Intermicellar Interactions and the Viscoelasticity of Surfactant Solutions

Subscriber access provided by UNIV OF CALIFORNIA SAN DIEGO LIBRARIES

Article

Intermicellar interactions and the viscoelasticity of surfactant solutions: complementary use of SANS and SAXS Viviane Lutz-Bueno, Marianne Liebi, Joachim Kohlbrecher, and Peter Fischer Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b04466 • Publication Date (Web): 21 Feb 2017 Downloaded from http://pubs.acs.org on February 23, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Intermicellar interactions and the viscoelasticity of surfactant solutions: complementary use of SANS and SAXS

Viviane Lutz-Bueno,

∗,†,‡

Marianne Liebi,

¶,§

Fischer

†Institute ‡Current

Joachim Kohlbrecher,

k

and Peter

†

of Food, Nutrition and Health, ETH Zurich, 8092 Zurich, Switzerland

address: Swiss Light Source, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

¶Swiss

Light Source, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

§Current kLaboratory

address: Max IV Laboratory, Lund University, 22592 Lund, Sweden.

for Neutron Scattering and Imaging, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

E-mail: [email protected],+41563104621

Abstract In ionic surfactant micelles, basic interactions among distinct parts of surfactant monomers, their counterion, and additives are fundamental to tune molecular selfassembly and enhance viscoelasticity. Here, we investigate the addition of sodium salicylate (NaSal) to hexadecyltrimethylammonium chloride and bromide (CTAC and CTAB) and 1-hexadecylpyridinium chloride and bromide (CPyCl and CPyBr), which have distinct counterions and headgroup structures, but the same hydrophobic tail. Different contrasts are obtained from small-angle neutron scattering SANS, which probes 1

ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 31

dierences between the nucleus of atoms, and X-rays SAXS, which probes dierences in electron density. If combined, this contrast allows us to dene specic intramicellar length scales and intermicellar interactions. SANS signals are sensitive to the contrast between the solvent (D2 O) and the hydrocarbonic tails in the micellar core (hydrogen), while SAXS can access the inner structure of the polar shell, as the headgroups, counterions and penetrated salt have higher electron densities compared to the solvent and to the micellar core. The number density, intermicellar distances, aggregation number and inter/intramicellar repulsions are discussed based on the dependence of structure factor and form factor on micellar aggregate morphology. Therefore, we conrm that micellar growth can be tuned by variations in exibility and size of headgroup as well as the ionic dissociation rate of its counterion. Additionally, we show that the counterion binding is even more signicant to development of viscoelasticity than headgroup structure of a surfactant molecule. This is a surprising nding, showing the importance of electrostatic charges in self-assembling process of ionic surfactant molecules.

Introduction Micellar aggregates, composed of surfactant molecules, self-assemble into various morphologies in response to concentration, additives, pH and temperature, among other factors.

1

The addition of salt to cationic surfactant solutions causes morphological transitions from globular to long cylindrical micelles, known as wormlike micelles.

2

This anisotropic micellar

growth can be enhanced by the interplay of charge neutralization and hydrophobic forces, if aromatic salts, such as sodium salicylate NaSal, are employed.

3

The entanglement of these

long, exible and linear wormlike micelles induces the viscoelasticity of surfactant solutions, suitable for applications from oil industry to germicides.

46

Only anisotropic micellar growth

is treated in this work, but two-dimensional micellar growth has been reported for micelles of cesium peruorooctanoate.

7

Small-angle scattering SAS of radiation with similar wavelength as the size of the ag-

2


Page 3 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

gregate is commonly used to determine the overall micellar morphology and dimensions.

8

Inuences of micellar polydispersity and anisotropy are averaged in a scattering volume, determined by beam size and sample thickness. The investigation of bulk structural properties is the main advantage of SAS techniques compared to others, such as cryo-transmission electron microscopy. SAS is ideal to determine bulk structural variations based on various factors, such as temperature, alignment, concentration and composition.

Still, SAS data

analysis, especially decoupling form factor from structure factor, requires previous knowledge of micellar shape and size, otherwise the results may be ambiguous.

9

For example,

polydispersity and shape deviations aect the magnitude of scattering curves in the same manner. As a consequence, the scattering measured from ellipsoidal micelles or polydisperse spherical micelles cannot be distinguished.

10

The combination of real and reciprocal imaging

techniques to characterize micellar systems is the best way to obtain quantitative information on the structure of micellar systems without ambiguities. Small-angle neutron scattering SANS probes the overall micellar size, as the contrast is given mainly between a micellar core, rich in hydrogen H, and the solvent deuterium

I

as a function of the

P (q)

and structure factor

oxide D2 O, used for contrast enhancement. The scattering intensity scattering vector

S(q). 11

q

is determined by the product of form factor

In the case of inter or intramicellar interactions, a correlation peak is formed by this

product, and related to mean intermicellar distances

dim . 12

the scattering vector region where the structure factor

S(q) is mostly inuential can be easily

Using this peak as a reference,

determined from SANS measurements, while assuming a form factor. Additionally to SANS, we employ small-angle X-ray scattering SAXS as a complementary technique to obtain detailed information on morphology of micellar aggregates as a function of salt addition. In ionic solutions, condensation of counterion on the micellar surface inuences the eective surface charge, and consequently the morphology and interactions between micelles.

