research papers

J. Appl. Cryst. (2010). 43, 959–969 doi:10.1107/S0021889810025379 959

Journal of

AppliedCrystallography

ISSN 0021-8898

Received 3 November 2009

Accepted 28 June 2010

# 2010 International Union of Crystallography

Printed in Singapore – all rights reserved

Structure of water-based ferrofluids with sodiumoleate and polyethylene glycol stabilization bysmall-angle neutron scattering: contrast-variationexperiments

Mikhail V. Avdeev,a* Artem V. Feoktystov,a,b Peter Kopcansky,c Gabor Lancz,c

Vasil M. Garamus,d Regine Willumeit,d Milan Timko,c Martina Koneracka,c Vlasta

Zavisova,c Natalia Tomasovicova,c Alena Jurikova,c Kornel Csachc and Leonid A.

Bulavinb

aFrank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, 141980

Dubna, Moscow Region, Russian Federation, bTaras Shevchenko Kyiv National University, Physics

Department, Volodymyrska 64, 01601 Kyiv, Ukraine, cInstitute of Experimental Physics, Slovak

Academy of Sciences, Watsonova 47, 04001 Kosice, Slovak Republic, and dGKSS Research Centre,

Max-Planck-Strasse 1, 21502 Geesthacht, Germany. Correspondence e-mail: avd@nf.jinr.ru

Contrast variation in small-angle neutron scattering (SANS) experiments is

used to compare the structures of a water-based ferrofluid, where magnetite

nanoparticles are stabilized by sodium oleate, and its mixture with biocompa-

tible polyethylene glycol, PEG. The basic functions approach is applied, which

takes into account the effects of polydispersity and magnetic scattering.

Different types of stable aggregates of colloidal particles are revealed in both

fluids. The addition of PEG results in a reorganization of the structure of the

aggregates: the initial comparatively small and compact aggregates (about

40 nm in size) are replaced by large (more than 120 nm in size) fractal-type

structures. It is postulated that these large structures are composed of single

magnetite particles coated with PEG, which replaces sodium oleate. Micelle

formation involving free sodium oleate is observed in both fluids. The structures

of the fluids remain unchanged with increasing temperature up to 343 K. New

and specific possibilities of SANS contrast variation with respect to multi-

component systems with different aggregates are considered.

1. IntroductionThe structure description of complex (particularly poly-

disperse and multicomponent) systems is an important

problem in modern nanoscience. Ferrofluids or magnetic fluids

(fine stable dispersions of magnetic nanoparticles in liquids)

belong to such a class of nanosystems. To ensure the long-term

stability of ferrofluids in both unmagnetized and magnetized

states, the magnetic nanoparticles are coated with a chemical

layer, which prevents particle coagulation by attractive van

der Waals and magnetic interactions. Since the 1960s, ferro-

fluids have been widely used in various industrial and tech-

nical fields. The present-day interest in these systems is also

associated with their prospects in medical applications under

current active development (Odenbach, 2002; Brusentsov et

al., 2007; Sun et al., 2008), such as drug targeting, magnetic

resonance imaging (contrast medium), magnetic hyperthermia

for cancer treatment etc. For this purpose, much effort is

concentrated on the synthesis of highly stable, reproducible

and controllable water-based ferrofluids, but such synthesis

still poses problems compared with other classes of ferrofluids

based on nonpolar organic solvents or alcohols.

There are two principal concepts of the stabilization of

water-based ferrofluids. First, magnetic particles are coated

with a double stabilizing layer of surfactants, which provides

so-called steric (noncharged) stabilization (see e.g. Shen et al.,

1999; Bica et al., 2004, 2007; Avdeev et al., 2006; Vekas et al.,

2007). The main idea is to increase the mean distance between

the particles, thus decreasing the attraction compared with the

Brownian repulsion. In addition, the elastic repulsion of the

surfactant layers during contact between the particles contri-

butes to the interaction potential. The important feature of

such stabilization for polar carriers is the presence of free

surfactant in the solution, which provides the physical

adsorption of the second surfactant sublayer. The second way

is when certain types of ions are adsorbed on the surfaces of

the magnetic particles (Massart et al., 1995). They determine

the charge stabilization of the ferrofluid, which is the result of

the formation of double electrostatic layers around the

particles in water. An intermediate situation occurs in the

approach where double stabilization by surfactants is accom-

panied by additional charge formation on the particle surface.

Thus, the additional surface charge is detected in water-based

ferrofluids, where nanoparticles of magnetite are coated with a

double layer of sodium oleate (Hajdu et al., 2008; Vorobiev et

al., 2004). This charge is lower than in direct ionic stabilization,

but it is an important factor which determines the stability

properties of these systems.

