Unusual Adsorption at the Air-Water Interface of a Zwitterionic Carboxybetaine with a Large Charge Separation

Article abstract of DOI:10.1021/acs.langmuir.6b00074

The structures of layers of three different dodecylcarboxybetaine surfactants adsorbed at the air-water interface have been determined by neutron reflection. The zwitterionic compounds differed in the length of the spacer separating the quaternary ammonium and carboxylate groups, which was (CH₂)₁, (CH₂)₄, or (CH₂)₈. The limiting area per molecule was found to be 45, 52, or 84 ?², respectively, and compared reasonably with results from surface tension showing that the Gibbs prefactor is 1 in each case. Isotopic labeling was used to distinguish between the position of the alkyl and spacer groups in the layer. The spacer was found to be well-immersed in water for the (CH₂)₁ and (CH₂)₄ spacers but significantly above water for the (CH₂)₈ spacer. The distribution of the (CH₂)₈ spacer along the surface normal was found to be similar to that of the dodecyl group; i.e., it projects out of the water, contrary to an earlier hypothesis that it forms a loop. Comparison of the overlap of water with dodecyl and spacer groups also indicates that the (CH₂)₈ spacer is well out of the water. This in turn suggests that the anionic carboxylic acid group, which is dissociated in solution, is not ionized in the adsorbed layer. A further observation is that the dodecylcarboxybetaine with the (CH₂)₈ spacer reaches surface saturation at one-tenth of the critical micelle concentration. This is highly unusual and is attributed to the long spacer destabilizing the micelle relative to the surface layer.

Full text of DOI:10.1021/acs.langmuir.6b00074

Article
pubs.acs.org/Langmuir
Unusual Adsorption at the Air−Water Interface of a Zwitterionic
Carboxybetaine with a Large Charge Separation
Kun Ma,† Pei Xun Li,† Chu Chuan Dong,† Robert K. Thomas,*,† and Jeffrey Penfold‡,§
†Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, U.K.
‡Rutherford-Appleton Laboratory, Chilton, Didcot OX11 0QX, U.K.
§Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, U.K.
S
* Supporting Information
ABSTRACT: The structures of layers of three different dodecylcarboxybetaine surfactants adsorbed at the air−water interface
have been determined by neutron reflection. The zwitterionic compounds differed in the length of the spacer separating the
quaternary ammonium and carboxylate groups, which was (CH2)1, (CH2)4, or (CH2)8. The limiting area per molecule was found
to be 45, 52, or 84 Å2, respectively, and compared reasonably with results from surface tension showing that the Gibbs prefactor
is 1 in each case. Isotopic labeling was used to distinguish between the position of the alkyl and spacer groups in the layer. The
spacer was found to be well-immersed in water for the (CH2)1 and (CH2)4 spacers but significantly above water for the (CH2)8
spacer. The distribution of the (CH2)8 spacer along the surface normal was found to be similar to that of the dodecyl group; i.e.,
it projects out of the water, contrary to an earlier hypothesis that it forms a loop. Comparison of the overlap of water with
dodecyl and spacer groups also indicates that the (CH2)8 spacer is well out of the water. This in turn suggests that the anionic
carboxylic acid group, which is dissociated in solution, is not ionized in the adsorbed layer. A further observation is that the
dodecylcarboxybetaine with the (CH2)8 spacer reaches surface saturation at one-tenth of the critical micelle concentration. This
is highly unusual and is attributed to the long spacer destabilizing the micelle relative to the surface layer.
For a zwitterionic case in which both groups are ionized, there
are no additional ions adsorbed and the Gibbs prefactor in the
expression on the right is therefore 1, but if only one of the
zwitterionic groups is ionized, then surface neutrality requires
the adsorption of a counterion and, unless the concentration of
this counterion is kept constant, the Gibbs prefactor then
becomes 2, as for a 1:1 ionic surfactant. The strength of
adsorption and the critical micelle concentration (CMC) tend
to be intermediate between those of nonionic and ionic
surfactants, and the presence of the two charges makes
zwitterionics very soluble (e.g., ref 1). These properties and
the lack of overall charge, which weakens the interaction with
species such as proteins, confer a mildness on zwitterionic
INTRODUCTION
■
The headgroups of zwitterionic surfactants contain a pair of
opposite charges separated by a spacer. If the spacer is not too
large, the surfactant will generally carry no net charge at the
natural pH and adsorption at the air−water interface is then
governed by the Gibbs equation. For a 1:1 ionic surfactant, this
is
dγ
RT
= −Γ d(ln as) + Γ d(ln ai) ≈ 2Γ d(ln cs)
s
i
s
(1)
where γ is the surface tension, Γ is the surface excess defined
relative to a surface plane for which Γwater is zero, a is the
activity and is usually approximated as concentration c, and the
subscripts s and i indicate surfactant ion and any other ions that
are also adsorbed, respectively. If the only ion adsorbed apart
from the surfactant is the surfactant counterion, then neutrality
requires the two surface excesses and the two concentrations to
be identical and the equation simplifies as shown on the right.