13

This leads to a polar shell region with high electron density, which will interact

more with X-rays than the core or the solvent, generating a dierent contrast if compared

3


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 31

to SANS. The decoupling between form factor method,

12,14

S(q)

P (q)


works as a contrast

when SAXS and SANS measurements are employed as complementary tech-

niques. By comparing SANS and SAXS data,

S(q)

and

P (q)

can be tted simultaneously,

leading to unique choices of parameters, thus more accurate ttings.

14

As the structure factor

is common for SANS and SAXS measurements, it reduces the number of tting variables to determine the form factors. tions

17

15

Hydration of micellar polar shell,

16

and intermicellar interac-

are often neglected in such studies. Hence in this work we focus mainly on elucidating

the inuence of intermicellar interactions on the development of viscoelasticity. The quantication of these eects on micellar network is important to conrm the relation between counterion dissociation and viscoelasticity enhancement of cationic surfactant solutions.

18

Experimental Samples The eects of surfactant headgroup and counterion on viscoelasticity are investigated for ve surfactant monomers with the same tail length of 16 carbons, based on interactions with sodium salicylate NaSal. We compare hexadecyltrimethylammonium chloride CTAC, 1-hexadecylpyridinium chloride CPyCl and benzyldimethyl hexadecylammonium chloride BDMC, which have dierent headgroup structures but same counterion, chloride Cl

−

. Hex-

adecyltrimethylammonium bromide CTAB and 1-hexadecylpyridinium bromide CPyBr were compared to CTAC and CPyCl, respectively, regarding the inuence of surfactant counterion, bromide Br

−

− − or chloride Cl , on their interactions with salicylate ions Sal .

surfactant concentration

Csurf

The

was xed at 100 mM for all solutions. This concentration is

located between the rst critical micellar concentration CMC 1 (when globular micelles selfaggregate) and the second critical micellar concentration CMC 2 (when anisotropic micellar growth into wormlike micelles occurs) for all surfactants. Increasing concentrations of NaSal

4


Page 5 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

CN aSal

R

were added, according to molar ratios

=

CN aSal /Csurf

micellar solutions, described rheologically in Lutz-Bueno et al.

from 0.1 up to 3. The same

18

, were measured in capil-

laries by small-angle X-ray scattering SAXS. To improve the small-angle neutron scattering SANS contrast between micellar core and solvent, equivalent solutions were prepared with deuterium oxide D 2 O as solvent. Even though viscosity changes slightly from pure H 2 O to

◦ 19 20 pure D2 O at 25 C and depends on solvent isotope as a function of chain length, these dierences are small enough to consider our solutions equivalent for SANS and SAXS.

Small-angle scattering SAS Small-angle neutron scattering SANS experiments were performed at the Swiss Spallation Neutron Source, SINQ, Paul Scherrer Institute.

The neutron wavelength was set to 6 Å.

Sample-to-detector distances of 2, 8, and 18 m attained a broad range of scattering vectors

q.

The solutions at rest were measured in quartz cuvettes with thickness of 1 mm.

dierential scattering cross section

dσ/dΩ(q)

The

was scaled based on incoherent scattering of

water, sample thickness and transmission. Small-angle X-ray scattering SAXS measurements were performed at the Swiss Light Source, cSAXS, Paul Scherrer Institute with wavelength of 1 Å. The X-ray beam was focused on the detector to 200 ×200

µm 2

onto boro silicate glass capillaries (Hilgenberg GmbH) with

1 mm of diameter. Ten positions were measured along the capillary. Ten scattering patterns were collected consecutively for each position, with exposure times of 0.1 s followed by a pause of 0.1 s. Then the next point, located 5 mm from the initial one, was measured. The 10 points (each one composed by 10 short measurements) were scanned 3 times, resulting in a total of 300 scattering patterns. They were monitored for radiation damage, and nally averaged to improve the statistics. A calibrated glassy carbon sample was used to scale the measured intensity

I(q)

to the dierential scattering cross section

dσ/dΩ(q). 21

All SAS curves shown in this work consider standard corrections and normalizations, such as background scattering, solvent scattering and transmission. For solutions, the increase in

5


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 31

interparticle interactions is usually estimated by measuring a series of concentrations. This method is not applicable to our systems as changing the concentration of the surfactant in solution changes the micellar morphology.

We maintain the surfactant concentration

constant, and cause well-controlled changes in morphology by adding dierent amounts of salt. In this way, salt concentration becomes the main factor acting on the neutralization of micellar surface charge, reducing intermicellar interactions, and enhancing viscoelasticity.

18

The presence of intermicellar correlations in non-dilute systems deviates the scattered intensity

I(q)

from a single-particle form factor

Fp (q).

If low anisotropy monodisperse glob-

ular micelles are present, the decoupling approach can be assumed,

11,22

and the scattering

intensity reads as:

I(q) = Nd P (q)S(q) where

Nd

is the number density of particles,

(1)

P (q) is the intraparticle form factor, dependent

S(q)

is the structure factor, dependent on interactions be-

tween particles. Usually, determining

P (q) is the main goal of SAS experiments, as particle's

on particle shape and size, and

shape and size can be retrieved. Here, we consider the structure factor Hayter and Penfold

23

S(q)

for spherical micelles, which is applicable only for

correlation peak is formed. The mean intermicellar distance

dim

calculated by

R
>

S(q)

>>

S(q)

>>

S(q) ≈ 1

(a) Morphological transitions from a rheological point of view.

headgroup structure and counterion on zero-shear viscosity tio

CN aSal /Csurf = R. Rc is when the

growth:

α

Inuence of

as a function of molar ra-

The following molar ratios dene regions of anisotropic micellar R∗ is related to the rodlike-

globular-to-rodlike transition occurs,

to-wormlike transition and dissociation constant

η0

26,27

Rmax

is where a maximum in

η0

is reached.

