
H), 3.71 (t, J = 4.6 Hz, 2H), 4.10−4.17 (m, 2H); element
±
0.2 K using a water circulating bath which pumped water into
analysis (% in mass): calculated C, 56.79; H, 10.72; N, 4.14;
found C, 56.70; H, 10.59; N, 4.15.
the sample hold in the fluoremeter. The aggregation number of
the micelle was determined by fluorescence measurement using
pyrene as the probe and cetylpyridinium bromide (CPB) as the
quencher. The samples for steady-state quenching were
prepared as follows: a surfactant/pyrene aqueous solution with
the concentrations of the surfactant and the pyrene being 50.0
Synthesis of N-Dodecyl-N,N-2-dihydroxyethyl-N-
methyl Ammonium Bromide (C DHAB). C DHAB was
12
12
9
synthesized by refluxing 10 g of 1-bromododecane and 5.7 g of
N,N-dimethylethanolamine in 60 mL of acetone at 70 °C for 8 h;
the purification was the same as that of C HDAB which gave a
1
2
−1
−7
−1
1
mmol·kg and 6·10 mol·kg respectively was prepared first. A
proper amount of CPB/ethanol solution with the concentration
of CPB being 20 mmol·kg− was then transferred into a flask;
after removing the solvent ethanol, it was dissolved by the
surfactant/pyrene aqeuous solution to obtain a surfactant/
pyrene/CPB solution with the required concentration of CPB. In
this way, a series of aqueous solutions with the concentrations of
white solid in 78 % yield. H NMR (CDCl , 400 MHz) δ: 0.90 (t,
3
J = 6.8 Hz, 3H), 1.27−1.38 (m, 18H), 1.75−1.78 (m, 2H), 3.35
1
(
(
3
s, 3H), 3.55 (t, J = 8.4 Hz, 2H), 3.71−3.82 (m, 4H), 4.15−4.22
m, 4H); element analysis (% in mass): Calculated: C, 55.43; N,
.80; H, 10.40, found: C, 55.48; N, 3.73; H, 10.42.
Density Measurement. The measurements of the densities
were carried out using a DMA 5000 M vibrating tube densimeter
the quencher being from (1.0 × 10− to 4.5 × 10 ) mol·kg
5
−4
−1
7
from Anton Paar. The apparatus consists of a U-shaped
were prepared for steady-state fluorescence measurements.
During the fluorescence measurements the excitation wave-
length was set at 337 nm, and the emission spectra were scanned
from 360 to 480 nm with a step of 1 nm. The intensities at the
first peak (373 nm) in the absence and presence of the quencher
were measured and used to calculate the aggregation number.
borosilicate glass tube with a platinum resistance thermometer
inside the thermostatic jacket. The precisions in measurements
of the density and the temperature given by the manufacturer
were ± 10−6 g·cm−3 and ± 0.001 K, respectively. At the beginning
of every set of experiments the apparatus was calibrated using dry
air and double-distilled water. The accuracy in the density
−
6
measurements was stated by the manufacturer to be ± 5·10
−3
RESULTS AND DISCUSSION
g·cm . Surfactant solutions with the concentration being about
■
1
−
6
0 mmol·kg were prepared by weighing and then diluted to a
Volumetric Properties. The densities of series of the
DTAB, C HDAB, and C DHAB aqueous solutions at temper-
atures between 293.15 K and 318.15 K in a 5 K interval were
measured, and their values are listed in column 2 of Table 2 for
DTAB, Table 3 for C HDAB, and Table 4 for C DHAB,
series of dilute solutions for density measurements. The
uncertainties of the concentrations were estimated to be about
12
12
0
.05 % of the values.
Conductivity Measurement. Conductivity measurements
12
12
were performed with a CON500 type conductometer from First
Clean Co. using a dip-type cell with a cell constant of 0.893
respectively. The values of the density measured for DTAB
solutions in this work were in good agreement with that reported
2
327
dx.doi.org/10.1021/je400463n | J. Chem. Eng. Data 2013, 58, 2326−2338

Journal of Chemical & Engineering Data
Table 2. Density ρ, Apparent Molar Volume V , Partial Molar Volume V
Article
Φ
̅
, and Isobaric Thermal Expansion Coefficient α for
P
a
DTAB at Different Molalities m under Temperature T = (293.15 to 318.15) K and Pressure p = 0.1 MPa
m/mmol·kg−
1
ρ/g·cm−3
V /cm ·mol
3
−1
3
−1
α ·10 /K
3
−1
T/K
̅
V/cm ·mol
Φ
P
2
93.15
98.15
03.15
0
0.998208
0.998345
0.998368
0.998388
0.998411
0.998434
0.998456
0.998480
0.998503
0.998524
0.998543
0.998556
0.998592
0.998622
0.998695
0.998775
0.998850
0.998918
0.998991
0.999061
0.999145
0.999217
0.997047
0.997176
0.997197
0.997216
0.997237
0.997259
0.997280
0.997302
0.997324
0.997343
0.997363
0.997376
0.997408
0.997435
0.997505
0.997580
0.997647
0.997712
0.997780
0.997845
0.997923
0.997992
0.995649
0.995770
0.995790
0.995807
0.995827
0.995847
0.995866
0.995886
0.995905
0.995923
0.995942
0.995956
0.995986
0.996013
0.996077
0.996147
6
7
7
8
9
.08
.07
.96
.97
.99
286.3 ± 0.3
286.2 ± 0.2
286.2 ± 0.2
286.1 ± 0.2
286.1 ± 0.2
286.1 ± 0.2
286.1 ± 0.2
286.0 ± 0.2
286.1 ± 0.1
286.4 ± 0.1
286.9 ± 0.1
287.4 ± 0.1
288.0 ± 0.1
289.2 ± 0.1
289.7 ± 0.1
290.3 ± 0.1
290.9 ± 0.1
291.2 ± 0.1
291.4 ± 0.1
291.5 ± 0.1
291.7 ± 0.1
286.4 ± 0.3
286.3 ± 0.2
286.4 ± 0.2
286.4 ± 0.2
286.6 ± 0.2
286.9 ± 0.2
287.2 ± 0.2
287.6 ± 0.2
288.3 ± 0.1
289.2 ± 0.1
290.1 ± 0.1
291.6 ± 0.1
292.8 ± 0.1
294.2 ± 0.1
294.1 ± 0.1
294.1 ± 0.1
294.1 ± 0.1
293.8 ± 0.1
293.3 ± 0.1
293.1 ± 0.1
293.5 ± 0.1
0.2173
0.2176
0.2179
0.2182
0.2185
0.2188
0.2193
0.2197
0.2199
0.2198
0.2195
0.2205
0.2208
0.2218
0.2229
0.2241
0.2249
0.2257
0.2266
0.2277
0.2286
10.96
11.99
12.99
13.98
15.03
15.96
18.02
