Document [original]

Oil-in-water microemulsion droplets of TDMAO/

decane interconnected by the telechelic C

150

-C

: clustering and network formation†

Paula Malo de Molina,*

Marie-Sousai Appavou

and Michael Gradzielski*

The eﬀect of a doubly hydrophobically end-capped water soluble polymer (C

-PEO

150

-C

) on the

properties of an oil-in-water (O/W) droplet microemulsion (R2.85 nm) has been studied as a function

of the amount of added telechelic polymer. Macroscopically one observes a substantial increase of

viscosity once a concentration of 5 hydrophobic stickers per droplet is surpassed and eﬀective cross-

linking of the droplets takes place. SANS measurements show that the size of the individual droplets is

not aﬀected by the polymer addition but it induces attractive interactions at low concentration and

repulsive ones at high polymer content. Measurements of the diﬀusion coeﬃcient by DLS and FCS show

increasing sizes at low polymer addition that can be attributed to the formation of clusters of

microemulsion droplets interconnected by the polymer. At higher polymer content the network

formation leads to an additional slow relaxation mode in DLS that can be related to the rheological

behaviour, while the self-diﬀusion observed in FCS attains a lower plateau value, i.e., the microemulsion

droplets remain eﬀectively ﬁxed within the network. The combination of SANS, DLS, and FCS allows us

to derive a self-consistent picture of the evolution of structure and dynamics of the mixed system

microemulsion/telechelic polymer as a function of the polymer content, which is not only relevant for

controlling the macroscopic rheological properties but also with respect to the internal dynamics as it is,

for instance, relevant for the release and transport of active agents.

Introduction

Microemulsions are a thermodynamically stable way of having

homogeneous and very nely dispersed mixtures of oil and

water. They may occur in the form of oil-in-water (O/W) and

water-in-oil (W/O) droplets, or as bicontinuous structures.

1,2

Their formation is facilitated by the presence of surfactant

3,4

and the extent of structuring depends on the strength of the

amphiphile present at the oil–water interface.

5,6

Accordingly,

they are attractive formulations for many applications where

such highly interdispersed systems are required, for instance,

when a hydrophobic active agent, substrate, or enzyme has to be

present in an aqueous environment. However, for many appli-

cations of microemulsions the control of their rheological

properties is a crucial question, which is not easily accom-

plished. Typically dilute microemulsions possess the viscosity

of its continuous component (or the average of the both for the

case of bicontinuous systems)

7,8

irrespective of their structure.

Water-based droplet microemulsions typically are water viscous

and higher viscosities are only achieved for dense packing of

droplets, i.e., above 30 vol%, and then for still somewhat

higher concentrations microemulsion gels (cubic phases) are

formed.

9–13

However, the latter is a phase transition, going from

a rather low viscous solution directly to a gel-like behaviour.

This might be interesting for some applications, but in many

situations having higher but continuously tuneable viscosities

would be preferred, and without having to resort to go to very

high surfactant concentrations.

One way in which the viscosity of droplet microemulsions

can be enhanced largely is by addition of a telechelic polymer

with hydrophobic stickers (for instance, an alkyl chain) that

adheres to the droplets and which is able to bridge the indi-

vidual droplets. Depending on the number of polymer mole-

cules contained, a physical network forms with corresponding

rheological properties. For this approach a number of examples

have been published

14–20

and such systems have also been

studied theoretically.

21,22

The eﬀectiveness of bridging is mainly

controlled by the end-to-end distance of the polymer and the

surface-to-surface separation of neighbouring droplets. MC

simulations have shown that interactions become quite eﬀec-

tive once both lengths become similar,

leading to substantial

Stranski-Laboratorium f¨

ur Physikalische und Theoretische Chemie, Institut f¨

Chemie, Straße des 17. Juni 124, Sekr. TC7, Technische Universit¨

at Berlin, D-10623

Berlin, Germany

Forschungszentrum J¨

ulich GmbH, J¨

ulich Centre for Neutron Science JCNS, Outstation

at MLZ, Lichtenbergstr. 1, 85747 Garching, Germany

Department of Chemical Engineering, University of California Santa Barbara, 3357

Engineering II, Santa Barbara, CA, USA

†Electronic supplementary information (ESI) available: Analysis of the SANS data

and additional plots. See DOI: 10.1039/c4sm00501e

Cite this: Soft Matter,2014,10,5072

Received 5th March 2014

Accepted 12th May 2014

DOI: 10.1039/c4sm00501e

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changes of the pair distribution functions of the droplets.

Once there is on average more than one bridging polymer per

droplet, a network with viscoelastic behaviour is formed. The

elasticity of the network depends on the number of polymers

per droplet, and the viscosity depends on the structural relax-

ation time, which is determined by the exit time of the hydro-

phobic sticker from the microemulsion droplets and it is

strongly related to the length of the sticker.

Recently also the

role of the number of telechelic arms has been addressed and it

has been shown that the polymer architecture can play an

important role in the control of the rheological properties; even

more so with respect to the internal dynamics of the physically

cross-linked microemulsions, where the dynamics, as seen by

dynamic light scattering, becomes increasingly complex and

slower with increasing number of telechelic arms.

The dynamic properties of microemulsion and telechelic

polymer mixtures are not completely understood despite their

impact on the rheological properties or the kinetics of sol-

ubilisate exchange. So far, most of the work regarding the

dynamics was concerned with DLS experiments, which for the

case of highly viscous networks showed two or three relaxation

modes.

23,25–27

The fastest mode (diﬀusive) was associated with

the concentration uctuations of the microemulsion droplets,

the intermediate mode (independent of q) with the network

relaxation of the gel that is related to the terminal relaxation

time and the self-diﬀusion of the polymer, and the slowest

mode with the droplets in the surrounding network. Depending

on the relaxation time of the stickers the intermediate mode

may drop out of the experimental window for the case for too

long hydrophobic stickers.

Alternatively, FRAPP (uorescence

recovery aer patterned photobleaching) has been employed to

complement DLS measurements, where FRAPP showed a

monoexponential relaxation that corresponds to the slowest

mode observed in DLS.

In this respect there is quite a bit

known regarding the dynamic properties of networks of inter-

connected O/W microemulsion droplets, but the picture is yet

far from being complete.

Accordingly, the aim of this work is to study such a struc-

turally well characterized microemulsion network in a

comprehensive fashion by combining dynamic light scattering

(DLS) and uorescence correlation spectroscopy (FCS)

measurements, which yield complementary information, as the

rst method measures collective diﬀusion, the second self-

diﬀusion. For that purpose we chose a microemulsion based on

a surfactant frequently employed in formulations, tetradecyl

dimethyl amine oxide (TDMAO),

decane as oil (similar to

paraﬃn oil), and the commercial rheological modier Rewopal

6000 DS (a polyethylene oxide (PEO) with an average number of

150 EO units and having two stearate moieties at its ends).

TDMAO has been shown to be able to solubilize hydrocarbons,

where the solubilisation capacity is higher the shorter the chain

of the solubilized alkane.

30,31

TDMAO microemulsions with

decane have been studied in some detail before and it was

observed that the saturated microemulsion droplets have an

almost identical size (R¼3.0 nm) over a large concentration

range,

10,32

which makes it a well-dened system to be studied.

The comprehensive dynamic picture obtained by combining

DLS and FCS measurements for microemulsion networks as a

function of the amount of added polymer (quantied by the

number of stickers per microemulsion droplet: r) combined

with the structural and rheological information then shall allow

for a systematic understanding of their dynamic properties.

This is especially relevant for instance for molecular transport

and delivery within such systems, as it is important for phar-

maceutical or cosmetic formulations.