The counterion

is indicated for comparison. Adapted from Lutz-Bueno et al.

18

.

(b) Micellar morphological transitions, from globular to wormlike micelles, due to opposite eects of neutralizing the micellar surface and decreasing intermicellar interactions, upon salt addition

R.

The impact of salt addition on form factor

are represented by i-vi for each region of growth.

8


P (q)


S(q)

Page 9 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

are reduced,

30

changing the packing parameter

celles to grow in length.

PP

This neutralization process is responsible for anisotropic growth

into elongated micelles, such as prolate ellipsoids (a rodlikes (a

b,

see

R∗

of surfactant monomers, causing mi-

6=

b = c, see

in Fig. 1(b)-iii), determining a suitable

Rc

in Fig. 1(b)-ii) and

P (q) for each case.

Once the

micellar surface charge is completely neutralized by dissociated salt molecules, the structure factor

S(q)

becomes unity and is neglected, as indicated in Fig. 1(b)-vi. This occurs when

long exible wormlike micelles with high viscoelasticity are formed with maximum in zero-shear viscosity.

Rmax ,

related to a

3

Pure surfactant: globular micelles and repulsion We compare rstly the eects of headgroup structure and surfactant counterion on size and interaction of pure surfactant globular micelles. If no salt is added, intermicellar repulsions lead to strong structure factor contributions and a correlation peak is measured (see SI for more details). For surfactant tails with 16 carbons, the maximum tail length imately 2.05 nm.

16

lmax

is approx-

As the surfactant tail length is maintained constant for all surfactants in

this study, lmax denes the maximum micellar core diameter. We assume that pure surfactant micelles aggregate into either globular (a

≈ b) or prolate ellipsoidal shape (a 6= b = c), 16,31,32

since the concentration of 100 mM is between CMC 1 and CMC2 (see Fig. 1(b)-i). At this concentration ( R = 0), surfactant solutions exhibit water-like viscosities.

Eect of surfactant counterion Figure 2 compares the eect of counterions, chloride Cl of neutrons (a) and X-rays (b) from CTA with semimajor axis

a

+

−

− or bromide Br , on SAS curves

micelles. These micelles are prolate ellipsoidal

= 4.2 nm and semiminor axis

b = c =

calculated lmax . Similar results are presented in Aswal et al.

15

2.6 nm, longer than the

, as well as the details of the

tting parameters. Bromides provide better electrostatic screening than chloride counterions, as they bound more eciently to the surfactant headgroup.

9


18,31

Focusing on interactions

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

qcorr

between micelles, Fig. 2(a) exhibits distances

dim

Page 10 of 31

at 0.58 and 0.49 nm

−1

, leading to mean interparticle

of 10.75 and 12.85 nm for CTAC and CTAB, respectively. We conclude that

fewer and larger micelles aggregate with CTAB compared to CTAC at same concentration. The counterion is the only dierence between both systems. To generate longer micelles must form fewer micelles (lower number density (higher aggregation number

Nagg )

dim ,

CTAB

Nd ) with more molecules per micelle

than CTAC, as the same total number of molecules are

available in solution (100 mM). The micellar size increases as the correlation peak is displaced to lower

q , indicating that at concentrations of 100 mM, more CTAB micelles have ellipsoidal

shapes compared to CTAC. CTAC forms more globular micelles with

b = c = 2.3 nm.

a =

2.8 nm and

This is explained by counterion condensation: bromide dissociates less from

the micellar surface than chloride counterions, generating weaker intermicellar repulsion, and less pronounced structure factors, broadening the correlation peak,

33

as shown in Fig. 2(a).

(a) SANS

qcorr, CTAB

qcorr, CTAC

Nagg = 128 dim = 12.85 nm

qcorr, CTAC Nagg = 75 dim = 10.75 nm

qcorr, CTAB

P(q)

P(q)

Figure 2: Eect of surfactant counterion on small-angle scattering data: comparison between + SANS (a) and SAXS (b) for CTA surfactants with bromide and chloride as counterions. The sketch on the bottom-left corner indicates the type of form factor model considered: dense core for SANS (a) and core-shell for SAXS (b).

The position

qcorr

and distance

dim

are similar for SAXS in Fig. 2(b), although the cross

section magnitudes are inverted, if compared to SANS. For X-rays, chloride ions have weaker contrast than bromide ions, simply based on their atomic numbers.

In addition, CTAC

micelles are more repulsive, enhancing the structure factors. The combination of these factors causes higher scattering cross section magnitude of CTAC micelles in Fig. 2(b). Notice that the scattering cross section exhibits a second peak (or a shoulder) for SAXS. from a low scattered intensity at zero angle and a peak in

P (q), 12

10


34

This results

being misleading for the

Page 11 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

determination of correlation peaks. This shoulder is more pronounced for CTAB than for CTAC, indicating a higher amount of condensed counterions with higher contrast in the polar shell region, enhancing the core-shell form factor contribution. Aswal et al. Br

−

counterions form a monolayer around the micelle surface, while Cl

more disperse layer, since they are less bound to headgroups.