20.01
24.94
29.94
35.01
39.95
45.05
49.73
54.98
60.01
0
2
6
7
7
8
9
.08
.07
.96
.97
.99
287.9 ± 0.3
287.9 ± 0.2
287.9 ± 0.2
287.9 ± 0.2
287.9 ± 0.2
287.8 ± 0.2
287.8 ± 0.2
287.7 ± 0.2
287.9 ± 0.1
288.0 ± 0.1
288.4 ± 0.1
289.0 ± 0.1
289.6 ± 0.1
290.7 ± 0.1
291.2 ± 0.1
291.9 ± 0.1
292.3 ± 0.1
292.7 ± 0.1
292.9 ± 0.1
293.0 ± 0.1
293.1 ± 0.1
288.0 ± 0.3
288.1 ± 0.2
288.1 ± 0.2
288.2 ± 0.2
288.3 ± 0.2
288.5 ± 0.2
288.8 ± 0.2
289.1 ± 0.2
289.8 ± 0.1
290.5 ± 0.1
291.4 ± 0.1
292.9 ± 0.1
294.1 ± 0.1
295.5 ± 0.1
295.5 ± 0.1
295.6 ± 0.1
295.5 ± 0.1
295.1 ± 0.1
294.6 ± 0.1
294.4 ± 0.1
294.7 ± 0.1
0.2598
0.2601
0.2604
0.2607
0.2610
0.2613
0.2617
0.2621
0.2623
0.2623
0.2621
0.2629
0.2632
0.2640
0.2650
0.2661
0.2668
0.2676
0.2685
0.2695
0.2703
0.3025
0.3028
0.3031
0.3034
0.3037
0.3040
0.3043
0.3047
0.3049
0.3050
0.3049
0.3054
0.3057
0.3065
0.3074
0.3082
10.96
11.99
12.99
13.98
15.03
15.96
18.02
20.01
24.94
29.94
35.01
39.95
45.05
49.73
54.98
60.01
0
3
6
7
7
8
9
.08
.07
.96
.97
.99
290.1 ± 0.3
290.0 ± 0.2
290.0 ± 0.2
290.0 ± 0.2
289.9 ± 0.2
289.9 ± 0.2
289.9 ± 0.2
290.0 ± 0.2
290.1 ± 0.1
290.1 ± 0.1
290.4 ± 0.1
290.9 ± 0.1
291.4 ± 0.1
292.4 ± 0.1
292.9 ± 0.1
290.2 ± 0.3
290.1 ± 0.2
290.2 ± 0.2
290.2 ± 0.2
290.3 ± 0.2
290.5 ± 0.2
290.8 ± 0.2
291.1 ± 0.2
291.6 ± 0.1
292.2 ± 0.1
292.8 ± 0.1
294.1 ± 0.1
295.2 ± 0.1
296.6 ± 0.1
296.7 ± 0.1
10.96
11.99
12.99
13.98
15.03
15.96
18.02
20.01
24.94
29.94
2
328
dx.doi.org/10.1021/je400463n | J. Chem. Eng. Data 2013, 58, 2326−2338

Journal of Chemical & Engineering Data
Article
Table 2. continued
m/mmol·kg−
1
ρ/g·cm−3
V /cm ·mol
3
−1
V
̅
/cm ·mol
3
−1
α ·10 /K
3
−1
T/K
Φ
P
3
3
4
4
5
6
5.01
9.95
5.05
9.73
4.98
0.01
0
0.996212
0.996271
0.996336
0.996396
0.996470
0.996535
0.994034
0.994144
0.994162
0.994178
0.994196
0.994214
0.994232
0.994250
0.994268
0.994286
0.994304
0.994320
0.994345
0.994370
0.994432
0.994498
0.994557
0.994615
0.994675
0.994733
0.994801
0.994860
0.992216
0.992319
0.992336
0.992350
0.992367
0.992383
0.992399
0.992416
0.992432
0.992448
0.992466
0.992480
0.992506
0.992532
0.992587
0.992647
0.992706
0.992760
0.992817
0.992871
0.992935
0.992993
0.990212
0.990306
0.990321
0.990334
0.990349
0.990364
0.990379
0.990394
0.990409
0.990424
0.990440
293.4 ± 0.1
293.9 ± 0.1
294.2 ± 0.1
294.4 ± 0.1
294.4 ± 0.1
294.6 ± 0.1
296.8 ± 0.1
296.8 ± 0.1
296.4 ± 0.1
295.9 ± 0.1
295.7 ± 0.1
295.9 ± 0.1
0.3089
0.3097
0.3105
0.3115
0.3122
0.3025
3
08.15
13.15
18.15
6
7
7
8
9
.08
.07
.96
.97
.99
292.2 ± 0.3
292.1 ± 0.2
292.1 ± 0.2
292.1 ± 0.2
292.1 ± 0.2
292.0 ± 0.2
292.1 ± 0.2
292.1 ± 0.2
292.0 ± 0.1
292.1 ± 0.1
292.1 ± 0.1
292.8 ± 0.1
293.2 ± 0.1
294.0 ± 0.1
294.4 ± 0.1
295.0 ± 0.1
295.4 ± 0.1
295.7 ± 0.1
295.8 ± 0.1
295.9 ± 0.1
296.1 ± 0.1
292.2 ± 0.3
292.1 ± 0.2
292.1 ± 0.2
292.1 ± 0.2
292.2 ± 0.2
292.3 ± 0.2
292.5 ± 0.2
292.8 ± 0.2
293.1 ± 0.1
293.6 ± 0.1
294.0 ± 0.1
295.5 ± 0.1
296.5 ± 0.1
297.8 ± 0.1
298.0 ± 0.1
298.1 ± 0.1
297.9 ± 0.1
297.6 ± 0.1
297.3 ± 0.1
297.2 ± 0.1
297.5 ± 0.1
0.3453
0.3456
0.3459
0.3462
0.3466
0.3468
0.3472
0.3475
0.3477
0.3479
0.3478
0.3481
0.3484
0.3491
0.3499
0.3506
0.3512
0.3520
0.3527
0.3537
0.3543
10.96
11.99
12.99
13.98
15.03
15.96
18.02
20.01
24.94
29.94
35.01
39.95
45.05
49.73
54.98
60.01
0
3
6
7
7
8
9
.08
.07
.96
.97
.99
294.4 ± 0.3
294.2 ± 0.2
294.3 ± 0.2
294.2 ± 0.2
294.3 ± 0.2
294.2 ± 0.2
294.2 ± 0.2
294.2 ± 0.2
294.2 ± 0.1
294.1 ± 0.1
294.2 ± 0.1
294.6 ± 0.1
294.9 ± 0.1
295.8 ± 0.1
296.2 ± 0.1
296.6 ± 0.1
296.9 ± 0.1
297.1 ± 0.1
297.3 ± 0.1
297.4 ± 0.1
297.5 ± 0.1
294.3 ± 0.3
294.1 ± 0.2
294.2 ± 0.2
294.1 ± 0.2
294.3 ± 0.2
294.3 ± 0.2
294.4 ± 0.2
294.6 ± 0.2
294.9 ± 0.1
295.1 ± 0.1
295.5 ± 0.1
296.6 ± 0.1
297.5 ± 0.1
299.1 ± 0.1
299.3 ± 0.1
299.2 ± 0.1
299.1 ± 0.1
298.9 ± 0.1
298.5 ± 0.1
298.3 ± 0.1
298.5 ± 0.1
0.3884
0.3887
0.3890
0.3893
0.3896
0.3899
0.3902
0.3905
0.3907
0.3910
0.3910
0.3911
0.3913
0.3919
0.3927
0.3931
0.3938
0.3945
0.3951
0.3961
0.3966
10.96
11.99
12.99
13.98
15.03
15.96
18.02
20.01
24.94
29.94
35.01
39.95
45.05
49.73
54.98
60.01
0
3
6
7
7
8
9
.08
.07
.96
.97
.99
296.1 ± 0.3
296.1 ± 0.2
296.1 ± 0.2
296.1 ± 0.2
296.1 ± 0.2
296.1 ± 0.2
296.1 ± 0.2
296.1 ± 0.2
296.1 ± 0.1
296.1 ± 0.1
296.1 ± 0.3
296.1 ± 0.2
296.1 ± 0.2
296.1 ± 0.2
296.2 ± 0.2
296.2 ± 0.2
296.3 ± 0.2
296.4 ± 0.2
296.6 ± 0.1
296.8 ± 0.1
0.4317
0.4320
0.4323
0.4326
0.4329
0.4332
0.4335
0.4338
0.4340
0.4343
1
1
1
1
1
0.96
1.99
2.99
3.98
5.03
2
329
dx.doi.org/10.1021/je400463n | J. Chem. Eng. Data 2013, 58, 2326−2338

Journal of Chemical & Engineering Data
Article
Table 2. continued
m/mmol·kg−
1
ρ/g·cm−3
V /cm ·mol
3
−1
V
̅
/cm ·mol
3
−1
α ·10 /K
3
−1
T/K
Φ
P
15.96
18.02
20.01
24.94
29.94
35.01
39.95
45.05
49.73
54.98
60.01
0.990454
0.990480
0.990503
0.990558
0.990616
0.990671
0.990721
0.990774
0.990824
0.990883
0.990938
296.1 ± 0.1
296.3 ± 0.1
296.6 ± 0.1
297.3 ± 0.1
297.6 ± 0.1
298.0 ± 0.1
298.3 ± 0.1
298.6 ± 0.1
298.7 ± 0.1
298.8 ± 0.1
298.9 ± 0.1
297.0 ± 0.1
297.8 ± 0.1
298.6 ± 0.1
299.9 ± 0.1
300.3 ± 0.1
300.5 ± 0.1
300.6 ± 0.1
300.4 ± 0.1
300.0 ± 0.1
299.8 ± 0.1
299.9 ± 0.1
0.4344
0.4343
0.4344
0.4350
0.4357
0.4359
0.4366
0.4372
0.4378
0.4387
0.4392
a
−6
−3
−7
The relative standard uncertainty u of m is u (m) = 0.0006; the standard uncertainties u are u(ρ) = 5·10 g·cm , u(T) = 0.01 K, u(α ) = 5·10
r
r
P
−1
K , and u(p) = 10 kPa.