Experimental section

Materials

Tetradecyl dimethyl amine oxide (TDMAO, C

N(CH

)

Aromox 4D-W970, 24–26%) was obtained from Julius Hoesch

(D¨

uren, Germany) as a gi. The solutions were freeze-dried until

no further water could be removed, at which point one had a

water content of 2.5 wt%, as determined via Karl-Fischer-titra-

tion, which was taken into account during all sample prepara-

tions. n-Decane (98%) was obtained from Sigma Aldrich and

used as supplied. Water was either of Millipore grade or for the

case of SANS experiments we employed D

O obtained from

Eurisotop (99.9% isotopic purity). The telechelic polymer

was Rewopal 6000DS, which is a polyethylene oxide distearate

and was a gifrom Evonik Industries. In all our calculations

we assumed a chemical formula of (C

COO)

150

7157 g mol

1

) for this polymer.

The samples were prepared by taking the required amount of

a stock solution of 200 mM of surfactant. The appropriate

amount of oil and water was added to achieve the nal

composition of the microemulsion (100 mM TDMAO/35 mM

decane–water). The polymer containing microemulsions were

prepared by mixing weighted amounts of microemulsions with

varying amounts of polymer and mixing with a vortex mixer

under heat (60 C) to ensure complete dissolution of the

polymer. The polymer addition thereby led to a variation of the

droplet volume fraction, which however is rather small (always

being less than 5%, see ESI†).

Methods

Small-angle neutron scattering (SANS). SANS experiments

were done on the instrument KWS2

of the JCNS at the Heinz

Maier-Leibnitz Zentrum (MLZ, FRMII, Munich, Germany), with

scattered neutrons recorded on a 68 68 cm

detector with 128

128 channels based on a

Li glass scintillator of 1 mm

thickness. A wavelength of 0.5 nm with sample-to-detector

distances of 1 and 7.7 m and a wavelength of 1.2 nm (wave-

length spread: FWHM 20%) with a sample-to-detector distance

of 7.7 m were employed with a collimation of 8 m, thereby

covering a q-range of 0.03–5.2 nm

1

, where qis the magnitude

of the scattering vector dened as:

q¼4p

lsinðq=2Þ(1)

with qbeing the scattering angle and lthe wavelength. Samples

were contained in quartz cuvettes (QS, Hellma) and measured at

25.0 C. The sensitivity of the detector elements was accounted

for by comparing to the scattering of a 1.0 mm sample of water,

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and the water measurement was also used for absolute scaling.

Sample thickness, transmission, dead time (of the detector),

and electronic background were considered and the back-

ground due to the scattering of the beam with an empty cell was

subtracted. The obtained data were nally radially averaged and

merged using standard routines with help of the soware

BerSANS.

Dynamic light scattering (DLS). DLS experiments were per-

formed at 25.0 C using a setup consisting of an ALV/LSE-5004

correlator, an ALV CGS-3 goniometer and a He–Ne Laser with a

wavelength of 632.8 nm. Cylindrical glass sample cells (diam-

eter: 5 mm) were placed in an index matching toluene vat.

Intensity correlation functions were recorded under diﬀerent

angles between 50and 130. In the case of Gaussian scatterers

the intensity correlation function g

(2)

(t) measured in a homo-

dyne experiment is related to the eld correlation function

(1)

(t) by the Siegert relation:

(2)

(t)¼1+B|g

(1)

(t)|

(2)

where Bis an instrumental constant that reects the deviations

from ideal correlation (and should ideally be B¼0.33 for our

experimental set-up).

The correlation function g

(1)

(t) can be written as the Laplace

transform of the distribution of relaxation rates G(G):

gð1ÞðtÞ¼ðN

GðGÞexpðGtÞdG(3)

G(G) was obtained by a regularized inverse Laplace trans-

formation of the DLS data using the CONTIN algorithm

implemented in the ALV soware.

An alternative way of analysing multimodal relaxation

processes is by tting g

(1)

(s) to a multiexponential function. For

the cases discussed here a very suitable functional form was

found to be a monoexponential decay for the fast relaxation

process together with a stretched exponential decay describing

the slower relaxation, which is given by:

(1)

(t)¼A

exp(t/s

)+A

exp(t/s

)

(4)

where the amplitudes A

, the relaxation times s

, and the

stretching parameter b

characterize the relaxation process.

Fluorescence correlation spectroscopy (FCS). FCS measure-

ments were performed with a Leica TCS SMD FCS system with

hardware and soware for FCS from PicoQuant (Berlin, Ger-

many) integrated into a high-end confocal system Leica TCS SP5

II instrument. Excitation of Nile red was performed using an Ar

ion laser at 514 nm. The obtained correlation functions were

tted with the following expression:

GðtÞ¼Gð0Þ 1þt

scg!1 1þ1

S2t

scg!0:5

(5)

where the rst factor accounts for the diﬀusion in x–ydirection

the second in z-direction (the triplet relaxation was neglected as

the relaxation processes considered here were taking place on a

much slower time scale, i.e., above 20 ms). Sis the structure

parameter of the confocal volume, which is the ratio of the

transversal radius R

to the longitudinal radius R

(S¼R

The confocal volume was calibrated by a measuring the char-

acteristic time of Rhodamine 6G (5 nM) in water with a known

diﬀusion coeﬃcient of 4.0 10

10

1

The exponent gis 1

for pure diﬀusion. If it diﬀers from 1, the diﬀusion is said to be

anomalous, and if g< 1, it is called subdiﬀusive. For the case of

diﬀusive motion the diﬀusion constant can be calculated from

the characteristic time svia:

D¼Rxy2

4sc

(6)

Rheology. Oscillatory rheological measurements were per-

formed with a rheometer AR G2 from TA Instruments. A sinu-

soidal shear strain g(t)¼g

sin(ut) was applied at a constant

angular frequency, u, and with an amplitude, g

. As a result a

sinusoidal strain s(with an amplitude s

) was recorded, which

was shied by a constant phase angle d. The complex dynamic

shear modulus G*(u)dened by G0(u)+iG00(u) is given by (G0:

storage modulus; G00: loss modulus):

G*ðuÞ¼s0

expðidÞ(7)

The linear viscoelastic regime was ascertained for all

measurements by an amplitude sweep at 10 rad s

1

Viscosity measurements were carried out using previously

calibrated Schott micro-Ubbelohde viscometers of type Ic and

IIc (diameter Ic: 0.84+/0.01 mm; IIc: 1.50+/0.01 mm, capil-

lary constants: Ic: 0.03 mm

1

; IIc: 0.3 mm

1

). The viscosity

was calculated from the uid ow time as

¼rKt (8)

where h

is the zero shear viscosity, rthe sample density, Ka

calibration constant and tthe measured ow time.

Results and discussion

In our work we concentrated on an O/W microemulsion con-

sisting of 100 mM TDMAO/35 mM decane in water (3.3 vol%),

which is close to the emulsication boundary of this micro-

emulsion system.

Increasing amounts of Rewopal 6000DS

were added to this base formulation. The added polymer

amounts are given in g/g (total solution) and alternatively by the

number of hydrophobic stearate stickers per microemulsion

droplet, r, where the latter was calculated assuming an

unchanged radius of the microemulsion droplets of 2.85 nm

and a polymer formula of (C

COO)

150

. This size had

been deduced similarly before from SANS experiments

31,33

and

was conrmed in this study to be independent of the polymer

admixture (see 3.1). The most relevant parameter for the poly-

mer is its end-to-end distance r

,i.e., the average distance

between the hydrophobic stickers. The end-to-end distance of

the pure PEO chain free in solution can be estimated via:

ree ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

CNN

p‘EO (9a)

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dssðpcÞ¼ ﬃﬃﬃﬃﬃﬃ

r2!R(9b)

where C

is the characteristic ratio (in our case 5.2, as deter-

mined from scattering experiments

), Nthe number of mono-

mer units (150), and ‘

the length of a monomer segment

(‘

¼0.2928 nm). With these numbers we arrive at an end-to-

end distance r

of 8.2 nm, which then should be the relevant

distance over which the Rewopal 6000DS can easily lead to a

bridging of droplets. This then can be compared to the average

spacing of the microemulsion droplets. Assuming a primitive

packing for the given radius of 2.85 nm we can calculate the

mean distance d

(eqn (9b)) between neighbouring surfaces of

droplets to be 8.6 nm (10.4 nm would be the value for fcc

packing). This means that the average spacing of the micro-

emulsion droplets is very similar to the end-to-end distance r

of the stickers. Therefore an eﬀective bridging is to be expected

and repulsive interaction between the droplets is expected due

to the fact that, on average, the stickers might be placed more

closely together than they would like to be in an equilibrium

polymer conformation (an additional repulsion will be intro-

duced by the presence of the water-soluble PEO units in

between the microemulsion droplets).