9

−

15

estimated that

counterions form a

This explains the dierences

in Fig. 2(b).

Eect of surfactant headgroup structure The inuence of headgroup size on self-assembling of globular micelles is compared in Fig. 3 for surfactants with similar tail length and counterion Cl tained at 100 mM. The correlation peaks

qcorr

−

, while the concentration is main-

in SANS data in Fig. 3(a) conrms that

surfactant headgroup size (CTAC < CPyCl < BDMC) is inversely proportional to micellar aggregation number

Nagg ,

and consequently directly proportional to number density

Nd .

Even though intermicellar interactions are aected by headgroup structure and size, their effects are less prominent than due to counterion type in Fig. 2(a), elucidating the importance of counterion dissociation on micellar self-aggregation. (b) SAXS

(a) SANS

qcorr, CTAC

Nagg = 75 dim = 10.75 nm

qcorr, BDMC

qcorr, CTAC

Nagg = 60 dim = 9.96 nm

qcorr, CPyCl

qcorr, CPyCl

Nagg = 69 dim = 10.49 nm

qcorr, BDMC

P(q)

P(q)

Figure 3: Eect of surfactant headgroup structure on SANS (a) and SAXS (b) scattering data of globular micelles formed by surfactant molecules with same tail and counterion. Headgroup size increases in the following order: CTAC < CPyCl < BDMC.

For the same concentration, surfactants with larger headgroups and similar tails will form more micelles, since the headgroup area is larger and requires less monomers to generate the same

rcore .

The polar shell is more hydrated for larger and lesser symmetric headgroups,

forming a rough interface between solvent and micellar core. This roughness results from

11


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 31

transitory dynamic thermal excursions of monomers between the micelle and the solvent. This interface is less ecient in providing electrostatic screening to headgroups, and solvent screening to the core,

17,35

agreeing that micellar growth rate upon salt addition is inversely

proportional to headgroup size.

18

All surfactants exhibit a shoulder in scattering cross sections in Fig. 3(b), typical of coreshell form factors, due to condensation of counterions within the polar shell. SAXS curves of CPyCl and BDMC are similar, as the high electron density of headgroup benzene rings is the main responsible for the contrast. Dierent magnitudes are observed by SANS. The further dissociation of chloride from the micellar aggregate contributes to micellar surface roughness, decreasing even more the solution contrast.

These eects together explain the

lower cross sections for CPyCl and BDMC micelles in Fig. 3(b) compared to CTAC.

Addition of NaSal: surface charge neutralization and micellar growth In the following sections we compare a series of solutions, composed of surfactant molecules with same tail and dierent headgroup structures upon addition of NaSal, based on the impact of reducing interparticle interactions on viscoelasticity. ular to ellipsoidal micelles at micelle neutralized by salt.

16

Rc

The transition from glob-

occurs to incorporate more surfactant molecules into a

This transition respects a dimensional constraint imposed by

the surfactant tail length, which avoids any energetically unfavorable empty space or water penetration inside the micellar core.

36

Anisotropic micellar growth is not only induced by

partial penetration of salicylate ions Sal

−

into the micellar core, but also by its absorption

on the micellar polar shell. Both eects contribute to decrease intra/intermicellar repulsions. Considering cationic micelles, partial penetration of Sal

−

into the micellar core is priority,

since there are gaps left by dissociated counterions. Only when these stronger repulsive regions between the headgroups are neutralized, the exchange between bound counterions and Sal

−

will occur.

18

In this manner, an aromatic salt acts as a counterion, interacting

not only electrostatically with the headgroups, but its hydrophobicity also contributes to

12


Page 13 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

morphological transitions, as they bind more strongly to the micellar structure than halide counterions.

31,37

Aswal and Goyal

38

observed that micellar growth is inversely proportional

to counterion hydration, thus the fact that organic salts are less hydrated, when penetrated into a micelle, enhances micellar growth. In this section, we compare the inuence of headgroup structure and counterion type on ionic exchange between halide counterion and salicylate ions Sal

−

at the micellar polar shell.

The addition of salt changes the morphology of surfactant micelles, thus equivalent form factors should be used, as summarized in Fig. 1(b).

S(q)

However, tting the structure factor

for any other shape than spherical (assuming center-symmetric charge distribution),

and small deviations from this condition, is challenging, shape and orientation.

33

32

since

S(q)

depends on particle

Furthermore, micellar size is not a constant, but rather a variable

determined by equilibrium processes depending on composition, concentration, temperature and external forces.

39

The radius of gyration of wormlike micelles is underestimated based

on a Guinier analysis, as intermicellar interactions are present even at

S(q) =

1.

35

For those

reasons, the interpretation of SANS and SAXS is, in this section, mostly qualitative.

Eect of NaSal on CTA + micelles Figure 4 compares SAXS and SANS curves of 100 mM of CTAC and CTAB solutions with increasing molar ratio

R

from 0 to 3.

performed for CTAB/NaSal.

3,32

Similar SANS experiments have been previously

The insets represent four selected solutions in log-log scale

for direct comparison of curve slopes for SAXS and SANS. The correlation peak appears at similar positions neutralization.

3

qcorr

for both radiations, pointing its directly correlation to repulsion before

The data in Fig. 4a and b were measured by SAXS, and a core-shell form

factor should be assumed. Samples with Br section intensities at low

R,

−

as counterion generate lower scattering cross

due to weaker contribution of the structure factor peak, since

the interaction between micelles are better screened. For SAXS, the Porod region with slope of

q −4

is reached for 1

0.4.