In biocompatible colloidal systems for medical applications,

the chemical composition of the particle surface is of parti-

cular importance to avoid the action of the reticuloendothelial

system, which is part of the immune system, in order to

increase the lifetime of the magnetic nanoparticles in the

bloodstream. If magnetic particles in ferrofluids are coated

with neutral and hydrophilic compounds such as poly-

ethylene glycol (PEG) (Timko et al., 2004; Tomasovicova et al.,

2006; Hong et al., 2007), the lifetime increases from minutes to

hours or even days. There is widespread use of PEG in a great

number of applications (Harris & Zalipsky, 1997), including

the coating of colloidal particles of various origins (Jo & Park,

2000; Xu et al., 2003; Yoon et al., 2005; Zhang et al., 2007).

In this paper, we investigate the above-mentioned water-

based ferrofluid stabilized by sodium oleate, which is then

modified by introducing biocompatible PEG. Several types of

aggregates revealed in both ferrofluids complicate their reli-

able structure analysis. In this connection, we focus our

investigation on the application of small-angle neutron scat-

tering (SANS), which is one of the most suitable methods for

studying the inner structure of colloidal particles in complex

aggregate-containing systems. In particular, the contrast-

variation technique (with H2O/D2O mixtures in the solvent) is

used to reveal the scattering length density (SLD) distribution

in various aggregates of non-magnetized samples at the scale

of 1–100 nm. Compared with previous contrast-variation

applications for ferrofluids in the monodisperse approxima-

tion (Cebula et al., 1983; Grabcev et al., 1994, 1999), we employ

here the approach known as the method of modified basic

functions (Avdeev, 2007), which takes into account the poly-

dispersity effect. This method has recently been investigated

in the structure analysis of water-based ferrofluids with elec-

trostatic (Avdeev, Dubois et al., 2009) and steric (Avdeev et al.,

2010) stabilization. The proposed data treatment can

complement the direct modelling of the scattering curves from

aggregated ferrofluids for differing content of the deuterated

component in the solvent (Shen et al., 2001; Wiedenmann,

2001; Wiedenmann et al., 2002; Hoell et al., 2003; Butter et al.,

2004), which requires additional independent information

about the aggregate structure.

The aim of the paper is to follow the changes in the struc-

ture of a water-based ferrofluid induced by a biocompatible

additive (PEG), so the aggregates revealed by SANS are

compared for the fluid before and after addition of PEG. The

stability of the observed formations with increasing tempera-

ture is checked as well. It should be noted that multi-

component polydisperse systems are difficult for detailed and,

often, unique interpretation. The generalized approaches (as

presented here) deal with integral parameters and play an

important role in the development of the characterization of

the complex system, which also requires complementary and

independent methods. Thus, the model proposed at the end of

this work is also based on data from other methods, including

magnetization analysis, scanning electron microscopy (SEM)

and photon cross-correlation spectroscopy (PCCS). PEG

adsorption is analysed by infrared (IR) spectroscopy and

differential scanning calorimetry (DSC).

2. Materials and methods

2.1. Sample preparation and complementary characteriza-tion

The preparation of the ferrofluids studied here was based

on a co-precipitation method that involved mixing two solu-

tions (FeSO4�7H2O and FeCl3�6H2O) with an alkaline aqueous

medium (25% NH3). As a result of the reaction, a black

precipitate of magnetite, Fe3O4, was formed. The stabilization

of the magnetite precipitate was achieved by the addition of

sodium oleate (C17H33COONa, theoretical ratio 0.73 g to 1 g

of Fe3O4) with stirring and heating until the boiling point was

reached, followed by centrifugation at 5000 r min�1 for

30 min. The system at this stage is discussed below as an initial

ferrofluid and referred to as Sample 1. As a second stabilizer,

PEG (Mw = 1000 g mol�1) was added to the system. PEG was

added to the ferrofluid in the form of 10%(w/v) solution, and

the mixture was stirred and heated to ca 323 K and then left to

cool to room temperature (Sample 2). The amount of PEG

added was 2.5 g per 1 g of Fe3O4.

The volume fractions of magnetite, ’m, in the prepared

samples were determined using a magnetization analysis

(Fig. 1) performed by a superconducting quantum inter-

ference device magnetometer at room temperature. The found

values of the saturation magnetization (Fig. 1) are 0.017 and

0.0054 for ’m for Samples 1 and 2, respectively. One can see

that the addition of PEG significantly reduces the amount of

magnetite dispersed into the liquid. The curves in Fig. 1 are

fully reversible, thus reflecting the so-called super-

paramagnetic state of magnetic nanoparticles in the fluid.

However, SEM (JEOL 7000F microscope) on the dried

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960 Mikhail V. Avdeev et al. � Nanoparticle aggregates J. Appl. Cryst. (2010). 43, 959–969

Figure 1Magnetization curves for Samples 1 (filled squares) and 2 (open squares),with the observed saturation magnetization.

samples showed mean particle sizes of about 40 and 100 nm in

the two fluids, respectively, which is higher than the super-

paramagnetic size limit. The distributions of the particle

hydrodynamic size (Fig. 2) were also measured by PCCS

(Nanophox, Sympatec GmbH, Germany). The mean sizes of

these distributions are larger than those found in the SEM

experiments, which is usual for hydrodynamic sizes. The

particle sizes determined by SEM and PCCS can be associated

with aggregates (which are different in the two samples);

normally, the characteristic size of magnetite particles

obtained in the course of a co-precipitation reaction does not

exceed 10 nm (Odenbach, 2002; Bica et al., 2007, 2004; Vekas

et al., 2009), which determines their superparamagnetic

behaviour in an external magnetic field, as in Fig. 1. The

structure of these aggregates was analysed using SANS and is

compared below for the two samples.