1
0
in the literature. The measured density data were used to
As can be seen from Table 6, the apparent molar volumes at
the micelle state are larger than those at the monomer state for
surfactants at all temperatures studied, which can be attributed to
the release of the structured water molecules around the
surfactants to the less ordered bulk water during the micellization
processes, since the structured water molecules pack more tightly
than the bulk ones.
11
calculate the apparent molar volumes (V ) by:
Φ
3
10 (ρ − ρ)
M
ρ
0
V =
+
Φ
mρ0ρ
(1)
where M and m are the molar mass and the molality of the
surfactant with the units being g·mol and mol·kg ,
respectively; ρ and ρ are the densities of the pure water and
the surfactant solution with the unit being g·cm . The values of
VΦ are listed in column 3 of Table 2, Table 3, and Table 4,
respectively, and they are plotted against the reciprocal molality
in Figure 2a for DTAB, b for C HDAB, and c for C DHAB.
From each of the figures one can see that, in the low surfactant
−
1
−1
The volume change ΔV of the micellization at a certain
mic
mon
0
temperature (ΔV = ΔV − ΔV ) follows the order of DTAB
Φ Φ
−3
< C HDAB < C DHAB. It may be attributed to the different
12 12
extent of the hydrogen bond formation between hydroxylethyl
groups of the nearby heads at the micellar state which causes the
release of water molecules from the hydration shell of the head
groups to the bulk water. This is different from what was
observed in the comparative studies of the micellizations of
dodecyldimethylethylammonium bromide (DTEAB) and
DTAB, where one of the methyl group is substituted by an
ethyl group in the head of DTEAB and there is no hydrogen
bond formation during micellization; hence the volume changes
1
2
12
concentration region, the value of V remains almost constant;
Φ
when the surfactant concentration reaches a certain value it
increases rapidly with the surfactant concentration.
According to the pseudophase separation mode, below the
CMC, all of the surfactant molecules exist in the monomer state,
and thus the apparent molar volume of the surfactant is that of
the monomer
13
of the micellization are almost the same for both surfactants. It
can also be seen from Table 6 that the values of ΔV for all
surfactants decrease with temperature increasing, which may be
attributed to the fact that the increase of temperature loosens the
hydration shell of surfactants; thus the volume difference
occupied by the structured water and the bulk water becomes
smaller.
mon
VΦ = VΦ
m ≤ CMC
(2a)
while above the CMC, the total volume occupied by the
surfactant is the sum of the contributions of the monomer and
the micelle; hence the apparent molar volume VΦ can be
expressed as:
14
̅
The partial molar volume (V) was calculated by
CMC
m
mic
mon
mic
⎛
∂V ⎞
VΦ = VΦ
+
(V
− VΦ
)
m > CMC
Φ
∂m ⎠
Φ
V
̅
= V + m⎜
⎟
Φ
⎝
T,P
(3)
(2b)
where VΦ and V Φm ic are the apparent molar volumes at the
monomer and micellar states, respectively. As can be seen in
Figure 2, the experimental apparent molar volumes for each of
the systems at each of the temperatures are well fitted by two
straight lines; the right horizontal one represents eq 2a, and the
left is described by eq 2b. By least-squares fitting the
experimental data, the slopes and the intercepts of the two
straight lines were obtained, and their intersection was
determined as the CMC. The values of CMC are listed and
compared with the reference values
good agreement within the experimental uncertainties. The
values of the slope CMC (VΦ − V ), the intercept V , and
the CMC allowed us to calculate VΦ for each of the systems at
The values of (∂V /∂m) in eq 3 can be obtained by the
numeric differential of the dependence of V on m determined
by the experiment. The values of the partial molar volumes of
DTAB, C HDAB, and C DHAB at different temperatures are
listed in column 4 of Table 2, Table 3, and Table 4, respectively.
The variation of the partial volume with the molality also showed
the turning points, and the corresponding CMC values were in
consistency with that obtained from the plots of the apparent
molar volume against the reciprocal molarity.
Φ
T,P
Φ
12
12
10,12
in Table 5, which are in
Isobaric Thermal Expansion Coefficient. The isobaric
thermal expansion coefficient (α ) was defined as:
mon
mic
mic
Φ
P
Φ
mon
α = 1
⎛∂V ⎞
mic
mon
⎜
⎟
⎠
various temperatures; the values of VΦ and VΦ are listed in
P
⎝
V ∂T
(4)
Table 6.