Similar behavior is observed during incorporation of NaSal into BDMC micelles in Fig. 7, even though the headgroup structure is more complex. For this system, the correlation peak is measured up to a maximum in zero-shear viscosity

η0

at

Rmax

19


= 0.4 (see Fig. 1) for SANS

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 31

and SAXS, suggesting that remaining intermicellar interactions even at the maximum in BDMC micelles form the

η0 (R) peak at smaller molar ratios than CPy +

even with chloride as counterion.

18

and CTA

+

η0 .

micelles,

It is explained by higher number density of BDMC

micelles, if compared to CTAC and CPyCl, even without NaSal. This is caused by the larger headgroup size of BDMC. It is possible that exible electron-rich benzenes in the BDM headgroup can bend to neutralize the repulsions of another BDM

+

+

headgroup, decreasing

the overall headgroup area and the packing parameter, acting as a counterion.

The high

hydration of BDMC polar shell could be a driving force for solubilization of salicylate ions into the core, thus

Rc occurs at lower concentrations than for other surfactants, independently

on counterion. Precipitation is observed for BDMC/NaSal at lower ionic exchange between Sal

−

R>

0.4, which could indicate

− and Cl , also agreeing with the displacement of

qcorr .

Micellar growth and mean intermicellar distance This section summarizes SANS and SAXS results of cationic micelles upon salt addition. It is known that large repulsive interactions between charged micelles in non-dilute surfactant solutions lead to high osmotic pressures.

29

For micelles, the osmotic compressibility is in-

versely proportional to the structure factor at zero scattering angle

S(0). 12,39

In turn,

S(0)

is proportional to the apparent micellar molecular weight, indicating the degree of hydration of the core and the micellar aggregation number

Nagg .

Another interpretation relates the

extrapolated scattering cross section at zero scattering vector

dσ/dΩ(0),

q = 0, called forward scattering

to the osmotic pressure derivative with respect to concentration.

in Fig. 4(c) and (d)

dσ/dΩ(0)

increases with molar ratio

R,

47

For example,

as the partial penetration of or-

ganic salt molecules into the micellar core densies the micelles, reducing its compressibility limit. The forward scattering their spatial arrangement,

48

dσ/dΩ(0)

depends only on the number of scatters and not on

thus this relationship is only valid for dilute solutions. Com-

paring the results from SAXS and SANS of all surfactants as a function of NaSal, we notice that SAXS measurements suppress

dσ/dΩ(0),

while SANS has a clear correlation between

20


Page 21 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

dσ/dΩ(0)

and micellar aggregation number,

49

which depends on molar ratio

R.

Figure 8(a) exhibits the dependence of forward scattering on molar ratio

R

for SANS

measurements of CTAC, CPyCl, BDMC, CTAB and CPyCl. Osmotic pressure is not calculates, as the dilution condition is not fullled, however a correlation between variations in

η0 (R)

dσ/dΩ(0)

and

is observed. Here, the type of surfactant counterion, bromide or chlo-

ride, impacts the rate of micellar growth, as expected.

Considering only surfactants with

bromide as a counterion, CTAB and CPyBr, we isolate the eect of headgroup structure.

+ Smaller headgroups, such as CTA , lead to higher forward scattering magnitudes, thus the aggregation number of these micelles has to be higher.

If only surfactants with chloride

are considered, the inuence of headgroup size follows similar trends as expected from rheology.

18

For all surfactants, the curves have similar slopes for

R > R∗ ,

pointing out the

regions where exchange between salicylate and halide counterions occurs, after the gaps due to counterion dissociation are lled. For

R < R∗ ,

there is an intense growth rate (only

visualized for chloride counterions). We assume that in this region, globular micelles grow into rodlike micelles, however they are not long nor exible enough to aect the rheological properties. The changes in growth rates in Fig. 8(a) can be linked to a maximum micellar length, which enhances viscoelasticity.

Charge neutralization not only enhances micellar

growth, but also their entanglement, leading to denser networks. It is clear that for

R > 1,

the counterion does not inuence

dσ/dΩ(0),

thus headgroup

structure is the only parameter causing these dierences, as observed for rheological measurements.

We assume that at equimolar concentrations, all the halide counterions have

been replaced with salicylate ions, thus there are no possible dierences between CTAC and CTAB, for example. Although headgroup structure still inuences micellar morphology. A decrease in

dσ/dΩ(0)

occurs for for

R > 1,

while zero-shear viscosity increases with

second viscosity peak (see Fig. 1). Similar decrease in

dσ/dΩ(0)

highly concentrated solutions of sodium dodecyl sulfate.

R=1

49

R

in a

was observed for a series of

The increase of

dσ/dΩ(0)

up to

is a proof of salt-induced growth based on the exchange between halide and organic

21


Langmuir

counterions, even for

R > Rmax , where simultaneous decrease in micellar length and branch-

ing of wormlike micelles are expected. For

R > 1,

excess salicylate ions in solution increases

intermicellar interactions, thus a higher structure factor contribution is observed at low

q.

