centers of the micelles. We have calculated S(Q) as derived by
Hayter and Penfold25,26 from the Ornstein–Zernike equation
and using the rescaled mean spherical approximation. The
micelle is assumed to be a rigid equivalent sphere of diameter
s ¼ 2(a2b)1/3 interacting through a screened Coulomb poten-
tial, which is given by
195 ꢂ 2 ꢁC; C, H, N analysis. Calculated for C34H74N2O2Br2
was C: 58.10; H: 10.61; N: 3.98%. Found C: 58.20; H: 10.75;
1
N: 4.01%. H NMR analysis, d 0.84 ppm (t, 6H 2CH3 alkyl
chain), 1.25–1.40 ppm (br m, 36 H, 18CH2 alkyl chain), 1.75
ppm (m, 4H, 2CH2 alkyl chain), 2.1 ppm (m, 4H, 2CH2 spacer
chain), 3.25 ppm (s, 6H, 2NþCH3), 3.62 ppm (t, 12 H,
2 ꢄ Nþ(CH2)3), 3.82 ppm (t, 4H, 2CH2-OH) and 4.18 ppm
(s, 2H, 2OH).
exp½ꢀkðr ꢀ sÞꢃ
uðrÞ ¼ u0s
; r > s
ð6Þ
r
where k is the Debye–Huckel inverse screening length and is
calculated by
¨
Hexanediyl-1,6-N-N0-bis(dodecyl hyroxyethyl methyl ammo-
nium bromide). Represented as (12-6-12 MEA) M.P.
206 ꢂ 2 ꢁC; C, H, N analysis. Calculated for C36H78N2O2Br2
was C: 59.16; H: 10.75; N: 3.83%. Found C: 59.49; H: 10.86;
ꢂ
ꢃ
1=2
8pNAe2I
103ekBT
k ¼
ð7Þ
1
N: 4.00%. H NMR analysis, d 0.84 ppm (t, 6 H, 2CH3 alkyl
chain), 1.25 ppm (br m, 40 H, 20 CH2 alkyl chain), 1.65
ppm (m, 4 H, 2CH2 spacer chain), 1.95 ppm (m, 4 H, 2CH2
spacer chain), 3.25 ppm (s, 6 H, 2NþCH3), 3.59 ppm (t, 12
H, 2Nþ(CH2)3), 3.75 ppm (t, 4 H, 2CH2-OH), 4.15 ppm (s, 2
H, 2OH).
where I is the ionic strength of the micellar solution and is
determined from the CMC and dissociated counterions of
the micelles. The fractional charge a ( ¼ Z/N, where Z is the
micellar charge) is the charge per surfactant molecule in the
micelle. The contact potential u0 is given by
Z2e2
Octanediyl-1,8-N-N0-bis(dodecyl hydroxyethyl methyl ammo-
nium bromide). Represented as (12-8-12 MEA)M.P.193 ꢂ 2 ꢁC;
C, H, N analysis. Calculated for C38H82N2O2Br2 was C: 60.14;
u0 ¼
ð8Þ
2
pee0sð2 þ ksÞ
where e is the dielectric constant of the solvent medium, e0 is
the permittivity of free space and e is the electronic charge.
Although micelles may produce polydisperse systems, we
have assumed them as monodisperse for the simplicity of the
calculation and to limit the number of unknown parameters
in the analysis. The dimensions of the micelle, aggregation
number and the fractional charge have been determined from
the analysis. The semi-major axis (b), semi-minor axis (a) and
the fractional charge (a) are the parameters optimized by
means of a nonlinear least squre fitting program while analyz-
ing the SANS data. The aggregation number is calculated by
using the relation N ¼ 4pa2b/3v, where v is the volume of
the surfactant monomer.
1
H: 10.89; N: 3.69%. Found C: 60.32; H: 11.00; N: 3.73%. H
NMR analysis, d 0.81 ppm (t, 6 H, 2CH3 alkyl chain), 1.17
ppm (br m, 40 H, 20CH2 alkyl chain), 1.35 ppm (t, 8 H,
4CH2 spacer chain), 1.74 ppm (m, 4 H, 2CH2 spacer chain),
3.20 ppm (s, 6 H, 2NþCH3), 3.59 ppm (t, 12 H, 2Nþ
(CH2)3), 3.93 ppm (t, 4 H, 2CH2-OH), 3.99 ppm (s, 2 H, 2OH).