In the following we studied this mixed microemulsion/tele-

chelic polymer system as a function of the amount of added

polymer, described by the number of stickers per micro-

emulsion droplet (r), by means of structural, dynamical and

rheological experiments. All the samples investigated were

homogeneous and long-time stable but varied very

pronouncedly with respect to their viscosity, which increases

largely upon the addition of the telechelic polymer. The aim is

to correlate the change of the macroscopic properties with the

mesoscopic structure and the dynamics of polymer bridged

microemulsion systems, with a particular emphasis on the local

structure and dynamics.

Small-angle neutron scattering (SANS)

In order to obtain a rened structural picture SANS measure-

ments were performed. We investigated how the structure of the

microemulsion is aﬀected by the addition of Rewopal 6000DS.

Fig. 1 shows the scattering intensity against the magnitude of

the wave vector, q, for O/W microemulsions with Rewopal

6000DS concentrations between 0 and 3 wt% (corresponding to

r¼0–15). At rst look, the unchanged position of the minimum

at high q(z1.5–1.6 nm

1

) and the very similar appearance of

the scattering curves for q>1nm

1

is a sign that the average

size and shape of the droplets are not inuenced by the poly-

mer. However, upon increasing the polymer concentration a

weak correlation peak arises, i.e., there is an increasing repul-

sion between the droplets. In addition, there is also a slight

upturn of the intensity at low qthat indicates either the pres-

ence of larger objects or an attractive interaction between the

droplets that is most pronounced at intermediate concentration

of polymer, i.e., for 1–2 wt% Rewopal 6000DS.

Arst model-free information was obtained by extrapolating

the SANS data by the Guinier-approximation to q¼0 (eqn (10a)),

from which the molecular weight M

was deduced (according

to eqn (10b), where we used a density dof 0.86 g ml

1

and for

the contrasts Drsee ESI†). The obtained values are summarized

in Table 1.

IðqÞ¼Ið0ÞexpRG2

3q2(10a)

Ið0Þ¼cgDr2MWSð0Þ

d2NA

(10b)

A quantitative analysis of the scattering data was done by

means of a model of polydisperse spheres interacting with an

attractive potential. The neutrons are scattered predominantly

by the microemulsion droplets and only for the higher q-range

Fig. 1 SANS scattering intensity as a function of the magnitude qof

the scattering vector for aggregates of the pure microemulsion (black

squares) and with increasing polymer concentrations between 0 and

3 wt% at a temperature of 25 C (subsequent curves are shifted by a

factor 2

for better clarity). Solid lines: ﬁts with eqn (11) and (13).

Table 1 Parameters obtained by the Guinier approximation (eqn (10))

from the SANS experiments; c

: total concentration in mass per

volume, I(0): intensity extrapolated to q¼0, S(0): structure factor at

q¼0 obtained from the ﬁts (eqn (11)), and M

: molecular weight

obtained from I(0) for diﬀerent amounts of added polymer (given in

wt% of total solution and number of stickers per droplet, r,

respectively)

pol

/wt% rc

/g L

1

I(0)/cm

1

S(0) M

/g mol

1

0 0 30.73 14.62 0.73 63 900

0.25 1.28 30.84 17.96 0.91 57 000

0.5 2.56 30.95 14.84 0.98 57 700

0.75 3.82 31.07 17.61 1.02 62 000

1 5.08 31.19 18.03 1.09 79 400

1.25 6.31 31.30 18.66 1.07 67 700

1.5 7.55 31.42 19.02 1.06 64 600

1.75 8.77 31.54 18.55 1.01 67 200

2 9.98 31.65 19.83 0.91 77 700

2.25 11.18 31.77 17.95 0.86 76 200

2.5 12.37 31.88 17.96 0.81 79 800

2.75 13.55 32.00 16.53 0.75 90 200

3 14.72 32.11 16.21 0.69 84 500

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some contribution from the scattering of the polymer chains

may be expected.

We neglected the polymer contribution aer

verifying that its eﬀect was not signicant for a quantitative

description of the experimental data. The scattered intensity for

polydisperse spheres as a function of the magnitude qof the

wave vector is expressed as follows:

I(q)¼FP(q,R)S(q,R

)+I

inc

(11)

where Fis the volume fraction of dispersed aggregates, P(q)is

the form factor accounting for shape and size of aggregates, S(q)

is the structure factor describing interactions between aggre-

gates, and I

inc

is the background that essentially accounts for

the incoherent scattering. To take into account the poly-

dispersity of the microemulsion droplets we assumed a log-

normal size distribution f(q,R,r

,s) and with this assumption

the form factor of polydisperse droplets was obtained as:

Pðq;RÞ¼ðN

Psðq;rdÞfðq;R;rd;sÞdr(12)

with:

Psðq;rdÞ¼Dr24p

3rd32 3sinðqrdÞqrdcosðqrdÞ

ðqrdÞ3!2

(12a)

fðq;R;rd;sÞ¼1N1

ﬃﬃﬃﬃﬃﬃ

prdsL

exp ðlnðrdÞmLÞ2

2sL2!2

(12b)

with:

sL¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

lns2

R2þ1

s(12c)

mL¼ln RsL2

2(12d)

where Dris the scattering length density (SLD) diﬀerence

between the microemulsion droplets and the average SLD of the

solution (Dr¼r

agg

hri, see ESI†), r

their radius, Rthe mean

radius,

N the number density of aggregates, and sthe standard

deviation of the distribution function. We consider the micro-

emulsion droplets to be homogeneous spheres and, therefore,

their SLD is the volume average of the scattering length density of

decane and TDMAO and hydrophobic stickers. For details of the

parameters employed in the calculation see Table S1.†In addi-

tion, we accounted for the experimental smearing, where the

experimental intensity I

exp

is the real scattered intensity dS/dU(q)

smeared by the resolution function R(q0,q,Dq):

IexpðqÞ¼ðþN

N

Rðq0;q;DqÞdS

dUðqÞdq0(13)

The resolution function R(q0,q,Dq) describes the distribution

of the q-vectors at a given instrumental conguration. Assuming

a Gaussian function for the resolution function,

eqn (13) yields:

IexpðqÞ¼ðþN

N

Dqﬃﬃﬃﬃﬃﬃ

pexp ðq0qÞ2

2Dq2!dS

dUðqÞdq0(14)

The q-resolution at a given qhas three contributions: the

nite size of the incident beam, the wavelength resolution and

the pixel size on the detector.

If we neglect the pixel size due to

its small dimension (7.5 7.5 mm

), Dqis described by:

Dq2¼Dq2ðlÞþDq2ðqÞ

¼"1

2ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2ln2

pDl

l2#q2þ"4p

l2

q2#Dq2(15)

Dl/lis related to the FWHM (full width at half maximum) value

of the triangular function of the wavelength distribution by

FWHM ¼l

(Dl/l) is related to the width of the direct beam.

For the structure factor S(q) the model of sticky hard spheres

(SHS) was employed. Baxter's SHS model

employs a hard

sphere model with an innitesimally narrow and innitely deep

square well described by the stickiness parameter a, that is a

measure of the attractiveness of the spheres at contact. The real

interaction potential is more complex. Numerical calculations

of the interaction potential for chains between two spheres

show an attraction in the order of kT, occurring at a separation

less than the end to end distance of the polymer and an

increasing repulsion with the polymer length and concentra-

tion.