P
2
330
dx.doi.org/10.1021/je400463n | J. Chem. Eng. Data 2013, 58, 2326−2338

Journal of Chemical & Engineering Data
Table 3. Density ρ, Apparent Molar Volume V , Partial Molar Volume V
Article
Φ
̅
, and Isobaric Thermal Expansion Coefficient α for
P
a
C HDAB at Different Molalities m under Temperature T = (293.15 to 318.15) K and Pressure p = 0.1 MPa
12
m/mmol·kg−
1
ρ/g·cm−3
V /cm ·mol
3
−1
3
−1
α ·10 /K
3
−1
T/K
̅
V/cm ·mol
Φ
P
2
93.15
98.15
03.15
08.15
7.98
0.998500
0.998537
0.998574
0.998610
0.998646
0.998684
0.998716
0.998747
0.998774
0.998831
0.998886
0.999025
0.999159
0.999299
0.999439
0.999582
0.999714
0.999856
0.997328
0.997364
0.997400
0.997434
0.997468
0.997503
0.997536
0.997566
0.997591
0.997647
0.997700
0.997835
0.997963
0.998101
0.998235
0.998372
0.998500
0.998637
0.995920
0.995954
0.995989
0.996020
0.996053
0.996087
0.996117
0.996147
0.996174
0.996226
0.996278
0.996408
0.996535
0.996667
0.996795
0.996930
0.997055
0.997186
0.994291
0.994324
0.994356
0.994387
0.994418
0.994451
302.2 ± 0.2
302.2 ± 0.2
302.2 ± 0.2
302.1 ± 0.2
302.1 ± 0.2
302.1 ± 0.2
302.3 ± 0.2
302.7 ± 0.1
303.2 ± 0.1
303.9 ± 0.1
304.6 ± 0.1
305.8 ± 0.1
306.8 ± 0.1
307.3 ± 0.1
307.6 ± 0.1
307.9 ± 0.1
308.2 ± 0.1
308.3 ± 0.1
303.9 ± 0.2
303.8 ± 0.2
303.8 ± 0.2
303.8 ± 0.2
303.8 ± 0.2
304.0 ± 0.2
304.0 ± 0.2
304.4 ± 0.1
304.9 ± 0.1
305.5 ± 0.1
306.2 ± 0.1
307.3 ± 0.1
308.3 ± 0.1
308.7 ± 0.1
309.1 ± 0.1
309.3 ± 0.1
309.6 ± 0.1
309.7 ± 0.1
305.9 ± 0.2
305.9 ± 0.2
305.8 ± 0.2
305.9 ± 0.2
305.9 ± 0.2
306.0 ± 0.2
306.1 ± 0.2
306.4 ± 0.1
306.7 ± 0.1
307.4 ± 0.1
307.9 ± 0.1
309.0 ± 0.1
309.8 ± 0.1
310.2 ± 0.1
310.6 ± 0.1
310.8 ± 0.1
311.0 ± 0.1
311.2 ± 0.1
308.0 ± 0.2
307.9 ± 0.2
308.0 ± 0.2
308.0 ± 0.2
307.9 ± 0.2
308.0 ± 0.2
302.0 ± 0.2
302.0 ± 0.2
302.0 ± 0.2
302.1 ± 0.2
302.7 ± 0.2
304.1 ± 0.2
305.9 ± 0.2
307.8 ± 0.1
309.3 ± 0.1
310.7 ± 0.1
310.9 ± 0.1
311.2 ± 0.1
311.2 ± 0.1
310.0 ± 0.1
309.8 ± 0.1
310.3 ± 0.1
310.6 ± 0.1
309.9 ± 0.1
303.7 ± 0.2
303.7 ± 0.2
303.7 ± 0.2
303.8 ± 0.2
304.4 ± 0.2
305.8 ± 0.2
307.4 ± 0.2
309.6 ± 0.1
311.0 ± 0.1
311.9 ± 0.1
311.9 ± 0.1
312.6 ± 0.1
312.5 ± 0.1
310.9 ± 0.1
311.4 ± 0.1
311.7 ± 0.1
311.9 ± 0.1
311.1 ± 0.1
305.8 ± 0.2
305.9 ± 0.2
305.9 ± 0.2
306.2 ± 0.2
306.6 ± 0.2
307.6 ± 0.2
308.8 ± 0.2
310.2 ± 0.1
311.5 ± 0.1
313.1 ± 0.1
313.4 ± 0.1
313.6 ± 0.1
313.4 ± 0.1
312.8 ± 0.1
312.6 ± 0.1
312.5 ± 0.1
313.1 ± 0.1
313.0 ± 0.1
307.9 ± 0.2
307.8 ± 0.2
307.9 ± 0.2
307.9 ± 0.2
308.2 ± 0.2
308.9 ± 0.2
0.2177
0.2180
0.2183
0.2188
0.2191
0.2195
0.2197
0.2196
0.2199
0.2204
0.2209
0.2215
0.2224
0.2231
0.2245
0.2252
0.2257
0.2272
0.2603
0.2605
0.2608
0.2612
0.2615
0.2619
0.2621
0.2621
0.2622
0.2627
0.2630
0.2638
0.2645
0.2652
0.2663
0.2670
0.2676
0.2688
0.3030
0.3033
0.3035
0.3039
0.3042
0.3045
0.3047
0.3047
0.3047
0.3051
0.3053
0.3061
0.3067
0.3074
0.3083
0.3090
0.3097
0.3106
0.3459
0.3462
0.3465
0.3467
0.3470
0.3472
9
.00
10.03
10.99
11.95
13.00
13.95
14.98
15.95
17.93
19.91
24.89
29.94
34.93
39.90
44.93
49.82
54.88
7.98
2
3
3
9
.00
10.03
10.99
11.95
13.00
13.95
14.98
15.95
17.93
19.91
24.89
29.94
34.93
39.90
44.93
49.82
54.88
7.98
9
.00
10.03
10.99
11.95
13.00
13.95
14.98
15.95
17.93
19.91
24.89
29.94
34.93
39.90
44.93
49.82
54.88
7.98
9
.00
10.03
10.99
11.95
13.00
2
331
dx.doi.org/10.1021/je400463n | J. Chem. Eng. Data 2013, 58, 2326−2338

Journal of Chemical & Engineering Data
Article
Table 3. continued
m/mmol·kg−
1
ρ/g·cm−3
V /cm ·mol
3
−1
V
̅
/cm ·mol
3
−1
α ·10 /K
3
−1
T/K
Φ
P
1
1
1
1
1
2
2
3
3
4
4
5
3.95
4.98
5.95
7.93
9.91
4.89
9.94
4.93
9.90
4.93
9.82
4.88
7.98
0.994481
0.994511
0.994537
0.994588
0.994637
0.994766
0.994888
0.995018
0.995142
0.995274
0.995395
0.995520
0.992462
0.992494
0.992525
0.992554
0.992584
0.992616
0.992644
0.992676
0.992701
0.992750
0.992800
0.992920
0.993043
0.993170
0.993291
0.993419
0.993537
0.993660
0.990446
0.990476
0.990506
0.990534
0.990562
0.990593
0.990621
0.990650
0.990679
0.990727
0.990776
0.990893
0.991013
0.991136
0.991254
0.991378
0.991490
0.991613
308.0 ± 0.2
308.2 ± 0.1
308.4 ± 0.1
309.1 ± 0.1
309.7 ± 0.1
310.5 ± 0.1
311.3 ± 0.1
311.6 ± 0.1
312.0 ± 0.1
312.1 ± 0.1
312.4 ± 0.1
312.6 ± 0.1
310.3 ± 0.2
310.1 ± 0.2
310.1 ± 0.2
310.1 ± 0.2
310.0 ± 0.2
310.0 ± 0.2
310.1 ± 0.2
310.0 ± 0.1
310.3 ± 0.1
310.9 ± 0.1
311.3 ± 0.1
312.3 ± 0.1
312.9 ± 0.1
313.1 ± 0.1
313.4 ± 0.1
313.6 ± 0.1
313.8 ± 0.1
313.9 ± 0.1
312.1 ± 0.2
312.1 ± 0.2
312.0 ± 0.2
312.0 ± 0.2
312.0 ± 0.2
311.9 ± 0.2
311.9 ± 0.2
312.0 ± 0.1
311.9 ± 0.1
312.4 ± 0.1
312.8 ± 0.1
313.7 ± 0.1
314.3 ± 0.1
314.5 ± 0.1
314.8 ± 0.1
314.9 ± 0.1
315.2 ± 0.1
315.3 ± 0.1
309.8 ± 0.2
311.2 ± 0.1
312.5 ± 0.1
314.3 ± 0.1
314.7 ± 0.1
314.6 ± 0.1
314.7 ± 0.1
313.9 ± 0.1
313.9 ± 0.1
313.7 ± 0.1
314.6 ± 0.1
314.8 ± 0.1
309.8 ± 0.2
309.6 ± 0.2
309.7 ± 0.2
309.7 ± 0.2
309.8 ± ± 0.2
310.3 ± 0.2
311.0 ± 0.2
312.0 ± 0.1
313.4 ± 0.1
315.4 ± 0.1
316.0 ± 0.1
316.2 ± 0.1
315.2 ± 0.1
315.0 ± 0.1
315.1 ± 0.1
315.0 ± 0.1
315.7 ± 0.1
315.6 ± 0.1
311.8 ± 0.2
311.7 ± 0.2
311.6 ± 0.2
311.6 ± 0.2
311.6 ± 0.2
311.8 ± 0.2
312.1 ± 0.2
312.9 ± 0.1
313.7 ± 0.1
315.9 ± 0.1
316.9 ± 0.1
317.5 ± 0.1
316.5 ± 0.1
316.4 ± 0.1
316.4 ± 0.1
316.7 ± 0.1
317.0 ± 0.1
316.1 ± 0.1
0.3474
0.3475
0.3473
0.3477
0.3478
0.3487
0.3491
0.3498
0.3505
0.3512
0.3519
0.3526
0.3890
0.3893
0.3896
0.3898
0.3901
0.3902
0.3904
0.3905
0.3902
0.3905
0.3906
0.3916
0.3918
0.3924
0.3929
0.3936
0.3944
0.3947
0.4324
0.4327
0.4330
0.4331
0.4334
0.4335
0.4337
0.4337
0.4333
0.4336
0.4336
0.4346
0.4347
0.4353
0.4356
0.4362
0.4371
0.4372
313.15
9
.00
10.03
10.99
11.95
13.00
13.95
14.98
15.95
17.93
19.91
24.89
29.94
34.93
39.90
44.93
49.82
54.88
7.98
318.15
9
.00
1
1
1
1
1
1
1
1
1
2
2
3
3
4
4
5
0.03
0.99
1.95
3.00
3.95
4.98
5.95
7.93
9.91
4.89
9.94
4.93
9.90
4.93
9.82
4.88
a
−6
−3
−7
The relative standard uncertainty u of m is u (m) = 0.0006; the standard uncertainties u are u(ρ) = 5·10 g·cm , u(T) = 0.01 K, u(α ) = 5·10
r
r
P
−1
K , and u(p) = 10 kPa.