Decanediyl-1,10-N-N0-bis(dodecyl
hydroxyethyl
methyl
ammonium bromide). Represented as (12-10-12 MEA) M.P.
203 ꢂ 2 ꢁC; C, H, N analysis. Calculated for C40H86N2O2Br2
was C: 61.05; H: 11.02; N: 3.56%. Found C: 61.25; H: 11.10;
1
N: 3.60%. H NMR analysis, d 0.81 ppm (t, 6 H 2CH3 alkyl
chain), 1.30 ppm (m, 40 H, 20CH2 alkyl chain),1.35 ppm (t,
8 H, 4CH2 spacer chain), 1.70 ppm (m, 8 H, 4CH2 spacer
chain), 3.24 ppm (s, 6 H, 2NþCH3), 3.67 ppm (t, 12 H,
2 ꢄ Nþ(CH2)3), 4.05 ppm (t, 4 H, 2CH2-OH), 5.12 ppm (s, 2
H, 2OH).
4. Results and discussion
4.1 Characterization
The structure and purity of synthesized series of bis-cationic
surfactants was confirmed through FTIR, elemental, and H
NMR analysis.
1
The IR spectra of the surfactants were recorded in KBr pel-
lets using Perkin Elmer FTIR spectrophotometer RX, of
a resolution 2 cmꢀ1. The absorption bands were observed at
3401–3656 cmꢀ1 (OH stretching), 2916 cmꢀ1 (CH stretching),
1108 cmꢀ1 (CN stretching), 1084 cmꢀ1 (CO stretching) and
720 cmꢀ1 (CH rocking of long alkyl chain).
4.2 Critical micellar concentration
The cmc values for 12-s-12 MEA novel series of bis-cationic
surfactants were determined by surface tension and conduc-
tance measurements. The cmc values obtained from both the
techniques show a similar trend with spacer chain length and
are given in Table 1. It is interesting to note that cmc data
of the 12-s-12 MEA bis-cationic surfactants are observed to
be 10–100 times lower than the conventional 12-s-12 DMA
bis-cationic surfactants.9–10 For 12-s-12 MEA, hydrogen
bonding with water can take place through oxygen atom of
–C2H4OH groups. This is likely to provide additional hydra-
tion at the head group level resulting in screening of Coulom-
bic forces of repulsion between charged heads and helping
Elemental analysis and 1H NMR spectra of products in
CDCl3 were determined using Perkin Elmer Series II elemental
analyzer and 300 MHZ Bruker NMR spectrophotometer,
respectively.
Butanediyl-1,4,-N,N0-bis(dodecyle
ammonium bromide). Represented as (12-4-12 MEA) M.P.
hydroxyethyl
methyl
Table 1 Critical micellar concentration (cmc), average degree of ionization (aave) and Gibb’s free energy of micellization (DGm) for 12-s-12 MEA
novel series of bis-cationic surfactants, at 30 ꢁCa
Spacer length
(s)
cmc by conductometry
C ꢄ 10ꢀ5
cmc by tensiometry
C ꢄ 10ꢀ5
(DGm)
M
M
(aave
)
kJ molꢀ1
4
6
3.49 ꢂ 0.10 (117 ꢂ 10)
4.49 ꢂ 0.10 (103 ꢂ 10)
3.99 ꢂ 0.15 (83 ꢂ 10)
3.12 ꢂ 0.10 (63 ꢂ 10)
2.78 ꢂ 0.10
4.33 ꢂ 0.10
3.18 ꢂ 0.10
2.59 ꢂ 0.10
0.26 (0.31)
0.31 (0.33)
0.36 (0.45)
0.39 (0.54)
ꢀ32.06
ꢀ30.01
ꢀ29.01
ꢀ29.01
8
10
The values given in brackets are of conventional 12-s-12 DMA bis-cationic surfactants with –Nþ(CH3)2 head groups, taken from ref. 8.
a
T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4
3510
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 5 0 8 – 3 5 1 4