Received: January 10, 2016
Revised: March 20, 2016
© XXXX American Chemical Society
A
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surfactants that is useful for biological applications2 and in
where the spacer was varied from CH2 to (CH2)10.13,14 In
both series, the critical micelle concentration (CMC) passes
through a pronounced maximum at around n = 4, where n is
the number of methylene units, and this was explained in terms
of the repulsion between the zwitterionic dipoles at the micellar
surface as a function of n (Chevalier et al. determined the actual
separation of the charges using NMR measurements on the
isolated molecules). Chevalier et al. conducted a more
complete study of a second series of dodecylcarboxybetaines.
formulations for personal care.3
The length of the spacer between the charges in a
zwitterionic has a strong effect on the interaction between
the two charges, especially if one of them is weak.4 In a
carboxybetaine (see Figure 1), the quaternary ammonium is a
In this series, the limiting area per molecule at the CMC, ACMC
,
increases steadily with spacer length from 52 at a spacer length
of one carbon to 92 Å2 at 10 carbons, but the CMC and the
limiting surface tension at the CMC, γCMC, both show strong
maxima in the region of three or four methylene groups.14 The
CMC was explained as for the phosphocholine series, but the
more steady increase in ACMC was interpreted in terms of a
balance of the dipolar repulsion and an increasing steric lateral
repulsion with spacer length that eventually causes the more
flexible long spacers to form a loop at the surface. Given that
the properties of these important surfactants can evidently be
fine-tuned by adjustment of the spacer length, the under-
standing of the surface and aggregation behavior as a function
of spacer length is important, and this is best done using a
technique that can explore the surface and/or aggregate
structure directly.
Neutron reflection in conjunction with deuterium labeling
offers a means for studying the distributions of surfactant
fragments along the direction normal to the surface15,16 and
should be able to identify structural changes associated with
changes in the spacer orientation or position relative to the
underlying water. In addition, the combination of neutron
reflection with surface tension measurements allows an accurate
assessment of the application of the Gibbs equation to the
surface tension data, which may also reveal interesting features
of the surface behavior (e.g., refs 17 and 18). For example, in
the surface tension data of Chevalier et al., there is an unusually
long linear stretch of the ST curve for the largest of the spacers
studied, but this was not mentioned in the original paper. We
have now measured neutron reflection from the surfaces of the
deuterated species, using differently labeled molecules to
separate the signals from the chain and spacer moieties, and
also repeated the surface tension measurements of Chevalier et
al. for a selection of the same series of dodecylcarboxybetaines
with spacers of one, four, and eight methylene groups (Figure
1).
Figure 1. Fully extended conformations of dodecylcarboxybetaine with
(a) one-, (b) four-, and (c) eight-methylene spacers (C12Cnbetaine).
The carboxylate has been drawn as the fully ionized form that
dominates in dilute solution, even for the most weakly acidic group in
C12C8betaine. The pKa values are (a) 2.46 and (b) 4.3 and (c) 4.6
(both estimated from dibasic carboxylic acid data).8
permanent charge but the carboxyl group is a weak acid group,
which would have a pKa typically in the range of 4−5 if it were
simply connected to an alkyl group. However, when the
carboxyl group is separated from a cationic group by only one
methylene group, the pKa drops substantially and the
zwitterionic is therefore fully charged at natural pH. For
example, in the α,ω-ammonioalkanoates, the change in pKa is
from 2.3 for a single-methylene spacer to 4.5 for a
hexamethylene spacer, which is close to the value of 4.7 for
acetic acid.5 In the ammonioalkanoates, both charged groups
are weak electrolytes and the behavior might be slightly
different when the cationic group is a quaternary alkylammo-
nium group. However, in dodecylcarboxybetaine with a single-
methylene spacer, the pKa is 2.46 and rises similarly to that of
the ammonioalkanoates as the spacer length increases.7 Thus,
the added stabilization of the dissociated state is gradually lost
as the length of the spacer is progressively increased. The effect
has been most thoroughly examined for the ionization of
dibasic carboxylic acids where the second dissociation is
strongly affected by the presence of the negative charge from
the first ionization, and the effect should be similar but opposite
in sign in a zwitterionic. These studies have shown that there
are several subtleties concerning the local dielectric environ-
ment,8−12 and these may also be important at the surface and in
micelles; however, the general result that the pKa of the
carboxylic acid group in the zwitterionic should increase by ∼2
units when the spacer changes from one to more than
approximately six methylene units is a reliable one. A
complication at the surface is that an undissociated carboxylic
acid part of the spacer/headgroup will be less hydrophilic/more
hydrophobic, and this may contribute in a different way to the
surface properties. In addition to the possible variation of
charge with chain length, the dipole associated with the charge
also varies linearly with separation in a rigid spacer but more
slowly in the typical flexible alkyl spacer of the zwitterionics that
have so far been studied.