where V is the volume of the sample. Equation 4 can be rewritten
C HDAB, and C DHAB at six different temperatures are listed
12 12
as:
in column 5 of Table 2, Table 3, and Table 4, respectively; the
uncertainty in determination of α was estimated to be about ±
P
αP = − 1
⎛ ∂ρ ⎞
−
7
−1
5
·10 K . As an example, a typical plot of the isobaric thermal
⎜
⎟
⎠
⎝
expansion coefficient against the molality of DTAB at 303.15 K is
ρ ∂T
(5)
P
illustrated in Figure 3. It can be observed that α increases with
P
The values of (∂ρ/∂T) in eq 5 can be obtained by differential of
the concentration of the surfactant, which may be interpreted by
that increase of the amount of the surfactant in an aqueous
solution results in the increase of the structured water molecules
around the surfactant, hence in the increase of the amount of the
P
the dependence of ρ on T, which was well-expressed by a
quadratic form. The values of isobaric thermal expansion
coefficients calculated by eq 5 for aqueous solutions of DTAB,
2
332
dx.doi.org/10.1021/je400463n | J. Chem. Eng. Data 2013, 58, 2326−2338

Journal of Chemical & Engineering Data
Table 4. Density ρ, Apparent Molar Volume V , Partial Molar Volume V
Article
Φ
̅
, and Isobaric Thermal Expansion Coefficient α for
P
a
C DHAB at Different Molalities m under Temperature T = (293.15 to 318.15) K and Pressure p = 0.1 MPa
12
m/mmol·kg−
1
ρ/g·cm−3
V /cm ·mol
3
−1
3
−1
α ·10 /K
3
−1
T/K
̅
V/cm ·mol
Φ
P
2
93.15
98.15
03.15
4.97
0.998465
0.998521
0.998568
0.998622
0.998675
0.998722
0.998774
0.998818
0.998867
0.998915
0.998953
0.998993
0.999080
0.999160
0.999367
0.999571
0.999778
0.999983
1.000187
1.000398
0.997294
0.997349
0.997394
0.997446
0.997498
0.997544
0.997597
0.997641
0.997686
0.997734
0.997771
0.997811
0.997897
0.997976
0.998178
0.998380
0.998580
0.998782
0.998981
0.999187
0.995890
0.995942
0.995986
0.996036
0.996086
0.996130
0.996180
0.996222
0.996268
0.996315
0.996353
0.996394
0.996476
0.996554
0.996752
0.996950
0.997146
0.997344
0.997539
0.997740
317.0 ± 0.3
317.2 ± 0.3
317.2 ± 0.3
317.3 ± 0.2
317.3 ± 0.2
317.4 ± 0.2
317.7 ± 0.2
317.9 ± 0.2
318.2 ± 0.2
318.7 ± 0.2
319.1 ± 0.1
319.8 ± 0.1
320.6 ± 0.1
321.2 ± 0.1
322.5 ± 0.1
323.4 ± 0.1
323.8 ± 0.1
324.2 ± 0.1
324.4 ± 0.1
324.6 ± 0.1
319.4 ± 0.3
319.4 ± 0.3
319.4 ± 0.3
319.5 ± 0.2
319.4 ± 0.2
319.4 ± 0.2
319.4 ± 0.2
319.6 ± 0.2
320.1 ± 0.2
320.4 ± 0.2
320.9 ± 0.1
321.5 ± 0.1
322.1 ± 0.1
322.6 ± 0.1
323.9 ± 0.1
324.7 ± 0.1
325.2 ± 0.1
325.6 ± 0.1
325.7 ± 0.1
325.9 ± 0.1
321.6 ± 0.3
321.7 ± 0.3
321.6 ± 0.3
321.7 ± 0.2
321.7 ± 0.2
321.7 ± 0.2
321.8 ± 0.2
322.0 ± 0.2
322.2 ± 0.2
322.5 ± 0.2
322.8 ± 0.1
323.2 ± 0.1
323.9 ± 0.1
324.4 ± 0.1
325.6 ± 0.1
326.3 ± 0.1
326.8 ± 0.1
327.1 ± 0.1
327.2 ± 0.1
327.4 ± 0.1
317.5 ± 0.3
317.6 ± 0.3
317.5 ± 0.3
317.7 ± 0.2
318.1 ± 0.2
318.9 ± 0.2
320.2 ± 0.2
321.5 ± 0.2
323.2 ± 0.2
325.4 ± 0.2
327.0 ± 0.1
327.7 ± 0.1
326.9 ± 0.1
327.1 ± 0.1
327.9 ± 0.1
327.2 ± 0.1
326.7 ± 0.1
326.5 ± 0.1
325.9 ± 0.1
326.7 ± 0.1
319.4 ± 0.3
319.4 ± 0.3
319.5 ± 0.3
319.5 ± 0.2
319.3 ± 0.2
319.6 ± 0.2
320.9 ± 0.2
322.8 ± 0.2
325.0 ± 0.2
326.7 ± 0.2
328.0 ± 0.1
328.4 ± 0.1
327.7 ± 0.1
328.1 ± 0.1
329.0 ± 0.1
328.4 ± 0.1
328.4 ± 0.1
327.4 ± 0.1
327.2 ± 0.1
328.1 ± 0.1
321.8 ± 0.3
321.9 ± 0.3
321.7 ± 0.3
321.8 ± 0.2
321.8 ± 0.2
322.3 ± 0.2
323.2 ± 0.2
324.3 ± 0.2
325.5 ± 0.2
326.9 ± 0.2
328.1 ± 0.1
329.1 ± 0.1
329.4 ± 0.1
329.4 ± 0.1
330.2 ± 0.1
329.6 ± 0.1
329.6 ± 0.1
328.7 ± 0.1
328.5 ± 0.1
329.5 ± 0.1
0.2172
0.2176
0.2180
0.2184
0.2187
0.2190
0.2192
0.2193
0.2195
0.2198
0.2197
0.2198
0.2205
0.2205
0.2214
0.2219
0.2233
0.2239
0.2248
0.2258
0.2596
0.2600
0.2603
0.2607
0.2610
0.2613
0.2615
0.2617
0.2618
0.2620
0.262
6.07
6.98
8.05
9.09
10.02
11.09
12.02
13.06
14.14
15.05
16.09
18.15
20.08
25.18
30.23
35.25
40.28
45.12
50.25
4.97
2
6.07
6.98
8.05
9.09
10.02
11.09
12.02
13.06
14.14
15.05
16.09
18.15
20.08
25.18
30.23
35.25
40.28
45.12
50.25
4.97
0.2621
0.2626
0.2628
0.2635
0.2641
0.2652
0.2658
0.2666
0.2675
0.3022
0.3026
0.3029
0.3032
0.3035
0.3038
0.3040
0.3042
0.3043
0.3044
0.3044
0.3045
0.3049
0.3052
0.3058
0.3064
0.3072
0.3078
0.3086
0.3093
3
6.07
6.98
8.05
9.09
10.02
11.09
12.02
13.06
14.14
15.05
16.09
18.15
20.08
25.18
30.23
35.25
40.28
45.12
50.25
2
333
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Journal of Chemical & Engineering Data
Article
Table 4. continued
m/mmol·kg−
1
ρ/g·cm−3
V /cm ·mol
3
−1
3
−1
α ·10 /K
3
−1
T/K
̅
V/cm ·mol
Φ
P
3
08.15
13.15
18.15
4.97
0.994266
0.994317
0.994359
0.994408
0.994456
0.994499
0.994548
0.994590
0.994637
0.994681