43,44

However, if the range of the potential is not too large, a

Baxter model can be used instead and the eﬀective hard sphere

radius (R

) will give information about the repulsion and the

stickiness parameter (a) about the net attraction.

The details for this model and the corresponding S

SHS

(q) are

given in the ESI.†

The model has as adjustable parameters:

- mean particle radius R.

- standard deviation sof the size distribution function

- hard sphere radius RHS

- attractive interaction parameter a(stickiness parameter)

- hard sphere volume fraction, although not entirely. We

tted for the lowest and highest polymer concentration, and

then in the remaining ts forced the hard sphere volume frac-

tion to increase linearly with the polymer concentration (based

on the fact that the volume of the shell increases linearly). See

ESI†for more details.

This model allows us to extract the size of the microemulsion

droplets and information regarding their interaction potential

(Table 2).

The t curves are included in Fig. 1 and show very good

agreement with the experimental data. The results for the t

parameters are summarized in Table 2. The radius of the

microemulsion droplets remains basically unchanged. The

pure microemulsion has a radius of 2.82 nm (somewhat less

than the fully saturated microemulsion that has an average

radius of 3.12 nm

), and then increases slightly with increasing

polymer concentration to about 2.94 nm for the maximum

polymer content. This increase can be attributed to introducing

a signicant amount of C

chains into the microemulsion

droplets at the high polymer concentration (for 3 wt% r¼14.7,

corresponds to 0.074 stearyl chains per TDMAO molecule). In

addition, we observe a slight increase of the polydispersity of

the microemulsion droplets with increasing polymer content.

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A very interesting observation is that there is a pronounced

attractive interaction introduced into the system by the addition

of the telechelic polymer. This attraction describes the upturn at

low qby the stickiness parameter a, which is a quantitative

measure for the attractive component of the interaction

potential (and directly related to the second virial coeﬃcient B

via eqn (16)) and also allows to predict the attractive phase

separation of such systems. The inverse 1/ais proportional to

the attractive interaction, and rst increases rapidly upon

polymer addition, goes over a maximum of attractive interac-

tion for r5 and then becomes smaller again (Fig. 2). At the

same time we observe a pronounced increase of the hard sphere

radius R

that increases continuously from 3.9 to 6.8 nm

(Fig. 2). This is also seen directly in the curves via the

appearance of a correlation peak for increasing polymer

concentration. This means that the presence of the polymer

chains makes the microemulsion droplets bulkier (more

repulsive). Apparently the presence of the water soluble polymer

chains enhances the repulsive interaction between the micro-

emulsion droplets, thereby leading to the correlation peak. It is

interesting to note that the extra volume eﬀectively occupied by

the polymer, that should be proportional to (R

HS3

R

)

increases linearly with the amount of polymer contained (see

Fig. S2, ESI†), thereby conrming the picture that the repulsion

is directly linked to the amount of water soluble polymer chains.

Similar results were already observed for microemulsion

droplets, when the distance between the droplets is larger than

the net interaction is attractive and when the polymer is

longer, the net interaction is repulsive.

Theory predicts that

attraction dominates the second virial coeﬃcient when chains

are less stretched, while repulsion controls the highly stretched

limit.

43,44

For constant r

and d, the addition of polymer

contributes both to an increase of attraction and repulsion.

These counterbalancing factors in the interdroplet interac-

tion can be summarized with respect to their total eﬀect by

looking at the second virial coeﬃcient B

(eqn (16)), which is a

very good average measure for the eﬀective attractive/repulsive

interaction between the droplets. This is very useful as the two

parameters describing the structure factor S(q), the hard sphere

radius R

and the stickiness parameter a, describe opposite

eﬀects but are not fully decoupled in their eﬀect on the scat-

tering curves. The dimensionless second virial coeﬃcient can

be calculated from:

B2¼1

Vdrop

4pRHS3

341

a¼RHS

R341

a(16)

where V

drop

is the volume of the droplets as given for a radius of

2.85 nm.

The variation of the second virial coeﬃcient is given in Fig. 3

and shows a very interesting behaviour. It starts for the pure

microemulsion at a value of about 10 which is well above the

value for a simple hard sphere. This can be explained by the fact

that in our calculation we took the radius of the microemulsion

droplet without considering the hydration shell, which is taken

into account by R

in the analysis. Upon polymer addition the

attractive interactions increase dramatically and B

becomes

markedly negative, reaching a minimum around 1 wt% Rewo-

pal 6000 DS, which corresponds to 4–5 stickers per droplet.

Apparently for this condition the formation of interconnected

clusters is maximized. Upon further addition of polymer, B

increases again and this repulsive interaction can be ascribed to

the action of the water-soluble polymer molecules which are

located between the microemulsion droplets and thereby lead

to an eﬀective repulsion between the latter. For concentrations

above 2.2 wt% (r10) it then is higher again than for a simple

hard sphere system.

Rheology

The most obvious change of the microemulsions upon addition

of the telechelic polymer is the viscosity increase. The original

Table 2 Results of the analysis of the SANS data (ﬁts with eqn (11) and

(13)) for diﬀerent concentration of added polymer c

pol

and droplet

volume fraction F: mean radius of the droplets R, standard deviation of

the log-norm distribution s, hard sphere radius R

, hard sphere

volume fraction F

, stickiness parameter a, and second virial coeﬃ-

cient B

pol

/wt% rF/% sR/nm R

/nm F

/% aB

0 0 3.57 0.109 2.82 3.68 4.0 N10.57

0.25 1.28 3.59 0.113 2.77 4.6 3.8 0.349 5.21

0.5 2.56 3.60 0.102 2.82 5.93 4.8 0.254 0.59

0.75 3.82 3.62 0.114 2.82 6.09 5.7 0.226 4.26

1 5.08 3.63 0.120 2.83 6.3 6.6 0.203 10.20

1.25 6.31 3.65 0.128 2.84 6.31 7.5 0.208 8.88

1.5 7.55 3.66 0.128 2.86 6.42 8.4 0.212 8.09

1.75 8.77 3.68 0.129 2.88 6.57 9.1 0.225 5.30

2 9.98 3.70 0.136 2.88 6.6 10.4 0.250 0.19

2.25 11.2 3.71 0.148 2.87 6.6 11.2 0.270 3.60

2.5 12.4 3.73 0.155 2.88 6.75 12.1 0.280 5.50

2.75 13.6 3.74 0.157 2.87 6.81 13.0 0.300 8.86

3 14.7 3.76 0.149 2.94 6.83 14.0 0.320 10.92

Fig. 2 Hard sphere radius R

(squares) and stickiness 1/a(circles) as

derived from the SANS ﬁts as a function of the polymer concentration

or number of stickers per microemulsion droplet, r. The dotted lines

are a guide to the eye.

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microemulsion is basically water viscous, while upon addition

of the polymer an increase of viscosity by more than four orders

of magnitude is observed. The zero-shear viscosity is given in

Fig. 4 and shows that this marked viscosity increase occurs

rather sharply in the range of polymer concentrations of 1.5–2

wt%, which corresponds to a number of stickers per droplet rof

7–10, i.e., well beyond the concentration where the maximum of

the attractive interaction between the droplets has been

observed (Fig. 2 and 3). It is interesting to note that below this

concentration, the increase of viscosity is rather small, which is

in agreement with the SANS data, where up to this value only an

attractive clustering of the particles is seen. This means that

initially individual clusters form (until r4–5) that do not lead

to a substantial viscosity enhancement and only for a higher

polymer content (r6) a space-lling viscous network starts to

be formed. Such a sharp viscosity increase has been seen before

for the case of similar microemulsion droplets but for a much

shorter interconnecting polymer and correspondingly higher

microemulsion concentrations

and in similar fashion has also

been reported for other mixtures of microemulsions and doubly

hydrophobically modied polymer.