EXPERIMENTAL DETAILS
■
The three dodecylcarboxybetaine surfactants with C1, C4, and C8
spacers between the quaternary ammonium and carboxy groups
(designated C12Cnbetaine in the rest of the paper) were synthesized
following the two-step procedure of Weers et al.7 Dodecyldimethyl-
amine was reacted with the appropriate bromoalkyl mono ester to
form the quaternary ammonium salt with the alkyl monoester using
ethyl acetate, 2-propanol, or ethanol as the solvent depending on the
alkyl group in the monoester. The crude ammonium salt was then
dissolved in UHQ water and treated with an ion exchange resin. The
hydrogen ion associated with the cationic resin promotes base-
catalyzed ester hydrolysis that results in the liberation of the betaine.
The final compounds were recrystallized from an acetone/methanol
mixture and obtained as white crystals that were freeze-dried. The
purity was assessed by the absence of a minimum in the plot of surface
tension versus ln c. The chain-deuterated surfactant was synthesized in
the same way as the protonated one by using chain-deuterated
dodecyldimethylamine.
Chevalier et al. have investigated the effect of the separation
of the charges on the surface behavior of two series of
zwitterionics, phosphocholines and dodecylcarboxybetaines,
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To highlight the neutron reflectivity signal from the headgroup,
C12C4betaine and C12C8betaine were also synthesized with their
headgroup deuterated. For the C4 spacer, the deuterated 5-
bromovalerate used in the procedure described above was made
using the reaction scheme
Protonated ethyl 9-bromononanoate for the C8 spacer was
synthesized from monoethyl decanoate as the starting compound.26
In a 500 mL round-bottom flask, a mixture of 20.4 g of red HgO (0.1
mol), 43.25 g of monomethyl decanoate (0.2 mol), and 200 mL of
CCl4 was heated under a 50 cm Vigreux column, with stirring, such
that the rate of distillation was approximately one drop per second.
After distillation in this manner for 15 min, addition of a solution of 30
g of bromine in 60 mL of CCl4, added over 70 min, was begun. In the
last stages, a majority of the bromine distilled over unchanged. When
bromine addition was complete, a further 60 mL of CCl4 was added
over 40 min, while distillation continued as before. Mercury salts were
removed from the cooled reaction mixture by filtration with suction
through a filter-aid mat. The clear filtrate was extracted with 50 mL of
5% aqueous NaOH, and the coagulated precipitate that formed was
removed from the two-phase solution by suction filtration. After the
CCl4 phase had been washed with ultrapure water from a UHQ ion
exchange purifier, the ethyl 9-bromononanoate was recovered by
distillation. The final product was obtained by using liquid
chromatography with petroleum ether and ethyl acetate mixture, and
the structure was confirmed by 1H NMR. Deuterated methyl 9-
bromononanoate (methyl group not deuterated) was prepared in
three stages, the last of which was the same bromination step as
described above. Decan-dioic acid was successively deuterated in a Parr
reactor using PtO catalyst, D2O, and Na2O2 as described previously to
give a product containing 98% D after three exchanges. The diacid was
esterified with methanol, and the monomethyl decanoate was isolated
from the free diacid and diester by distillation. Bromination as
described above finally gave methyl 9-bromononanoate, which was
used for the preparation of the hC12dC8betaine, where h denotes fully
protonated and d fully deuterated.
HBr,H2SO
4
C4D8O ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ HOC4D8Br
DHP,TsOH(cat.)