0.994719
0.994756
0.994837
0.994913
0.995110
0.995305
0.995497
0.995692
0.995884
0.996082
0.992443
0.992492
0.992533
0.992580
0.992626
0.992667
0.992714
0.992755
0.992801
0.992847
0.992884
0.992923
0.993001
0.993076
0.993267
0.993460
0.993649
0.993840
0.994027
0.994223
0.990430
0.990478
0.990518
0.990564
0.990609
0.990649
0.990695
0.990735
0.990780
0.990825
0.990862
0.990900
0.990980
0.991051
0.991242
0.991431
0.991620
0.991807
0.991991
0.992184
323.7 ± 0.3
323.7 ± 0.3
323.7 ± 0.3
323.7 ± 0.2
323.7 ± 0.2
323.7 ± 0.2
323.7 ± 0.2
323.8 ± 0.2
323.8 ± 0.2
324.2 ± 0.2
324.4 ± 0.1
325.1 ± 0.1
325.7 ± 0.1
326.1 ± 0.1
327.1 ± 0.1
327.7 ± 0.1
328.2 ± 0.1
328.4 ± 0.1
328.5 ± 0.1
328.7 ± 0.1
325.8 ± 0.3
325.9 ± 0.3
325.8 ± 0.3
325.9 ± 0.2
325.9 ± 0.2
325.9 ± 0.2
326.0 ± 0.2
326.0 ± 0.2
326.0 ± 0.2
326.1 ± 0.2
326.3 ± 0.1
326.7 ± 0.1
327.4 ± 0.1
327.7 ± 0.1
328.7 ± 0.1
329.2 ± 0.1
329.7 ± 0.1
329.9 ± 0.1
330.0 ± 0.1
330.1 ± 0.1
327.8 ± 0.3
327.8 ± 0.3
327.7 ± 0.3
327.7 ± 0.2
327.7 ± 0.2
327.7 ± 0.2
327.7 ± 0.2
327.7 ± 0.2
327.7 ± 0.2
327.8 ± 0.2
328.0 ± 0.1
328.4 ± 0.1
328.8 ± 0.1
329.3 ± 0.1
330.1 ± 0.1
330.6 ± 0.1
330.9 ± 0.1
331.2 ± 0.1
331.3 ± 0.1
331.4 ± 0.1
323.7 ± 0.3
323.7 ± 0.3
323.7 ± 0.3
323.7 ± 0.2
323.6 ± 0.2
323.7 ± 0.2
324.2 ± 0.2
325.0 ± 0.2
326.6 ± 0.2
328.8 ± 0.2
330.3 ± 0.1
331.4 ± 0.1
330.8 ± 0.1
330.5 ± 0.1
330.9 ± 0.1
330.9 ± 0.1
330.8 ± 0.1
329.7 ± 0.1
329.6 ± 0.1
330.6 ± 0.1
325.9 ± 0.3
325.9 ± 0.3
325.9 ± 0.3
326.1 ± 0.2
326.2 ± 0.2
326.2 ± 0.2
326.2 ± 0.2
326.4 ± 0.2
327.1 ± 0.2
328.7 ± 0.2
330.4 ± 0.1
331.9 ± 0.1
332.3 ± 0.1
332.1 ± 0.1
332.3 ± 0.1
331.8 ± 0.1
332.1 ± 0.1
331.3 ± 0.1
331.0 ± 0.1
331.3 ± 0.1
327.5 ± 0.3
327.5 ± 0.3
327.4 ± 0.3
327.6 ± 0.2
327.7 ± 0.2
327.8 ± 0.2
327.8 ± 0.2
328.0 ± 0.2
328.6 ± 0.2
329.9 ± 0.2
331.3 ± 0.1
332.5 ± 0.1
333.3 ± 0.1
333.7 ± 0.1
333.2 ± 0.1
332.9 ± 0.1
333.0 ± 0.1
332.7 ± 0.1
332.1 ± 0.1
332.5 ± 0.1
0.3450
0.3453
0.3456
0.3459
0.3462
0.3465
0.3467
0.3469
0.3470
0.3471
0.3471
0.3472
0.3474
0.3478
0.3483
0.3488
0.3494
0.3500
0.3507
0.3513
0.3880
0.3883
0.3885
0.3887
0.3891
0.3894
0.3897
0.3898
0.3898
0.3899
0.3899
0.3900
0.3901
0.3906
0.3910
0.3916
0.3918
0.3925
0.3932
0.3935
0.4312
0.4315
0.4317
0.4319
0.4322
0.4325
0.4329
0.4330
0.4330
0.4330
0.4330
0.4331
0.4331
0.4336
0.4339
0.4345
0.435
6.07
6.98
8.05
9.09
10.02
11.09
12.02
13.06
14.14
15.05
16.09
18.15
20.08
25.18
30.23
35.25
40.28
45.12
50.25
4.97
3
6.07
6.98
8.05
9.09
10.02
11.09
12.02
13.06
14.14
15.05
16.09
18.15
20.08
25.18
30.23
35.25
40.28
45.12
50.25
4.97
3
6.07
6.98
8.05
9.09
10.02
11.09
12.02
13.06
14.14
15.05
16.09
18.15
20.08
25.18
30.23
35.25
40.28
45.12
50.25
0.4352
0.4358
0.4360
2
334
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Journal of Chemical & Engineering Data
Article
Table 4. continued
a
−6
−3
−7
The relative standard uncertainty u of m is u (m) = 0.0006; the standard uncertainties u are u(ρ) = 5·10 g·cm , u(T) = 0.01 K, u(α ) = 5·10
r
r
P
−1
K , and u(p) = 10 kPa.
concentration coincides well with the CMC value for DTAB at
03.15 K. Similar discontinuities and the consistency in the CMC
values were observed for aqueous solutions of C HDAB,
3
1
2
C DHAB, and DTAB at all temperatures studied. After the
12
micellization, the amount of the structured water around the
surfactant significantly reduces; thus the discontinuities on the
plots of α against the concentration of the surfactant are
P
expected.
i
P
The apparent thermal expansion coefficient α (i = monomer
or micellar state) of the surfactant at the monomer state or the
micellar state can be calculated through
i
i
⎛
⎜
⎞
⎛
⎞
⎟
1
∂V
1 ∂ρ
i
Φ
α =
⎟ = −
⎜
P
i
i
V ⎝ ∂T ⎠
ρ ⎝ ∂T ⎠
Φ
(6)
P
P
i
ρ
The values of (∂ /∂T) in eq 6 can be obtained by differential of
the dependences of ρ on T, which were well-described by linear
P
i
forms for both monomer and micellar states of all systems we
i
studied. Table 6 also lists the values of α , from which one can see
P
mic
that at the micellar state αP decreases with the increase of the
hydroxyethyl substituent number, which may be attributed to the
fact that the hydrogen bonding formation between hydroxyethyl
groups disorders the structured water around the headgroups,
which reduces the extent to further loosen their structure order
during increasing the temperature; while at the monomer state,
the distinction between C HDAB and C DHA in the isobaric
12
12
mon
thermal expansion αP is not obvious, because the hydrogen
bonding between the headgroups hardly forms in the dilute
surfactant monomer aqueous solutions.