For example, excess of potassium bromide KBr is known to suppress the growth of wormlike

R *

2 0 1 0 8 6

R *

R * 4

C T A C P y B D M C T A C P y

C l

2

B r

C C l C B B r

1 0 .1

0 .2

0 .4

0 .6 0 .8 1

2

3

1 0

4 0

(b ) a g g

3 5 3 0

N

im

4 0

(a )

M e a n in te r m ic e lla r d is ta n c e d

-1

6 0

[n m ]

50

]

micelles.

F o r w a r d s c a t t e r i n g d σ/ d Ω(0) [ c m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 31

2 5

1 0

B r

H G

2

0 .0

0 .1

0 .2

0 .3

R

2 0

C l

1 5 v is c o e la s tic ity w a te r - lik e

1 0 H G 0 .0

4

0 .1

0 .2

0 .3

0 .4

M o la r r a tio R

M o la r r a tio R

dσ/dΩ(0) as a function of molar ratio R for SANS data. (b) Mean intermicellar distance dim as a function of molar ratio R for all systems. dim values were calculated based on correlation peaks at qcorr in SANS curves. Notice a clear dependence of dim (R) on counterion type. The increase in headgroup size is indicated by the label HG. Changes in slope are indicated by black arrows, which correlate to critical molar ratios Rc ∗ and R obtained from rheology (see Fig. 1). The dashed lines are just guides for the eyes. dim > 12 nm seems to incite anisotropic micellar growth, enhancing viscoelasticity. This dim corresponds to an aggregation number Nagg of approximately 100 surfactant molecules per Figure 8: (a) Forward scattering

micelle.

The mean intermicellar distance

dim as a function of molar ratio R is compared in Fig. 8(b)

for all surfactant/NaSal systems for

R
Rc = 0.1

conrm that addition of organic salt causes anisotropic

micellar growth for all systems by decreasing the total number of micelles

Nagg .

in Fig. 1.

Nd

and increasing

The development of viscoelasticity is linked to a mean intermicellar distance of about 12

nm, which is three times larger than the micellar diameter of 4 nm, typical of surfactant tails

23


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

with 16-carbon. Notice that this distance is related to a

Page 24 of 31

Nagg = 100 surfactant molecules per

micelles. The addition of salt screens inter and intramicellar repulsions forcing the micelle to grow by agglomerating globular micelles. This leads to an ideal distance reached when fewer larger micelles are formed, to avoid eects of micellar interactions, enabling the development of viscoelasticity based on micellar entanglement. Notice that for solutions with correlation peak is not present, thus

dim

R ≥ 0.4 the

could not be estimated.

Conclusion Here we employed X-ray and neutron radiation to measure small-angle dierential scattering cross section

dσ/dΩ as a function of scattering vector q

dierent molar ratios

R.

for a series of cationic surfactants for

Well-known rheological measurements of zero-shear viscosity

function of salt addition or

η0 as a

R, while maintaining the surfactant concentration constant, dene

growth stages of globular into wormlike micelles. The dierent contrasts of the solutions to neutrons (in SANS) and X-rays (in SAXS) facilitated the determination of the individual contributions from form factor

P (q)


S(q),

to clarify the dependence of

anisotropic micellar growth on electrostatic interactions. For globular micelles, the scattering curves were well-represented by an ellipsoidal form factor for SANS, while for SAXS an ellipsoidal shell-core model was used, because of the high contrast of polar shell compared to core and solvent. Anisotropic micellar growth, usually described based on monomer structures and micellar dimensions, depends equally on intermicellar interactions. The presence of correlation peaks allows the determination of mean intermicellar distances aggregation numbers and micellar dimensions.

dim

which are directly related to

We conclude that the addition of sodium

salicylate NaSal to cationic surfactant solutions do not only inuence micellar dimensions and viscoelasticity, but also intra/intermicellar interactions. The development of wormlike micelles occurs for an overlap molar ratio

R∗

in which the correlation peak disappears from

24


Page 25 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

scattering curves, proving that enhancement of viscoelasticity through micellar entanglement can only occur once micellar surface charge is fully neutralized.

dim

as a function of salt addition conrms that one of the main factors, determining

critical molar ratio

Rc

and inciting anisotropic micellar growth, is counterion dissociation

and its reaction with salt, i.e. the micellar surface charge. As the formation of a micellar network is consistent with surface charge neutralization, the binding of counterion is even more signicant than headgroup structure of a surfactant molecule.

This is a surprising

nding, showing the importance of electrostatic charges in self-assembling process of ionic surfactant molecules.

Acknowledgments V.L.-B acknowledges nancial support from ETH Zurich (Grant No. ETH-2212-2) and Ana Diaz, for her help during the beamtime at Swiss Light Source - cSAXS.

References (1) Goyal, P. S.; Aswal, V. K. Micellar structure and intermicelle interactions in micellar solutions: results of small angle neutron scattering studies. Curr. Sci.

2001, 80, 972

979.

(2) Magid, L. J.; Li, Z. Flexibility of elongated sodium dodecyl sulfate micelles in aqueous sodium chloride: a small-angle neutron scattering study. Langmuir

2000, 1002810036.

(3) Aswal, V. K.; Goyal, P. S.; Thiyagarajan, P. Small-angle neutron-scattering and viscosity studies of CTAB/NaSal viscoelastic micellar solutions. J. Phys. Chem. B

1998,

102, 24692473.

(4) Ezrahi, S.; Tuval, E.; Aserin, A. Properties, main applications and perspectives of worm micelles. Adv. Coll. Interf. Sci.