The sharp increase of the viscosity can be ascribed to a

percolation transition induced by the eﬀective interconnecting

of the microemulsion droplets by the telechelic polymer. Such a

percolation typically leads to a power law behaviour of the

viscosity which can be described as: h(c

–c)

k

below the

percolation concentration c

and h(c

c)

above the

percolation concentration.

The power laws t very well to our

experimental data as shown in Fig. 4 and from these ts we

obtain a c

of 1.54 wt% (r¼7.4) and k

¼0.7 and k

¼1.7,

respectively. Here it might be noted that slightly lower values of

1.4–1.6 for k

have been found for other microemulsions upon

the addition of a bifunctional telechelic polymers,

16,25,46

i.e.,

here the viscosity increase appears to occur in a slightly more

cooperative fashion.

The samples with more than 1.5 wt% Rewopal 6000 DS are

suﬃciently viscous to be measured by means of oscillating

rheological measurements, where they show viscoelastic

Fig. 3 Dimensionless second virial coeﬃcient as a function of the

added polymer concentration calculated with eqn (16) with the

structural parameters obtained from the SANS data. Solid line: B

¼4

(pure hard sphere).

Fig. 4 Zero-shear viscosity h

at 25 C of the mixtures of micro-

emulsions as a function of the concentration of C

-EO

150

-C

measured with a capillary viscometer until a concentration of 2 wt%

and with the instrument AR-G2 above this concentration. Solid line: h

¼0.0016((1.54 c)/wt%)

0.7

. Dashed line: h

¼3.6((c1.54)/wt%)

1.7

Fig. 5 (a) Storage (G0) and loss (G00) moduli as a function of angular

frequency (u) for microemulsion with 2.16 and 3.38 wt% of C

-EO

150

(b) Cole–Cole plot of the loss modulus G00 as a function of the

storage modulus G0for mixtures of microemulsion consisting of 100

mM TDMAO/35 mM decane–water with diﬀerent amounts of C

150

-C

added. The lines in (b) represent ﬁts with eqn (17).

Measurements were done with the instrument AR-G2 at a constant

temperature of 25 C.

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behaviour that is close to that of a Maxwellian uid. There are

some systematic deviations as shown for example in Fig. 5,

where the slopes for the storage modulus G0and loss modulus

G00 are systematically lower than the theoretically predicted

values of 2 and 1, respectively.

Fig. 5b shows the Cole–Cole plot, which is the representation

of the loss modulus G00 as a function of the elastic modulus G0

that allows for detailed observation of viscoelastic systems.

For

the Maxwell model the data for G0and G00 should lie on a

semicircle described by a generalized Maxwell model (eqn

(17)):

G00/Pa ¼((G0G

G0

)/Pa

)

(17)

The ts of eqn (17) to the experimental data were consis-

tently found to be best described for m¼0.482 (mwould be 0.5

for perfect Maxwellian behaviour), which means that there is

some systematic but not too large deviation from Maxwellian

behaviour. We could deduce reliably the shear modulus G

the samples from the ts to eqn (17) and the relaxation time s

from the angular frequency at which G0¼G00,s

¼1/u

The structural relaxation time s

is rather constant at 10

ms irrespective of the polymer concentration. This indicates

that this relaxation might be related to the residence time of the

stearyl moieties in the microemulsion droplets that can be

estimated to be 20 ms from relaxation kinetics.

The obtained G

is given in Fig. 6 and shows a pronounced

increase from about 100 to 1000 Pa (see Table 3) with increasing

polymer concentration which sets in beyond a threshold

concentration of 1.3 wt% (r6.2) Rewopal 6000 DS. Empiri-

cally the evolution of G

with the concentration c

of the poly-

mer (in wt%) can be described by a power law of the form: G

(307/Pa)((c

1.32)/wt%)

1.7

(see Fig. S3, ESI†). This critical

concentration value of 1.32 wt% is somewhat lower than that

observed in the viscosity measurements (1.54 wt%). The expo-

nent 1.7 is somewhat higher than the 1.42 found by Appell et al.

for a similar system

but close to the 1.8 found for a polymer

bridged W/O microemulsion.

In contrast, for the viscosity

increase also much higher exponents of 3.6–5.2 have been

reported for W/O microemulsions.

It can also be noted that for

higher polymer concentrations the increase is rather linear and

one might expect that simply every telechelic polymer contrib-

utes equally to the viscosity. This may be explained by the fact

that in the viscosity analysis one only sees a rather substantial

viscosity, which requires an eﬀective interconnection of the

droplets, while the analysis of the viscoelastic moduli gives the

value for the onset of elastic properties.

The experimental G

can also be compared to the theoretical

value for a simple network model given by:

kT (18)

where

is the number density of elastically active structural

elements. If all the polymer molecules were actively connecting

microemulsion droplets, their concentration (

pol

) would be

identical to

. For example, for c

pol

¼3 wt%, G

would be 12.4

kPa. The experimental data in Fig. 6 is about 10% of that

theoretical estimate (as seen from the values of G

pol

kT given

in Table 3). From the linear increase at higher polymer

concentration one can conclude that here about 22% of the

theoretical increase expected from eqn (18) is achieved. All this

is an indication that the network is not yet perfect (only a

smaller fraction of the polymer chains leads to bridges), and

that each polymer chain stores substantially less energy than kT.

Collective diﬀusion –dynamic light scattering (DLS)

In order to gain further insight into the mesoscopic dynamic

behaviour of the investigated polymer bridged microemulsions,

we performed DLS measurements. Fig. 7 shows the intensity

autocorrelation functions g

(2)

(t) for various concentrations of

Rewopal 6000DS added to the microemulsion. The pure

microemulsion shows a monoexponential relaxation, which

corresponds to the simple diﬀusion of microemulsion droplets

with a hydrodynamic radius of 2.43 nm. This is slightly smaller

than the value obtained by SANS but might be attributed to the

nite concentration and even more to a slight charging of the

microemulsion droplets due to protonation of the TDMAO

(there is no salt contained to screen the charges). The corre-

sponding repulsive interaction leads to an increase of the

apparent diﬀusion coeﬃcient, as it has been observed before for

such microemulsion droplets

. Upon addition of polymer, the

correlation function shows a slower relaxation, which indicates

the formation of bigger objects. At still higher polymer

concentration the curves start deviating from a simple mono-

exponential relaxation, and a second relaxation mode is

observed. The second mode appears at the concentration where

the solutions become highly viscous (1.75 wt%, r¼7). Its

amplitude and characteristic time increase with increasing

polymer concentration. This second relaxation mode has to be

associated with structural relaxations of an interconnected

network of microemulsion droplets.

In order to analyse the relaxation process and verify the

number of relaxation modes, the decay time distributions were

obtained by inverse Laplace transformation. The evolution of

Fig. 6 Shear modulus G

of microemulsions–HM polymer mixtures as

a function of the concentration of C

-EO

150

-C

measured with the

instrument AR-G2 at a constant temperature of 25 C. Solid line: G

/Pa

¼307((c1.32)/wt%)

1.7

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these distribution functions is presented in Fig. S4†and one

observes that the slower mode increases in intensity and moves

to longer times with increasing concentration of the Rewopal

6000DS, and the slow mode is always much wider than the fast

mode. One can distinguish two regimes of polymer concentra-

tion. First, below 1 wt% the distribution is monomodal. Then at

higher polymer concentration the relaxation process is appar-

ently bimodal and may well be described by two relaxation

processes, where the slower one is a rather broad one. Accord-

ingly, we analyzed the autocorrelation curves quantitatively in

terms of a sum of a normal and a stretched exponential decay of

(1)

(t) as described by eqn (19) (f: fast mode; sl: slow mode),

where the amplitudes and the stretching parameter bprovide

useful information regarding the dynamical behavior of the

systems.

(1)

(t)¼A

exp(G

t)+(1A

)exp(G

(19)

hGsli¼Gsl

bGð1=bÞ(20)

Here hG

iis the average relaxation rate from which by inversion

the average relaxation time can be calculated (Table 4) and

G(1/b) the gamma function.