BrC4D8OH ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ BrC4D8OTHP
(i)Mg,ether,(ii)CO2,(iii)H2O
BrC4D8OTHP ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ HOOCC4D8OTHP
LiCl,H2O,DMSO
HOOCC4D8OTHP ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→⎯ HOOCC4D8OH
HBr,H2SO
4
HOOCC4D8OH ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ HOOCC4D8Br
EtOH,TsOH(cat.)
HOOCC4D8Br ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ EtOOCC4D8Br
(2)
starting from perdeuterated THF. Concentrated H2SO4 (3 mL) and
then 48 mL of HBr [48% (w/v), 0.42 mol] were added dropwise to 30
g of deuterated THF (0.4 mol) at 0 °C.19,20 The mixture was stirred
and refluxed for 90 min and, after cooling to 0 °C, was neutralized with
NaHCO3, and 50 mL of UHQ water was added. The 4-bromo-1-
butanol product was extracted with diethyl ether, washed with brine,
and dried with magnesium sulfate. The yield after removal of solvent
was 86%. The 2-tetrahydropyranyl group was then introduced as a
protecting group for the alcohol group.21 Thirty milliliters of
dihydropyran (0.34 mol) was added via a syringe to a cooled solution
(0 °C) of 4-bromo-1-butanol (40 g, 0.26 mol) in 100 mL of anhydrous
ether containing 100 mg of p-toluenesulfonic acid. After 1 h at ambient
temperature, the reaction mixture was twice washed with a saturated
sodium bicarbonate solution and then with brine. The organic layer
was dried over anhydrous potassium carbonate and filtered. The crude
4-bromobutyl tetrahydropyranyl ether, obtained after removal of
solvent, was purified by liquid chromatography with a petroleum
ether/ether mixture. The bromo group was replaced with carboxylate
using a Grignard reaction; 4.18 mL (20 g) of 4-bromobutyl
tetrahydropyranyl ether and 50 mL of anhydrous THF were added
dropwise to a 4-bromobutyl tetrahydropyranyl ether/THF solution in
a round-bottom flask to maintain a steady reflux. The freshly made
Grignard reagent was poured into excess dry ice for carboxylation of
the THP-protected compound. The reaction mixture was then
warmed slowly to ambient temperature and extracted with water
(100 mL). The aqueous solution was washed with diethyl ether, and
the extracts were dried and concentrated under reduced pressure. The
The surface tension measurements were performed on a Kruss
̈
K10T digital tensiometer by the du Nouy ring method with a
̈
platinum/iridium ring. The apparatus was calibrated and corrected
following the manufacturer’s protocols. All experiments were
conducted at 298 1 K.
Neutron reflection (NR) measurements were performed on the
INTER and SURF reflectometers at the Rutherford-Appleton
Laboratory (Didcot, U.K.). The instruments and the procedure for
making the measurements have been described fully elsewhere.27,28
Measurements were taken at an incident angle of 1.5°, which gives a
range of momentum transfer, κ [=(4π sin θ)/λ, where θ is the glancing
angle of incidence], from 0.03 to 0.35 Å−1, and a flat incoherent
scattering background was subtracted. The conversion of the measured
signal to absolute intensity was made by calibration with D2O.
Independent measurements to determine surface excess were made for
the chain-deuterated and spacer-deuterated surfactants in null
reflecting water (NRW). Under these circumstances, the reflected
signal is entirely from the surfactant layer. The surface excess of
surfactant was determined by fitting the NR data with a simple slab
model using the standard optical matrix method to calculate the
reflectivity.29 In this model, the layer is characterized by its thickness, τ,
and scattering length density, ρ. Once the values of τ and ρ are
determined, they can be converted into the area per molecule at the
surface, A, using
THP ether was deprotected following the method of Maiti et al.22
A
stirred mixture of 20 g of THP ether (0.1 mol), 20 g of LiCl (0.5 mol),
and 18 mL of H2O (1 mol) in DMSO (100 mL) was heated at 90 °C
for 6 h under N2 protection.23 The reaction mixture was cooled to
room temperature, diluted with H2O (100 mL), and extracted with
ether (3 × 100 mL). The crude hydroxyvaleric acid was dried over
anhydrous sodium sulfate and purified on a silica gel column using
ethyl acetate and light petroleum (60−80 °C) with a yield of 81% (9.2
g). The acid was brominated following the method of Buchi;24 9.2 g of
the acid was added to an ice-cold mixture of 40 mL of 40% HBr and
10 mL of H2SO4. After the mixture had been stirred at room
temperature overnight and then in a steam bath for 5 h, the crude 5-
bromovaleric acid was extracted with ether and purified on a silica gel
column using petroleum ether (yield of 9 g, 49%). Finally, ethyl 5-
∑ b
ρ =
(3)
Aτ
where b values are the known scattering lengths of the fragments in the
layer, which are given in Table 1 of the Supporting Information. A
more extensive series of measurements to determine the structure of
the layer were taken above the CMC and used the NRW
measurements above as well as three measurements in D2O, of
hC12hCnbetaine, dC12hCnbetaine, and hC12dCnbetaine. A modification
of the partial structure factor method16 was used to analyze this data
and is described in the discussion below.