Micellization Thermodynamics. The conductivity is
plotted against the concentration for each of surfactant solutions
and each of the temperatures in Figure 4a for C HDAB and
1
2
Figure 2. Dependence of the apparent molar volume on the reprocical
Figure 4b for C DHAB, respectively, from which one can clearly
12
molality of the surfactants: a, DTAB; b, C HDAB; c, C DHAB. The
12
12
see a turning point for each of the curves. By least-squares fitting
of the experiment data before and after the point, two straight
lines can be obtained whose intersection was taken as the CMC.
The values of the CMC obtained by the conductivity
measurements are listed in row 6 for C HDAB and row 10 for
symbols represent the experimental data: ☆, 318.15 K; ●, 313.15 K; △,
3
08.15 K; ▲, 303.15 K; ○, 298.15 K; ■, 293.15 K; the lines are the
results of the fits.
12
structured water being loosened due to increase of the
temperature. There is a clear discontinuity in the plot of αP
against the concentration as shown in Figure 3, where the
C DHAB in Table 5. The CMC values detected by using the
conductivity method were in good consistence with that
determined by measurements of the density and agreed well
12
a
Table 5. CMC Values of DTAB, C12HDAB, and C12DHAB at Temperature T = (293.15 to 318.15) K and Pressure p = 0.1 MPa
T/K
293.15
298.15
303.15
DTAB
308.15
313.15
318.15
dm
−1
CMC /mmol·kg
14.3 ± 0.3
14.7 ± 0.4
15.4 ± 0.4
15.9 ± 0.3
16.4 ± 0.4
17.6 ± 0.7
r
−1
b
b
b
c
b
b
b
CMC /mmol·L
14.3
14.6
15.1 ,15.3
15.9
16.6
17.5
C HDAB
12
CMCcm/mmol·kg−1
13.1 ± 0.4
13.7 ± 0.3
13.4 ± 0.7
13.9 ± 0.4
13.20
13.5 ± 0.7
14.1 ± 0.4
13.9 ± 0.6
14.5 ± 0.3
13.92
14.2 ± 0.5
14.9 ± 0.3
14.22
14.9 ± 0.8
15.6 ± 0.3
14.83
dm
−1
CMC /mmol·kg
r
−1
d
d
d
d
d
CMC /mmol·L
13.43
C DHAB
12
CMCcm/mmol·kg−1
12.1 ± 0.3
12.1 ± 0.3
12.3 ± 0.4
12.4 ± 0.4
12.46
12.6 ± 0.5
12.6 ± 0.4
13.0 ± 0.5
13.0 ± 0.2
13.09
13.3 ± 0.7
13.5 ± 0.6
13.36
13.8 ± 0.6
13.9 ± 0.4
13.89
dm
−1
CMC /mmol·kg
r
−1
d
d
d
d
d
CMC /mmol·L
12.62
a
cm
dm
r
CMC : determined by conductivity measurement in this work, CMC : determined by density measurement in this work, CMC : from reference.
b
c
d
The standard uncertainties u are u(T) = 0.01 K and u(p) = 10 kPa. Reference 10. Reference 12. Reference 6.
2
335
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Journal of Chemical & Engineering Data
Article
Table 6. Volumetric Properties of DTAB, C HDAB, and C DHAB at Monomer and Micellar States at Temperature T = (293.15
1
2
12
a
to 318.15) K and Pressure p = 0.1 MPa
T/K
293.15
298.15
287.9 ± 0.1
303.15
DTAB
308.15
313.15
318.15
VΦmon/cm ·mol
3
−1
286.1 ± 0.1
293.4 ± 0.1
7.3 ± 0.2
290.0 ± 0.1
296.3 ± 0.1
6.3 ± 0.2
292.1 ± 0.1
294.1 ± 0.1
298.7 ± 0.1
4.6 ± 0.2
296.1 ± 0.1
300.2 ± 0.1
4.1 ± 0.2
b
b
2
88.2
292.2
VΦmic/cm ·mol
3
−1
294.7 ± 0.2
297.5 ± 0.1
b
b
2
94.8
6.8 ± 0.3
297.5
3
−1
ΔV/cm ·mol
5.4 ± 0.2
b
b
6
.6
5.3
αmon·10 /K
3
−1
1.4086
0.9167
1.3996
0.9127
1.3899
0.9080
1.3797
0.9042
1.3702
0.9005
1.3613
0.8961
αmic·10 /K
3
−1
C HDAB
12
mon
3
−1
VΦ /cm ·mol
302.1 ± 0.2
310.5 ± 0.1
8.4 ± 0.3
1.3091
303.9 ± 0.2
311.8 ± 0.1
7.9 ± 0.3
1.3012
305.9 ± 0.2
313.1 ± 0.1
7.2 ± 0.3
1.2927
307.9 ± 0.1
314.2 ± 0.1
6.3 ± 0.2
1.2841
310.0 ± 0.1
315.5 ± 0.1
5.5 ± 0.2
1.2757
311.8 ± 0.1
316.7 ± 0.1
4.9 ± 0.2
1.2680
mic
3
−1
VΦ /cm ·mol
3
−1
ΔV/cm ·mol
mon
3
−1
α
·10 /K
αmic·10 /K
3
−1
0.7948
0.7915
0.7883
0.7854
0.7824
0.7792
C DHAB
12
mon
3
−1
VΦ /cm ·mol
317.4 ± 0.1
327.1 ± 0.1
9.7 ± 0.2
1.3104
319.3 ± 0.1
328.3 ± 0.1
9.0 ± 0.2
1.3025
321.7 ± 0.1
329.4 ± 0.1
7.7 ± 0.2
1.2929
323.7 ± 0.1
330.6 ± 0.1
6.9 ± 0.2
1.2849
325.8 ± 0.1
331.9 ± 0.1
6.1 ± 0.2
1.2766
327.6 ± 0.1
333.0 ± 0.1
5.4 ± 0.2
1.2694
mic
3
−1
VΦ /cm ·mol
3
−1
ΔV/cm ·mol
mon
3
−1
αP ·10 /K
αPmic·10 /K
3
−1
0.7268
0.7241
0.7216
0.7190
0.7162
0.7139
a
i
−7 −1
b
The standard uncertainties u are u(α ) = 5·10 K , u(T) = 0.01 K, and u(p) = 10 kPa. Reference 20.
P
Figure 3. Illustration of dependence of isobaric thermal expansion
coefficients of the DTAB aqueous solutions on the concentration at
2
93.15 K.
6
with those reported in the literature. It can also be found that the
values of CMC slightly increase with the temperature for all three
surfactants. This phenomenon was commonly reported for the
ionic surfactants and can be explained by that the hydrophobic
interaction of the surfactant tails becomes weaker and the static
repulsion between the headgroups is strengthened due to the
decrease of the association degree of the counterion when
temperature increases, both of which hinder the micelle
formation. The CMC values of the three surfactants follow the
order of DTAB > C HDAB > C DHAB at the same
temperature. As mentioned above, the formation of hydrogen
bonds between hydroxyethyl groups in micelles is enhanced by
increase of the hydroxyethyl substituents in the headgroup,
which leads to the micellization at the relatively lower surfactant
concentration.