Eqn (19) ts the experimental data very well. This analysis is

complementary to having two or three relaxation modes as the

stretched exponential can eﬀectively mimic a biexponential

decay for a not too large diﬀerence between the two relaxation

rates. Actually, it might be noted that in our g

(2)

(t) curves the

presence of a third relaxation mode is less clearly visible than in

the case of PEO-distearate investigated by Appell et al.

An important question is whether the relaxation processes

are diﬀusive or not. The q-dependence of the relaxation rates

was analyzed and showed that the fast mode has a q

2

depen-

dence (see Fig. S5†) and therefore can be associated with the

collective diﬀusion coeﬃcient D

f,coll

of the microemulsion

droplets or clusters formed by them. Its value decreases with

increasing polymer concentration (Fig. 8) and reaches a rather

constant value at 1 wt% Rewopal 6000DS. An interpretation

would be that in this concentration regime bigger agglomerates

(clusters) of the microemulsion droplets are formed, as already

indicated by the SANS measurements and, in agreement

with the rheological observations, these clusters are eﬀectively

2–3 times bigger in size than the individual microemulsion

droplets. For higher polymer content D

f,coll

increases again

slightly, which means that the collective diﬀusion of the smaller

structural units is not further reduced by the presence of the

polymer and the formation of an interconnected network of

microemulsion droplets. Here it should be noted that collective

diﬀusion does not really mean the actual transport of

individual droplets but is related to the relaxation of the density

uctuations in that system (further information regarding the

self-diﬀusion can be deduced from the FCS experiments

described in 3.4.).

Table 3 Viscoelastic parameters, shear modulus G

, relaxation time s

, and reduced shear modulus compared to the theoretical value according

to eqn (18) with the polymer concentration

pol

for

, for the polymer containing microemulsions as deduced from the generalized Cole–

Cole ﬁt (eqn (15))

pol

/wt% 1.72 1.96 2.18 2.44 2.67 2.9 3.14 3.38

r8.4 9.4 10.4 11.7 12.8 13.8 15.0 16.2

/Pa 103 170 209 306 496 754 912 974

/ms 16.7 9.1 8.3 8.9 10.3 9.5 10.2 10.0

pol

T0.017 0.025 0.028 0.037 0.054 0.076 0.085 0.084

Fig. 7 Intensity autocorrelation function g

(2)

(t) of microemulsions with

several concentrations of C

-EO

150

-C

added measured at a scat-

tering angle of q¼90and a temperature of 25 C. The lines are the ﬁts

with eqn (19).

Table 4 Values for the amplitude of the fast relaxation mode A

, the

eﬀective diﬀusion coeﬃcient D

eﬀ

(¼G

) derived from the fast

relaxation mode, the relaxation time of the slow process s

(obtained

at 90), exponent of the q-dependence of the relaxation rate n

and

the stretching exponent b

of the slow mode (obtained as the average

of the angle-dependent measurements)

pol

/wt% rA

eﬀ

/10

11

1

/ms hs

i/ms n

0 0 1.0 9.77

0.25 1.19 1.0 9.04

0.5 2.39 1.0 6.39

0.75 3.59 0.98 4.88 0.33 0.36 1.93 0.83

1 4.79 0.87 4.52 0.81 0.98 2.39 0.74

1.25 5.98 0.73 4.37 1.98 2.98 2.79 0.60

1.5 7.17 0.73 3.49 27.0 61.0 2.17 0.47

1.77 8.44 0.72 3.8 18.6 30.0 1.05 0.57

2.04 9.75 0.62 3.73 20.1 35.3 1.51 0.54

2.3 11.0 0.67 4.09 45.8 59.6 0.58 0.68

2.56 12.3 0.5 4.23 86.7 116 0.38 0.66

3.09 14.8 0.5 5.02 102 128 0.21 0.71

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The slow mode is more complex and not purely diﬀusive.

From the log–log representation (Fig. 9) it becomes clear that

the power law (Gq

slow

) dependence of the relaxation rate

changes markedly with increasing polymer concentration. The

slow relaxation process becomes much slower (Fig. 7 and 9 and

Table 4) with increasing polymer concentration. For low poly-

mer content, n

slow

is approximately 2, thereby indicating diﬀu-

sive relaxation, then rst increases up to a value of almost 3 for

1.25 wt% Rewopal 6000DS, and then for still higher a polymer

content n

slow

decreases substantially and approaches 0 around

2.5 wt% Rewopal 6000DS (see Fig. 9b), i.e., the relaxation

becomes independent of the size scale considered. Higher q

dependencies than q

2

have been observed for crowded

systems, where the slower relaxation time arises from caging or

obstruction eﬀect of neighboring particles or clusters.

Relaxation times that are qindependent are observed in

transient networks, where the slow relaxation time is correlated

to the structural relaxation time.

23,26,28

In our system at low

polymer concentrations the polymer induces the formation of

droplet clusters with the corresponding increase in eﬀective

volume fraction and viscosity (see Fig. 4) and the qdependence

of the slow relaxation increases. Once the network is fully

formed, the slower relaxation becomes qindependent. Such a

transition of the qdependence upon gelation has already for

instance been reported for the thermoresponsive gelling of

nonionic cellulose ether in the presence of ionic surfactants.

For this higher polymer concentration the slow relaxation

time is in the range of 20–100 ms (Table 4) in the same order of

magnitude of the rheological relaxation time (Table 3), but, in

contrast to the rheological times, one nds a systematic

increase of s

slow

with increasing polymer concentration.

Another interesting property is the stretching parameter b

which is close to 1 for low polymer content but then becomes

smaller with increasing polymer content (Table 4). This is

consistent with the observation that the second relaxation rate

is still diﬀusive at low polymer content. However, for the range

of higher polymer content the stretching parameter b

deviates

increasingly from unity, while at the same time the exponent n

deviates increasingly from the diﬀusive value of 2, i.e., this

mode is due to a more complex relaxation, that can be ascribed

to the viscoelastic network formed in the microemulsion

copolymer systems. Once the network is formed, b

goes to a

rather constant value.

The qdependance n

slow

rst increases in the range of cluster

formation, where B

goes to a minimum, and then rapidly goes

to zero for the highly viscous systems of an interconnected

network of O/W droplets. A further conrmation of the relation

between the slow mode and the elastic properties of the network

was asserted by the direct proportionality of A

slow

and G

(Fig. S6†).

Self-diﬀusion –uorescence correlation spectroscopy (FCS)

While DLS gives information about collective diﬀusion, FCS

measurements yield a complementary insight into the dynamic

behavior of the polymer bridged microemulsion systems as FCS

measures exclusively self-diﬀusion of the labeled domains. The

droplets were selectively uorescently labeled with Nile Red at a

concentration of 2.5 nM. Then FCS was measured as a function

of the concentration of added Rewopal 6000DS. These

measurements show for the pure microemulsion droplets a

diﬀusion coeﬃcient very similar to that seen by DLS (9.77, DLS

vs. 8.99 10

11

1

for FCS; compare Table 4 and S2,†but it

should be noted that due to the typical calibration uncertainty

of the confocal volume the precision of the FCS diﬀusion

coeﬃcient is not better than 20% in absolute units).

Fig. 8 Reduced collective diﬀusion coeﬃcient D

f,coll

of the fast

mode calculated as D

f,coll

¼1/(s

fast

). D

is the diﬀusion coeﬃcient of

the microemulsion without polymer. The dotted line is a guide to the

eye.

Fig. 9 (a) Slow relaxation time inverse s

slow1

as a function of the

magnitude qof the scattering vector. Solid lines: ﬁts with equation

slow1

q

slow

. (b) q-dependence exponent n

slow

as a function of the

polymer concentration added to microemulsion.