Results and Discussion. The surface tension measurements for
the three dodecylcarboxybetaines are shown in Figure 2 with fits based
on a quadratic in ln c and a Gibbs prefactor of unity. Included for
comparison are the results for the C10 spacer reproduced from
bromovalerate was synthesized following the method of Kurata.25
A
catalytic amount of 4-toluenesulfonic acid was added to a mixture of
excess EtOH (40 mL) and 5-bromopentanoic acid (9 g, 0.05 mol), and
after the mixture had refluxed at 70−80 °C overnight, the crude
product was rotary evaporated and purified on a silica gel column
using petroleum ether (yield of 7.6 g, 73%). Because of the difficulty of
using NMR to determine the purity of perdeuterated materials, the
sequence of reactions given above was first conducted with protonated
1
materials (using H NMR for analysis) and then repeated exactly for
the deuterated system.
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Table 2. Uniform Layer Fitting Results for C12C1betaine,
C12C4betaine, and C12C8betaine Using Two Different
Isotopic Compositions of Surfactant in Null Reflecting
Water at 298 K
c
ρτ
A
Γ
contrast
(mM) ( 5% Å−1 × 106) ( 5% Å2) ( 5% μmol−2
)
dC12hC1betaine
0.19
0.56
0.94
1.40
1.87
5.61
0.33
0.99
1.65
2.48
3.30
9.90
0.33
0.99
1.65
2.48
3.30
9.90
0.10
0.31
0.52
0.77
1.03
3.09
0.10
0.31
0.52
0.77
1.03
3.09
32.3
46.8
51.4
55.4
55.4
57.8
32.8
35.6
39.6
43.6
48.4
48.5
8.0
80
55
50
47
47
45
78
71
64
58
53
52
82
68
66
58
52
52
85
87
88
83
85
84
86
85
84
84
85
84
2.1
3.0
3.3
3.5
3.5
3.7
2.1
2.3
2.6
2.9
3.1
3.2
2.0
2.4
2.5
2.9
3.2
3.2
2.0
1.9
1.9
2.0
2.0
2.0
1.9
2.0
2.0
2.0
2.0
2.0
dC12hC4betaine
hC12dC4betaine
dC12hC8betaine
hC12dC8betaine
Figure 2. Surface tension measurements for dodecylcarboxybetaines
with methylene spacers of one, four, and eight units (points) and fits
to the Gibbs equation using a quadratic in ln c and a prefactor of unity.
Also included are surface tension data (footnote a) from Chevalier et
al.14 for the compound with a spacer of 10 methylene groups.
9.6
10.0
11.2
12.5
12.6
29.5
29.0
28.6
30.4
29.4
29.8
17.2
17.5
17.7
17.7
17.5
17.6
Chevalier et al.14 A feature of particular interest is that the γ−ln c plot
for our largest spacer, C8, is linear over a very long-range of
concentration and this was also found by Chevalier et al. for their
largest spacer, C10, which is the reason for including this extra data in
the Figure. The numerical results are compared with the results from
Chevalier et al. in Table 1. Apart from the surface excess for the C4
compound and a constant shift in calibration of the surface tension the
results agree within experimental error.
The neutron reflectivity profiles of the partially deuterated
carboxybetaines were measured over a range of concentrations from
below to above the CMC of each component. Apart from
C12C1betaine, the isotopic compositions measured were
dC12hCnbetaine and hC12dCnbetaine, each in null reflecting water
(NRW), where d and h denote the deuterated and protonated part of
the surfactant, respectively. The data from NRW give two independent
and direct measurements of the surface excess from each of the
partially deuterated species because the signal is only from the
surfactant layer. The results of fitting a single uniform layer model to
the NRW data are given in Table 2. The value of the surface excess, Γ,
at this contrast depends on the product of scattering length density
and layer thickness (ρτ in Table 2; see also eq 2), and although
individually these vary with a significant error, the product is
independent of the model used for the profile of the layer. We do
not use these layer thicknesses for a discussion of the layer structure,
and they are therefore omitted from Table 3. A more extended analysis
of the surface structure, using a wider range of measurements, is
presented below.