2006, 128-130, 77102. 25


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 31

(5) Feng, Y.; Chu, Z.; Dreiss, C. A. Smart wormlike micelles: design, characteristics and applications ; Springer: New York, 2015; pp 1103.

(6) Verma, R.; Mishra, A.; Mitchell-Koch, K. R. Molecular modeling of cetylpyridinium bromide, a cationic surfactant, in solutions and micelle. J. Chem. Theory Comput.

2015, 11, 54155425. (7) Iijima, H.; Kato, T.; Yoshida, H.; Imai, M. Small-angle x-ray and neutron scattering from dilute solutions of cesium peruorooctanoate. Micellar growth along two dimensions. J. Phys. Chem. B

1998, 102, 990995.

(8) Goyal, P. S. Phase Transitions ; 1994; Vol. 50; pp 143176.

(9) Cabane, B.; Duplessix, R.; Zemb, T. High resolution neutron scattering on ionic surfactant micelles: SDS in water. J. Phys.

1985, 46, 21612178.

(10) Pedersen, J. S.; Cannavacciuolo, L.; Schurtenberger, P. In Giant Micelles Prop. Appl. ; Zana, R., Kaler, E. W., Eds.; CRC Press, 2007; pp 179222.

(11) Kotlarchyk, M.; Chen, S. H. Analysis of small angle neutron scattering spectra from polydisperse interacting colloids. J. Chem. Phys.

1983, 79, 2461.

(12) Zemb, T.; Charpin, P. Micellar structure from comparison of X-ray and neutron smallangle scattering. J. Phys.

1985, 46, 249256.

(13) Wu, C.; Chen, S.; Shih, L.; Lin, J. S. Direct measurement of counterion distribution around cylindrical micelles by small-angle X-ray scattering. Phys. Rev. Lett.

1988, 61,

645648.

(14) Zemb, T.; Diat, O. What can we learn from combined SAXS and SANS measurements of the same sample containing surfactants? J. Phys. Conf. Ser.

26


2010, 247, 012002.

Page 27 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(15) Aswal, V. K.; Goyal, P. S.; Amenitsch, H.; Bernstor, S. Counterion condensation in ionic micelles as studied by a combined use of SANS and SAXS. Pramana

2004, 63,

333338.

(16) Tanford, C. Micelle shape and size. J. Phys. Chem.

1972, 76, 30203024.

(17) Hayter, J. B.; Penfold, J. Self-consistent structural and dynamic study of concentrated micelle solutions. J. Chem. Soc. Faraday Trans. 1

1981, 77, 18511863.

(18) Lutz-Bueno, V.; Pasquino, R.; Liebi, M.; Kohlbrecher, J.; Fischer, P. Viscoelasticity enhancement of surfactant solutions depends on molecular conformation: inuence of surfactant headgroup structure and its counterion. Langmuir

2016, 32, 42394250.

(19) Kestin, J.; Imaishi, N.; Nott, S.; Nieuwoudt, J.; Sengers, J. Viscosity of light and heavy water and their mixtures. Phys. A

1985, 134, 3858.

(20) Berr, S. S. Solvent isotope eects on alkyltrimethylammonium bromide micelles as a function of aklyl chain length. J. Phys. Chem.

1987, 91, 47604765.

(21) Zhang, F.; Ilavsky, J.; Long, G. G.; Quintana, J. P. G.; Allen, A. J.; Jemian, P. R. Glassy carbon as an absolute intensity calibration standard for small-angle scattering. Metall. Mater. Trans. A

2010, 41, 11511158.

(22) Pedersen, J. S. Analysis of samll-angle scattering data from colloids and polymer solutions: modelling and least squares tting. Adv. Colloid Interface Sci.

1997, 70, 171210.

(23) Hayter, J. B.; Penfold, J. An analytic structure factor for macroion solutions. Mol. Phys.

1981, 42, 109118.

(24) Bastiat, G.; Grassl, B.; François, J. Micellar copolymerization of associative polymers: study of the eect of acrylamide on sodium dodecyl sulfate-poly(propylene oxide) methacrylate mixed micelles. J. Coll. Interf. Sci.

2005, 289, 359370.

27


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 31

(25) Breÿler, I.; Kohlbrecher, J.; Thünemann, A. F. SASt: A comprehensive tool for smallangle scattering data analysis. J. App. Crystal.

2015, 48, 15871598.

(26) Buckingham, S. A.; Garvey, C. J.; Warr, G. G. Eect of head-group size on micellization and phase behavior in quaternary ammonium surfactant systems. J.Phys.Chem.

1993,

97, 1023610244.

(27) Bales, B. L.; Zana, R. Characterization of micelles of quaternary ammonium surfactants as reaction media I: dodecyltrimethylammonium bromide and chloride. J. Phys. Chem. B

2002, 106, 19261939.

(28) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. Theory of self-assembly of lipid bilayers and vesicles. Biochim. Biophys. Acta

1977, 470, 185201.

(29) Amos, D.; Markels, J.; Lynn, S.; Radke, C. Osmotic pressure and interparticle interactions in ionic micellar surfactant solutions. J. Phys. Chem. B

1998, 102, 27392753.

(30) Vass, S.; Ple²til, J.; Laggner, P.; Gilányi, T.; Borbély, S.; Kriechbaum, M.; Jákli, G.; Décsy, Z.; Abuja, P. M. Models of micellar structure tested by SANS and SAXS in cesium dodecyl sulfate solution. J. Phys. Chem. B

2003, 107, 1275212761.