Figure 4. Variation of the conductivity with the concentration of the
surfactants in aqueous solutions: a, C HDAB; b, C DHAB. The
12
12
symbols represent the experimental data: ☆, 318.15 K; ●, 313.15 K; △,
3
08.15 K; ▲, 303.15 K; ○, 298.15 K; ■, 293.15 K, the lines are results of
1
2
12
the fits.
listed in row 3 for C HDAB and row 7 for C DHAB of Table 7,
12
12
respectively. As can be seen from Table 7, the values of β for both
surfactants decrease with the increase of temperature, which is
commonly observed for ionic surfactants and may be attributed
to increase of the dissociation entropy of counterions with
temperature. At a certain temperature the value of β decreases
with the increase of the substituent hydroxyethyl group, which is
in consistent with what was observed by Chatterjee et al. in their
The slopes of the plot of the conductivity against the
concentration of the surfactant in the post-CMC region (k)
and the pre-CMC region (k′) in Figure 4 were used to calculate
the dissociation degree (α) of the counterions by α = k/k′, and
the association degree (β) was obtained by β = 1 − α, which is
2
336
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Journal of Chemical & Engineering Data
Article
0
mic
Table 7. Association Degree of the Counterions β and Standard Gibbs Free Energy Change ΔG , of Micellization for C HDAB
12
a
and C DHAB at Temperature T = (293.15 to 318.15) K and Pressure p = 0.1 MPa
12
T/K
293.15
298.15
303.15
308.15
313.15
318.15
C HDAB
12
β
0.766 ± 0.005
−35.94 ± 0.44
0.764 ± 0.005
0.761 ± 0.005
−36.91 ± 0.48
−41.97
0.758 ± 0.005
−37.33 ± 0.47
−42.48
0.756 ± 0.005
−37.78 ± 0.47
−43.06
0.754 ± 0.005
−38.10 ± 0.50
−43.52
ΔG /KJ·mol−1
0
−36.42 ± 0.48
mic
b
b
b
b
b
−
41.37
C DHAB
12
β
0.764 ± 0.005
−36.24 ± 0.43
0.758 ± 0.005
0.753 ± 0.005
−37.06 ± 0.46
0.748 ± 0.005
−37.40 ± 0.46
−42.80
0.743 ± 0.005
−37.81 ± 0.50
−43.39
0.740 ± 0.005
−38.17 ± 0.48
−43.87
ΔG /KJ·mol−1
0
−36.65 ± 0.45
b
mic
b
b
b
b
−
41.65
−42.29
a
b
The standard uncertainties u are u(T) = 0.05 K and u(p) = 10 kPa. Reference 6.
studies of the series of hydroxyethyl substituted cetylammonium
15
bromide surfactants. This may be attributed to the fact that the
volume of the hydroxyethyl group is larger than that of the
methyl group which leads to the increase of the distance and
hence the decrease of the positive charge density on the micelle
interface; thus the binding ability of negatively charged
counterions to the micelle surface is reduced.
The micellization of a one mole single tail ionic surfactant may
be interpreted by that it reacts with β mole counterions. Thus the
0
mic
standard Gibbs free energy ΔG of micellization may be defined
by the change of the Gibbs free energy in an ideal dilute
surfactant solution with the surfactant concentration being 1
−1
0
16
Figure 5. Dependence of ln(I /I) on the concentration of the quencher.
0
mol·kg . The value of ΔG may be calculated by
mic
The symbols represent the experimental data: ■, C HDAB (C = 50.0
1
2
0
0
−1
●
−1
mmol·kg ); , C DHAB (C = 50.0 mmol·kg ); the lines are the
ΔG = (1 + β)RT ln(CMC/m )
(7)
12
mic
results of the fits.
where m =1 mol·kg −1. The values of ΔG for C HDAB and
C DHAB are listed in Table 7 and compared with those
0
0
mic
12
The radius (r) of the micelle formed by the surfactant can be
calculated using the volumetric data and the aggregation number
through a simple geometric model:
1
2
obtained by using the isothermal titration calorimetry reported
6
by Tong et al. The differences were mainly resulted from the
contributions of the association degree of the counterions at the
mic
6
V = 43 πr =
N(V − αVBr
−
)
3
Φ
micellar state, which were neglected by Tong et al. As it can be
m
0
mic
seen from eq 7 the absolute value of ΔG should decrease with
NA
(9)
β; however it increases, and β decreases with the increase of
where V is the volume of a micelle, N is the Avogadro constant,
and VBr is the volume of Br . The surface area (Amic) occupied
by a surfactant molecule can be obtained though Amic = 4πr /N.
m
−
A
temperature as shown in Table 7, which is in accordance with
−
1
7,18
those reported in literature.
It indicates that the temperature
2
0
dependence of ΔG is dominated by CMC. It can also been
seen from Table 7 that the values of ΔG slightly decrease with
mic
0
mic
The values of r and Amic are listed and compared with that
17,18
reported in the literature
in Table 8, from which one can see
the increase of the number of the hydroxyethyl groups, which is
resulted from the change of CMC with the increase of the
number of hydroxyethyl groups in the head of the surfactant.
Aggregation Number. The aggregation numbers (N) of the
micelle formed by C HDAB and C DHAB are determined by
Table 8. Radius of the Micelle r and the Surface Area Amic
Occupied by a Surfactant Molecule in the Micellar State in
Aqueous Solutions at Temperature T = 298.15 K and Pressure
1
2
12
a
p = 0.1 MPa
using the steady-state fluorescence. The aggregation numbers are
obtained using the following relation:
DTAB
C HDAB
C DHAB
12
1
2
b
I0
I
N[Q]
C − CMC
r/nm
Amic/nm2
1.80/1.8
1.86 ± 0.02
0.82 ± 0.01
1.87 ± 0.02
0.86 ± 0.01
ln
=
c
0.79/0.78
(8)
a
The standard uncertainties u are u(T) = 0.05 K and u(p) = 10 kPa.
Reference 17. Reference 18
where I and I are the fluorescence intensities at 373 nm in the
b
c
0
absence and presence of the quencher, respectively; [Q] and C
are the concentrations of the quencher and the surfactant with
−1
the units being mmol·kg . The plots of ln(I /I) against [Q] are
0
shown in Figure 5. Linear least-squares fits of the experimental
data gave the slopes which together with known values of C and
CMC were used to calculate the aggregation numbers N. The
obtained values of N were 52 ± 2 for C HDAB and 51 ± 2 for
that our results are in excellent agreement with the literature ones
and they increase with the substituent number of the hydroethyl
group in the headgroup. The increase of Amic with the substituent
number of the hydroethyl group is in consistence with what we
proposed in above discussion of the association degree β of the
counterion to the micelle, which was found to decrease with the
increase of the substituent number of the hydroxyethyl group in
the headgroup.
1
2
C DHAB, respectively; the value of N for DTAB was reported
12
19
to be 51 by the literature, and it seems that the hydroxyethyl
substituent has little effect on the aggregation number of the
micelle formed by this series of surfactants.
2
337
dx.doi.org/10.1021/je400463n | J. Chem. Eng. Data 2013, 58, 2326−2338

Journal of Chemical & Engineering Data
Article
(
16) Grosmaire, L.; Chorro, M.; Chorro, C.; Partyka, S.; Zana, R.
AUTHOR INFORMATION
Corresponding Author
Tel.: +86 21 64250804. Fax: +86 21 64250804. E-mail:
shenwg@ecust.edu.cn.
■
*
Alkanediyl-α,ω-Bis(dimethylalkylammonium Bromide) Surfactants: 9.
Effect of the Spacer Carbon Number and Temperature on the Enthalpy
of Micellization. J. Colloid Interface Sci. 2002, 246 (1), 175−181.
(17) Mehta, S. K.; Bhasin, K. K.; Chauhan, R.; Dham, S. Effect of
temperature on critical micelle concentration and thermodynamic
behavior of dodecyldimethylethylammonium bromide and
dodecyltrimethylammonium chloride in aqueous media. Colloids Surf.,
A 2005, 255, 153−157.
Funding
This work was supported by the National Natural Science
Foundation of China (Projects 20973061 and 21173080).
Notes
(18) Khatua, D.; Gupta, A.; Dey, J. Characterization of micelle
formation of dodecyldimethyl-N-2-phenoxyethylammonium bromide
in aqueous solution. J. Colloid Interface Sci. 2006, 298, 451−456.
The authors declare no competing financial interest.
(19) Rodenas, E.; Dolcet, C.; Valiente, M.; Valeron, E. C. Physical
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