line behavior of the surface tension of the compound with the long
spacer, which indicates a constant surface excess over a large
concentration range, is also replicated by the constant surface excess
in the neutron data. Thus, this compound reaches its plateau
adsorption at 1/10th of the CMC. This is highly unusual, and we
are not aware of a similar case. Taking our data and those of Chevalier
et al. indicates that this is a definite feature of the compounds with the
long spacer. In papers in which the application of the Gibbs equation is
discussed, the evidence seems in general to indicate that nonionic
surfactants reach a plateau before but close to the CMC, whereas ionic
species do not,17,18 although there is no thermodynamic reason why a
plateau of adsorption should be associated with the CMC. A plateau
well below the CMC suggests that the micelle is relatively unstable
compared with the saturated monolayer. This could be a result of a
difficulty in accommodating a long spacer chain in a micelle, and we
discuss this further below in conjunction with the layer structure.
The two independent measurements at each concentration give
values that are in good agreement with each other. They are also in
good agreement with the surface tension−Gibbs equation results from
our own surface tension data in Table 1. This immediately confirms
that the Gibbs prefactor is 1, i.e., that all three surfactants at natural pH
are fully dissociated in the bulk solution despite the substantial
increase in pKa expected for the C8 spacer.7 The interesting straight
Table 1. Limiting Values of CMC, γCMC, ACMC, and ΓCMC (from application of the Gibbs equation with a prefactor of unity) for
Three Dodecylcarboxybetaines
component
CMC ( 20% mM)
surface tension ( 0.5 mN m−1
)
ACMC ( 15% Å2)
ΓCMC ( 15% mol/m2)
a
a
a
b
C12C1betaine
C12C4betaine
C12C8betaine
1.9 (2.0 )
39.8 (36.7 )
44 (52, 50 )
3.8
3.1
2.2
a
a
a
3.3 (3.4 )
45.4 (44.6 )
53 (68 )
c
b
c
1.0 (1.5 )
42.1 (41.6 )
77 (77 )
a
b
Results from Chevalier et al. are given in parentheses for C12C1betaine and C12C4betaine. Results from Hines et al.30 The surface tension
measurements were taken at 298 K. Results from Chevalier et al. are given in parentheses for C12C7betaine14 (they did not measure C12C8betaine).
c
D
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Table 3. Structural Parameters Derived from Fitting Neutron Reflection Data from Three Betaines at 3 × CMC Using Five
Different Contrasts with NRW and D2O (symbols explained in the text)
a
b
compound
lc 3 Å
ls 3 Å
δcs
δsw
1 Å
w
3 Å
11
A
3 Å2
48
C12C1betaine
C12C4betaine
C12C8betaine
11
13
1
5
−6
−4
−0.5
−3
−6
11
11
52
80
15
12
−1.5
a
b
Depends directly on lc and ls. The parameter defining the cutoff of the water space filling region is indirectly incorporated into δsw.
The structures of the saturated layers of the three betaines were
Thus, there is no empty space below the cutoff distance. Above this,
the water decays following a half-Gaussian. This distribution can be
considered as defining the region of water over which the capillary
waves exert an effect. The Fourier transform of this has to be
calculated numerically, but again the important parameters for
assessing the structure are the equivalent δcw or δsw parameters
determined by the correlations between the water and the surfactant
fragments. The procedure is to use a set of trial parameters and to
compute R and optimize a simultaneous fit to the full set of reflectivity
profiles, basically to determine the individual structure factors,
especially the cross terms in eq 4. For this analysis, the number of
independent parameters for the betaines is 7, and these are the surface
excess of surfactant, the widths of the alkyl chain and betaine
fragments, the separations of betaine from alkyl chain and from water,
and the cutoff for the water and decay length for the water profile. For
a tighter comparison of these three similar surfactants, we now
introduce a different parametrization within the framework of the
equations given above.