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Upon adding the bridging polymer Rewopal 6000DS, there is

a rapid increase of the relaxation time in the uorescence

correlation functions (Fig. 10 and Table S2†), that occurs in the

range of 0 to 2 wt% Rewopal 6000DS. The self-diﬀusion coeﬃ-

cient D

is correspondingly reduced (Fig. 11 and Table S2†)ina

similar fashion as seen by DLS. However, the reduction of the

self-diﬀusion coeﬃcient D

is much more pronounced (see

Fig. 8 and S5†), which means that the self-diﬀusion is much

more frozen in by the network formation. The fast decrease of

the self-diﬀusion coeﬃcient D

conrms the idea of the

formation of clusters of microemulsion droplets interconnected

by the polymer, which is similarly seen in FCS and DLS. Upon

further increase of r,D

remains almost constant and low,

thereby indicating that the O/W droplet are largely reduced in

their mobility. This is diﬀerent to DLS, where the network

formation leads to a slight increase of D

eﬀ

(as the network

formation allows for faster collective diﬀusion), while D

describing the movement of individual droplets remains low, as

they are basically xed in space (it might be noted that here we

cannot exclude molecular diﬀusion of the Nile red by a hopping

process, due to its solubility of 0.2 mg ml

1

in water).

At the same time with increasing rthe relaxation mechanism

becomes less uniform, which was quantied by tting the

experimental relaxation data by eqn (6) and deducing the

parameter g, which describes the deviation from simple diﬀu-

sion (that would correspond to g¼1). Accordingly, the dynamic

behavior of the polymer/surfactant mixtures depends largely on

their mixing ratio and on their total concentration.

Fig. 11 shows the anomalous diﬀusion exponent gthat

describes the monodispersity of the relaxation mechanism

(both the characteristic diﬀusion time s

and the anomalous

diﬀusion exponent gare also given in Table S3†). gis constant

up to a value of 1.0 wt% (r5) and then decreases linearly with

increasing r, which is exactly in the range where the percolation

in the samples, i.e., the formation of a highly viscous network,

takes place. Accordingly, the appearance of an anomalous

diﬀusion is related to the formation of this network in solution,

which means that the arrest of the individual microemulsion

droplets is directly seen by FCS. It might be noted here that our

FCS observations diﬀer substantially from those reported by

Cipelletti et al. obtained by FRAPP on a principally similar O/W

droplet system bridged by a PEO-DS. In their case the diﬀusion

observed by FRAPP was related to the slowest relaxation time

seen by DLS,

while in our case it is originally the same as the

fast mode of DLS and it then diﬀers increasingly for higher r

values. The hydrodynamic radius R

calculated from the self-

diﬀusion coeﬃcient D

(Table S2†) of the microemulsion

without polymer yields a value of 2.66 nm and the subsequent

change of D

with increasing polymer concentration is rst

quite similar to that seen by DLS. Only for high polymer content

it then is substantially lower. In that context it should also be

noted that FCS probes diﬀusion over a distance of 1mm,

which is comparable to the distances probed by DLS, but much

smaller than those of the FRAPP experiment.

Conclusions

Our comprehensive structural, dynamical and rheological

investigation of a diluted O/W microemulsion allows to derive a

detailed structural and dynamical picture of the changes occur-

ring upon adding increasing amounts of a telechelic polymer

able to bridge diﬀerent microemulsion droplets and how this is

related to the macroscopically observed increase of viscosity.

At low polymer concentration the bridging polymer simply

introduces an attractive interaction between the droplets, which

leads to the formation of interconnected clusters of droplets

(see Fig. 12), as also predicted by MC simulations.

22,55

This is

evidenced from SANS and also from DLS and FCS, where a

much slower diﬀusion of these clusters is observed. The

maximum clustering is observed for a number of about 5

hydrophobic stickers per microemulsion droplet (r¼5), as seen

by the minimum of the second virial coeﬃcient, that is a good

measure for the eﬀective interaction in this complex self-

assembled system. However, at this point the viscosity of the

samples is still rather low.

Fig. 10 FCS decay curves of microemulsion with C

-EO

150

-C

diﬀerent concentrations. The lines are the ﬁts with eqn (6) yielding the

parameters listed in Table S2.†The inset plots the characteristic

diﬀusion time s

as a function of the polymer concentration.

Fig. 11 Reduced self diﬀusion coeﬃcient D

s,ME

(squares) calcu-

lated as D

¼w

/(4s

) and anomalous diﬀusion exponent g(circles)

as a function of the concentration of C

-EO

150

-C

(obtained by

analysis with eqn (6)). D

s,ME

is the self diﬀusion coeﬃcient of the

microemulsion without polymer. The dotted line is a guide to the eye.

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Only for a somewhat higher polymer concentration of r¼7,

one observes a rather sharp increase of viscosity that can be

attributed to a space-lling formation of a polymer-mediated

network of microemulsion droplets (Fig. 12), i.e., here percola-

tion takes place. At this point also a much slower relaxation

mode starts to be seen in DLS (and as similarly observed before

for cross-linked microemulsion systems

23,25–28

that increases

with further increasing polymer content, and at this point FCS

shows the onset of anomalous diﬀusion. The amplitude of the

slower relaxation mode seen by DLS is directly proportional to

the shear modulus G

. For this completely interconnected

network of microemulsion droplets one has a largely enhanced

viscosity and pronounced viscoelastic properties of the systems,

where the collective diﬀusion seen by DLS is increasing again

(due to the interaction between the droplets introduced by the

presence of the polymer), whereas the self-diﬀusion seen by FCS

remains very low as the individual droplets are eﬀectively frozen

in the viscoelastic network. In that context it might also be

interesting to note that dynamic investigations on a related

microemulsion/telechelic star polymer system by means of

neutron spin-echo (NSE), which probes dynamics over the 1–20

nm range, showed that on that time scale the apparent diﬀusion

coeﬃcient was only reduced by a relatively small extent and

network formation, and was more eﬃcient for a 2-arm bridging

polymer compared to ones with more bridging arms.

This is

opposite to the trend observed for the rheology, where

rheological parameters increase with the number of arms,

but

demonstrates the complexity of the dynamic details in such

interconnected microemulsion networks.

Accordingly, the dynamic behaviour of the polymer/surfac-

tant mixtures depends largely on their mixing ratio and on their

total concentration and the structural evolution is described by

the structural picture given in Fig. 12. First, at low polymer

content, interconnected clusters are formed and only for higher

content of telechelic polymer a space-lling network with elastic

properties appears. Very interesting in that context are the

results from FCS, that describe the self-diﬀusion of the micro-

emulsion droplets and show a very slow internal dynamics for

higher polymer content, while at the same time collective

diﬀusion increases again. These ndings are very interesting as

they show in detail how the internal dynamics, that are corre-

lated for instance to the transport and release of active agents

from such a system, are controlled by the amount of telechelic

polymer contained. The macroscopic rheological properties can

directly be related to the amplitude and relaxation time of the

slow mode of DLS. The combination of DLS and FCS results

with the rheological observations then allows for a compre-

hensive understanding of these mixed systems, as it is essential

for an optimized formulation of such microemulsion systems,

which is important for many applications.

Acknowledgements

This work was funded by the DFG grant GR1030/9-1. For the

rheological measurements we are grateful to Prof. M. Solero and

the DAAD for funding this exchange program (D/07/10253). The

EU is thanked for funding the confocal microscope and its

attached FCS unit (EFRE 20072013 2/18). We acknowledge the

JCNS for granting beamtime as well as for funding of the SANS

experiments. Furthermore we would like to thank S. Prevost, K.

Bressel and R. Joksimovic for help with the SANS measure-

ments. P.M.M. gratefully acknowledges a grant from DAAD-La

Caixa. Evonik is thanked for the giof Rewopal 6000 DS.