(31) Magid, L. J.; Han, Z.; Warr, G. G.; Cassidy, M.; Butler, P. D.; Hamilton, W. A. Eect of counterion competition on micellar growth horizons for cetyltrimethylammonium micellar surfaces:

electrostatics and specic binding. J. Phys. Chem. B

1997,

101,

79197927.

(32) Menon, S. V. G.; Goyal, P. S.; Dasannacharya, B. A.; Paranjpe, S. K.; Mehta, R. V.; Upadhyay, R. V. When does a living polymer live?

case of CTAB/NaSal. Phys. B

1995, 214, 604606. (33) Aswal, V. K.; Goyal, P. S. Selective counterion condensation in ionic micellar solutions. Phys. Rev. E

2003, 67, 18. 28


Page 29 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(34) Barnes, I. S.; Corti, M.; Degiorgio, V.; Zemb, T. X-ray and neutron-scattering measurements on concentrated non-ionic amphiphile solutions. Prog. Coll. Polym. Sci.

1993,

93, 205:206.

(35) Hayter, J. B.; Penfold, J. Determination of micelle structure and charge by neutron small-angle scattering. Coll. Polym. Sci.

1983, 261, 10221030.

(36) Perche, T.; Auvray, X.; Petipas, C.; Anthore, R.; Rico, I.; Lattes, A.; Bellissent, M. Small angle neutron and X-ray scattering study of the formation of micelles of CTAB in formamide. J. Phys. I

1992, 2, 923942.

(37) Aswal, V. K. Eect of the hydrophilicity of aromatic counterions on the structure of ionic micelles. J. Phys. Chem. B

2003, 107, 1332313328.

(38) Aswal, V. K.; Goyal, P. S. Counterions in the growth of ionic micelles in aqueous electrolyte solutions: a small-angle neutron scattering study. Phys. Rev. E

2000, 61,

29472953.

(39) van der Schoot, P.; McDonald, J. A.; Rennie, A. R. Static scattering by linear micelles. Langmuir

1995, 11, 46144616.

(40) Das, N. C.; Cao, H.; Kaiser, H.; Warren, G. T.; Gladden, J. R.; Sokol, P. E. Shape and size of highly concentrated micelles in CTAB/NaSal solutions by small angle neutron scattering (SANS). Langmuir

2012, 28, 1196211968.

(41) Croce, V.; Cosgrove, T.; Maitland, G.; Hughes, T.; Karlsson, G. Rheology, cryogenic transmission electron spectroscopy, and small-angle neutron scattering of highly viscoelastic wormlike micellar solutions. Langmuir

2003, 19, 85368541.

(42) Chen, W. R.; Butler, P. D.; Magid, L. J. Incorporating intermicellar interactions in the tting of SANS data from cationic wormlike micelles. Langmuir

29


2006, 22, 65396548.

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 31

(43) Collins, K. D. Charge density-dependent strength of hydration and biological structure. Biophys. J.

1997, 72, 6576.

(44) Varade, D.; Joshi, T.; Aswal, V. K.; Goyal, P. S.; Hassan, P. A.; Bahadur, P. Eect of salt on the micelles of cetyl pyridinium chloride. Coll. Surf. A

2005, 259, 95101.

(45) Vlachy, N.; Jagoda-Cwiklik, B.; Vácha, R.; Touraud, D.; Jungwirth, P.; Kunz, W. Hofmeister series and specic interactions of charged headgroups with aqueous ions. Adv. Coll. Interf. Sci.

2009, 146, 4247.

(46) Abezgauz, L.; Kuperkar, K.; Hassan, P.; Ramon, O.; Bahadur, P.; Danino, D. Eect of Hofmeister anions on micellization and micellar growth of the surfactant cetylpyridinium chloride. J. Coll. Interf. Sci.

2010, 342, 8392.

(47) Corti, M.; Degiorgio, V. Micellar properties and critical uctuations in aqueous solutions of nonionic amphiphiles. J. Phys. Chem.

1981, 85, 14421445.

(48) Jacrot, B.; Zaccaï, G. Determination of molecular weight by neutron scattering. Biopolymers

1981, 20, 24132426.

(49) Arleth, L.; Bergström, M.; Pedersen, J. S. Small-angle neutron scattering study of the growth behavior, exibility, and intermicellar interactions of wormlike SDS micelles in NaBr aqueous solutions. Langmuir

2002, 18, 53435353.

(50) Aswal, V. K.; Goyal, P. S. Role of counterion distribution on the structure of micelles in aqueous salt solutions: small-angle neutron scattering study. Chem. Phys. Lett.

2002,

357, 491497.

(51) Plazzotta, B.; Diget, J. S.; Zhu, K.; Nyström, B.; Pedersen, J. S. Small-angle X-ray scattering as a useful supplementary technique to determine molecular masses of polyelectrolytes in solution. J. Polym. Sci.

2016, 54, 19131917.

30


Page 31 of 31

Graphical TOC Entry

R=0

lin e

P(q)rodlike

ed

zero-shear viscosity (Pa.s)

ar

P(q)wormlike nch bra

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

P(q)ellipse P(q)sphere

S(q) ≈ 1

Rmax

Rc R*

molar ratio (R)

31


Intermicellar Interactions and the Viscoelasticity of Surfactant Solutions

Recommend Documents