determined at 3 × CMC using the chain-deuterated and spacer-
deuterated surfactants (not for the C1 spacer) in NRW and D2O and
the fully protiated surfactant in D2O. The five different isotopic
reflectivity profiles were analyzed using an extension of the kinematic
model. Although the basis of the kinematic model has been fully
described and applied elsewhere,15,16,31 for the sake of clarity we
reproduce the main equations here. The betaines can be divided into
two fragments, alkyl chain and the betaine group, which includes the
spacer chain and the two charged groups. In the kinematic
approximation, the reflectivity is then given by
16π2
2
R =
(b 2hcc + b 2hss + bw hww + 2b bhcs + 2b b hcw
c
s
c s
c w
κ2
+ 2bb hsw)
(4)
s w
where the subscripts c, s, and w denote alkyl chain, spacer group, and
water, respectively, and hii values are the self- and hij values the cross-
partial structure factors defined as
We have shown elsewhere that the width of the distribution of a
surfactant fragment is determined in part by the length of the
projection of the fragment along the normal direction, denoted l, and
in part by the thermal roughness, w, from the capillary waves such that
the parameter σ in eq 6 is given by15,33
hii = Re(n
hij = Re(n
(κ) is the one-dimensional Fourier transform of ni(z). The
̂
i(κ)n
̂
i(κ)) = |n
̂
i(κ)|2
̂
i(κ)nj(κ))
̂
(5)
where ni
̂
σ2 = l2 + w2
(11)
distributions of the surfactant fragments along the surface normal can
Because the capillary waves affect the whole layer, w should be the
same for all the fragments, including the water decay in eq 10. In
addition, because the two fragments of the surfactant are attached, the
distance between their centers must be constrained to be
be represented by Gaussian distributions
4z2
⎛
ni(z) = ni0 exp⎜−
⎝
⎞
⎟
⎠
σi2
(6)
1
2
where ni0 is proportional to the surface density, σi is the width
parameter (full width at height/e), and z is the distance along the
surface normal. The self-partial structure factors, hii, are then
δ = (ls lc)
cs
(12)
where the
depends on whether the angle between the two
projections along the surface normal is greater or less than 90°. There
are now only six independent parameters, which are the surface excess,
the two fragment projections along the surface normal, the thermal
roughness, the water cutoff, and either the chain−water separation or
the spacer−water separation. Furthermore, because the thermal
roughness w is expected to be mainly determined by the surface
tension, and the surface tensions are not very different for the three
betaine surfactants, it is reasonable to make the approximation that w
is the same for all three, which further reduces the number of
parameters for the set of surfactants. The fits to the reflectivity profiles
and the corresponding fragment distributions based on this model are
plotted in Figures 3 and 4, and the parameters are listed in Table 3.
The results in Figure 4 are plotted as the volume fraction of the
various fragments, obtained using the scattering lengths in Table 1 of
the Supporting Information. The fits should be judged as a set in that
the unusually tight constraints put on the fitting model lead to some
fits that could be improved either by relaxing the constant w restriction
or by allowing the independent variation of δcs. Thus, the fits for the
samples with only the deuterated spacer (the lowest ones in Figure 3)
would be better fitted with a greater thermal contribution. However, as
outlined above, the important parameter is the separation, and the
constraints on the fitted parameters highlight the differences in the
structural correlations between the fragments for the three surfactants.
There are two trends that are easily identified. The first is that the
projection of the C12 chain along the surface normal increases with the
betaine spacer length. The length as defined by the 1/e width of a
Gaussian is ∼0.9 of the true length,15 and the extended length of the
2
2
2
⎛
exp⎜
⎝
⎞
⎟
⎠
πσini0
4
κ σi
hii =
8
(7)
For the Gaussian distributions of the alkyl chain and alkyl spacer, the
cross-partial structure factor, hij, has the simple form
hij = (hiihjj)1/2 cos(κδij)
(8)
where δij is the separation of the centers of the two distributions along
the surface normal direction. The σ parameters are determined by a
mixture of the intrinsic thickness of a fragment layer and the thermal
fluctuations, and because these may sometimes be comparable, it can
be difficult to extract useful structural information from them.
However, the value of δ is determined by correlations between the
fragments in each molecule, and these are largely determined by the
intralayer structure and generally give rise to the main interference
effects in the reflectivity. The distribution of water is more complicated
and, following a previous model, is taken to be determined by space
filling up to a certain distance into the surfactant layer followed by a
decay to zero
ϕ (z) = 1 − ϕ − ϕ; z ≤ ξ
where ϕ values are volume fractions and ξ is a cutoff distance,32 and
(9)
w
c
s
(z − ξ)2
⎡
⎣
⎤
ϕ (z) = ϕ (ξ) exp⎢−
⎥; z ≥ ξ
w
w
σ2
⎦
(10)
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Figure 4. Distributions of the different fragments in layers of
carboxybetaines at the air−water surface that best fit the reflectivity
data of Figure 3. The spacer consists of the quaternary ammonium
group and carboxy groups separated by (a) one, (b) four, and (c) eight
methylene groups. The center of the spacer distribution was fixed at
zero for each system for the sake of convenience.