Notes and references

1 W. Jahn and R. Strey, J. Phys. Chem., 1988, 92, 2294–2301.

2 D. Langevin, Annu. Rev. Phys. Chem., 1992, 43, 341–369.

3 T. P. Hoar and J. H. Schulman, Nature, 1943, 152, 102–103.

4 M. Gradzielski, Curr. Opin. Colloid Interface Sci., 2008, 13,

263–269.

5 G. Gompper and M. Schick, Phys. Rev. Lett., 1990, 65, 1116–

1119.

6 M. Gradzielski, D. Langevin, T. Sottmann and R. Strey,

J. Chem. Phys., 1996, 104, 3782–3787.

7 M. Gradzielski and H. Hoﬀmann, Handbook of Microemulsion

Science and Technology, Marcel Dekker Inc., New York, 1999,

pp. 357–386.

8 J. Peyrelasse, M. Moha-Ouchane and C. Boned, Phys. Rev. A:

At., Mol., Opt. Phys., 1988, 38, 4155–4161.

9 K. Fontell, Colloid Polym. Sci., 1990, 268, 264–285.

10 M. Gradzielski, H. Hoﬀmann and G. Oetter, Colloid Polym.

Sci., 1990, 268, 167–178.

Fig. 12 Schematic drawing of the structural evolution of micro-

emulsion/telechelic polymer systems as a function of the amount of

added linking polymer. (a) Low polymer content, just some bridging,

(b) intermediate polymer content, cluster formation, (c) high content,

network formation.

Paper Soft Matter

Open Access Article. Published on 14 May 2014. Downloaded on 24/02/2016 16:20:44.

This article is licensed under a

Creative Commons Attribution 3.0 Unported Licence.

View Article Online

11 M. Gradzielski, H. Hoﬀmann, J.-C. Panitz and A. J. Wokaun,

J. Colloid Interface Sci., 1995, 169, 103–118.

12 E. N¨

urnberg and W. Pohler, Prog. Colloid Polym. Sci., 1984,

69,64–72.

13 C. Provost and R. Kinget, Int. J. Pharm., 1988, 44,75–85.

14 M. Gradzielski, A. Rauscher and H. Hoﬀmann, J. Phys. IV,

1993, 3,65–79.

15 M. Odenwald, H.-F. Eicke and W. Meier, Macromolecules,

1995, 28, 5069–5074.

16 H. Bagger-J¨

orgensen, L. Coppola, K. Thuresson, U. Olsson

and K. Mortensen, Langmuir, 1997, 13, 4204–4218.

17 M. Filali, R. Aznar, M. Svenson, G. Porte and J. Appell, J. Phys.

Chem. B, 1999, 103, 7293–7301.

18 F. E. Antunes, K. Thuresson, B. Lindman and M. G. Miguel,

Colloids Surf., A, 2003, 215,87–100.

19 S. Maccarrone, H. Frielinghaus, J. Allgaier, D. Richter and

P. Lindner, Langmuir, 2007, 23, 9559–9562.

20 A. Zilman, J. Kieﬀer, F. Molino, G. Porte and S. A. Safran,

Phys. Rev. Lett., 2003, 91, 015901.

21 V. Testard, J. Oberdisse and C. Ligoure, Macromolecules,

2008, 41, 7219–7226.

22 J. M. G. Sarraguca, A. A. C. C. Pais and P. Linse, SoMatter,

2009, 5, 140–147.

23 E. Michel, G. Porte, L. Cipelletti and J. Appell, Langmuir,

2004, 20, 984–990.

24 P. Malo de Molina, C. Herfurth, A. Laschewsky and

M. Gradzielski, Langmuir, 2012, 28, 15994–16006.

25 E. Michel, M. Filali, R. Aznar, G. Porte and J. Appell,

Langmuir, 2000, 16, 8702–8711.

26 M. Schwab and B. St¨

uhn, J. Chem. Phys., 2000, 112, 6461–

6471.

27 T. Blochowicz, C. G¨

ogelein, T. Spehr, M. M¨

uller and

B. St¨

uhn, Phys. Rev. E: Stat., Nonlinear, SoMatter Phys.,

2007, 76, 041505.

28 E. Michel, L. Cipelletti, E. d'Humieres, Y. Gambin,

W. Urbach, G. Porte and J. Appell, Phys. Rev. E: Stat.,

Nonlinear, SoMatter Phys., 2002, 66, 031402.

29 Kirk-Othmer, Encyclopedia of Chemical Technology, John

Wiley & Sons, Inc., New York, 2004, vol. 2, p. 463.

30 G. Oetter, Dissertation, Universit¨

at Bayreuth, 1989.

31 M. Gradzielski and H. Hoﬀmann, Adv. Colloid Interface Sci.,

1992, 42, 149–173.

32 M. Gradzielski, H. Hoﬀmann and D. Langevin, J. Phys.

Chem., 1995, 99, 12612–12623.

33 A. Radulescu, V. Pipich, H. Frielinghaus and M.-S. Appavou,

J. Phys.: Conf. Ser., 2012, 351, 012026.

34 U. Keiderling, Appl. Phys. A: Mater. Sci. Process., 2002, 74,

S1455–S1457.

35 B. J. Berne and R. Pecora, Dynamic Light Scattering: With

Applications to Chemistry, Biology, and Physics, Courier

Dover Publications, 2000.

36 S. W. Provencher, Comput. Phys. Commun., 1982, 27, 213–

227.

37 D. S. Banks and C. Fradin, Biophys. J., 2005, 89, 2960–

2971.

38 P.-O. Gendron, F. Avaltroni and K. J. Wilkinson, J. Fluoresc.,

2008, 18, 1093–1101.

39 S. Kawaguchi, G. Imai, J. Suzuki, A. Miyahara, T. Kitano and

K. Ito, Polymer, 1996, 38, 2885–2891.

40 J. S. Pedersen and M. C. Gerstenberg, Macromolecules, 1996,

29, 1363–1365.

41 J. S. Pedersen, D. Posselt and K. Mortensen, J. Appl.

Crystallogr., 1990, 23, 321–333.

42 R. J. Baxter, J. Chem. Phys., 1968, 49, 2770–2774.

43 S. R. Bhatia and W. B. Russel, Macromolecules, 2000, 33,

5713–5720.

44 X.-X. Meng and W. B. Russel, J. Rheol., 2006, 50, 169.

45 D. Stauﬀer, A. Coniglio and M. Adam, Adv. Polym. Sci., 1982,

44, 103–158.

46 N. Puech, S. Mora, V. Testard, G. Porte, C. Ligoure, I. Grillo,

T. Phou and J. Oberdisse, Eur. Phys. J. E: SoMatter Biol.

Phys., 2008, 26,13–24.

47 E. A. G. Aniansson, S. N. Wall, M. Almgren, H. Hoﬀmann,

I. Kielmann, W. Ulbricht, R. Zana, J. Lang and C. Tondre,

J. Phys. Chem., 1976, 80, 905–922.

48 F. Kern, F. Lequeux, R. Zana and S. J. Candau, Langmuir,

1994, 10, 1714–1723.

49 T. Annable, R. Buscall, R. Ettelaie and D. Whittlestone,

J. Rheol., 1993, 37, 695–726.

50 U. Z¨

olzer and H.-F. Eicke, J. Phys. II, 1992, 2, 2207–2219.

51 P. J. Flory, J. Chem. Phys., 1950, 18, 108–111.

52 M. Gradzielski and H. Hoﬀmann, J. Phys. Chem., 1994, 98,

2613–2623.

53 K. L. Ngai, A. K. Rajagopal and S. Teitler, J. Chem. Phys., 1988,

88, 5086–5094.

54 B. Nystroem and B. Lindman, Macromolecules, 1995, 28, 967–

997.

55 J. M. G. Sarraguca, A. A. C. C. Pais and P. Linse, Langmuir,

2008, 24, 11153–11163.

56 I. Hoﬀmann, P. Malo de Molina, B. Farago, P. Falus,

C. Herfurth, A. Laschewsky and M. Gradzielski, J. Chem.

Phys., 2014, 140, 034902.

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