Figure 3. Neutron reflectivity profiles for different isotopic species of
dodecyl carboxybetaines with methylene spacers of (a) one, (b) four,
and (c) eight units (points) and the best fits (lines) using the
structures shown in Figure 4. For the sake of clarity, the individual
profiles in each set are successively displaced downward by 1 unit.
C12 chain is 16 Å. Thus, in the presence of the C1 spacer, the
projection of the C12 chain and its known length leads to a tilt of ∼30°
from the vertical, but this becomes more or less vertical in the presence
of the C8 spacer. The second trend is that the spacer chain of the
betaine group changes orientation even more dramatically. For the C1
compound, the intrinsically short length of the spacer means its
thickness is close to the thermal roughness. For the C8 compound, the
fully extended length is estimated to be ∼15 Å (10 Å from the C8H16
and 5 Å from the two charged groups). Thus, the tilt of the spacer as
as a whole is ∼30° from the vertical, almost exactly the same as the
dodecyl chain in the C1 surfactant. This is a surprising result because it
shows that the carboxyl group must be completely out of the water,
rather than looped as suggested by Chevalier et al., and we will discuss
this further below. Note that because of the way we have combined the
projections of alkyl chain and spacer the δcs is required to be consistent
with the description above and therefore adds no new information.
A different and more subtle measure of the nature of the surface
layer is the overlap of each unit with water, i.e., the integral of the
product of the distributions of the unit and water along the surface
normal. A small overlap between a hydrophobic unit and water
suggests that the hydrophobic unit is more effectively screening the
high-energy surface of the water than if there is a large overlap. It is
easy to use the distributions of Figure 3 to calculate and normalize
these overlaps so that they are directly comparable among the three
systems. The calculated overlaps are 3.8, 3.3, and 3.0 between the
dodecyl chain and water and 8.1, 5.3, and 3.7 between spacer and
water for the C1, C4, and C8 spacers, respectively, where the values are
normalized both to the volume fraction per dodecyl chain and to the
area per molecule. These numbers show that within error the apparent
effectiveness of the dodecyl chain is more or less the same across the
series. However, the C1 and C4 spacers overlap strongly with water,
and the methylene groups of these spacers must be significantly
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immersed. This does not matter much for C12C1betaine, but it leads to
a significant loss of surface energy for C12C4 betaine, leading to a larger
γCMC, as seen in Figure 2. However, the low value of the overlap for the
C8 spacer shows that it is as effective at screening the water per unit
volume fraction as the dodecyl group. The overall screening of water
per unit area of surfactant is therefore approximately the same for
C12C1betaine and C12C8betaine. However, the contribution from the
spacer group will be partially offset by the exposed polar carboxyl at
the surface, which will have a surface energy higher than that of a
methyl group, and overall, the γCMC value could then be a bit higher
for the C8 compound, as observed.
Chevalier et al., the straight line region starts to appear from
approximately the C4 spacer, i.e., approximately the same point as the
maximum in the CMC and γCMC. This link is consistent with the
mechanism suggested by the neutron reflection results.
ASSOCIATED CONTENT
■
S
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.lang-
muir.6b00074.
The fact that the C8 spacer is well extended and has an overlap with
water that is approximately the same as the dodecyl chain shows that
the carboxyl group must be on average more or less completely out of
the water. An ionized carboxyl group would be unstable in the low-
dielectric environment of the outer part of the layer, and combined
with its much higher pKa, this raises the possibility that C12C8betaine is
adsorbed in its undissociated carboxylic acid form. The conventional
argument against the presence of what would then be the simple
cationic form of the betaine at the surface is that the prefactor in the
Gibbs equation would be 2. Wustneck et al.6 have indeed shown that
the adsorption of the salt of C12C1betaine, i.e., the salt with HBr of
HCl, does follow the Gibbs equation with a prefactor of 2. However,
the conventional argument for a prefactor of 2 is not appropriate
unless the zwitterion is in salt form. The equilibrium between the bulk
and surface can be equivalently expressed as either (see ref 34 for the
treatment of the independence of components in the Gibbs equation)
Supplemental Table 1 (PDF)
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: robert.thomas@chem.ox.ac.uk.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
We thank STFC for the provision of neutron beam time at the
ISIS facility. K.M. thanks the China Scholarship Council for the
award of a scholarship.
−
OOCC8D16NHMe2+(bulk) ⇆ −OOCC8D16NHMe2+(surface)
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