Despite the aggregation observed, the studied fluids showed

good stability in the absence of an external magnetic field. No

significant changes in their properties were observed within a

period of one year after preparation.

To detect the immobilization of sodium oleate and PEG on

the magnetic particles, IR spectra (FTLA 2000, ABB) were

obtained by the KBr pellet method. The dried samples were

pulverized with pure dry KBr, the mixtures were pressed in a

hydraulic press to form transparent pellets and the spectra of

the pellets were measured. DSC (Perkin–Elmer DSC7) was

applied as well, to compare the two ferrofluids and a pure

PEG solution. The results of these techniques are discussed

below.

2.2. Details of SANS experiments

The ferrofluids were investigated by small-angle scattering

of nonpolarized neutrons within six months of preparation.

Contrast variation with H/D substitution was used to reveal

features of their internal structures at a scale of 1–100 nm. The

initial samples were dissolved in a 1:3 ratio in different

mixtures of light and heavy water to achieve D2O content of 0,

10, 20, 30, 40, 50, 60 and 70% in the final fluids. Pure H2O/D2O

mixtures with the same D2O content as in the experimental

samples were used as buffer solutions.

The experiments were carried out on the SANS-1 small-

angle instrument at the FRG-1 steady-state reactor of the

GKSS Research Centre (Geesthacht, Germany) (Zhao et al.,

1995). No external magnetic field was applied to the samples.

In this case, the isotropic (over the radial angle ’ in the

detector plane) differential cross section per sample volume

(scattering intensity) is obtained as a function of the

momentum transfer q = (4�/�)sin(�/2), where � is the incident

neutron wavelength and � is the scattering angle. The

measurements were made at a neutron wavelength of 0.81 nm

(monochromatization ��/� = 10%) and with a series of

sample-to-detector distances (SDDs) within the interval 0.7–

9.7 m (detector size 50 cm) to cover a q range of 0.04–2 nm�1.

The standard procedure for calibrating the cross section of the

water sample (Jacrot, 1976) was performed, together with

corrections for the background, sample-cell scattering and

incoherent background (subtraction of the scattering from the

corresponding buffer). At high SDDs (>4.5 m), calibration

patterns were obtained by recalculation of the curves for H2O

at an SDD of 1.8 m with the corresponding distance coeffi-

cients. The samples and buffers were placed in quartz cells

(Hellma) 1 mm thick and kept at room temperature (298 K)

during exposure to the neutron beam. The experiments were

also carried out at different temperatures (up to 343 K) for the

samples in H2O in order to judge the temperature stability of

the ferrofluids from a structural viewpoint.

Additionally, scattering curves were obtained for 1% solu-

tions of neat sodium oleate and PEG in D2O, in order to

obtain experimental data on the contributions of these

components in the free (non-adsorbed) state, which can occur

in ferrofluids, to the scattering from the studied Samples 1

and 2.

2.3. SANS data treatment

The experimental data were treated in terms of the

approach of Avdeev (2007) which, in addition to the classical

contrast-variation technique (Stuhrmann, 1995), takes into

account the polydispersity and magnetic scattering. The scat-

tering intensity is expressed as

IðqÞ ¼ ~IIsðqÞ þ� ~��~IIcsðqÞ þ ð� ~��Þ2~IIcðqÞ; ð1Þ

where

� ~�� ¼ �e � �s ð2Þ

is the modified contrast, i.e. the difference between the

effective mean SLDs of the particles, �e, and the liquid carrier,

�s. The modified basic functions ~IIcðqÞ, ~IIsðqÞ and ~IIcsðqÞ comprise

information on the nuclear and magnetic SLD distributions

within the particles, as well as the polydispersity function

(Avdeev, 2007). Among the three basic functions, the simplest

to interpret is ~IIcðqÞ ¼ hIcðqÞi, the average of the scattering

shape function Ic(q) of the Stuhrmann (1995) type over the

polydispersity function describing a particle-number distri-

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J. Appl. Cryst. (2010). 43, 959–969 Mikhail V. Avdeev et al. � Nanoparticle aggregates 961

Figure 2The hydrodynamic particle-size distributions in Samples 1 (solid line) and2 (dotted line), measured using PCCS.

bution with respect to different types of particle. The corre-

sponding term ð� ~��Þ2 ~IIcðqÞ prevails in the scattering intensity

[equation (1)] at sufficiently high contrast, so one can write

ð� ~��Þ2~IIcðqÞ ¼ INðqÞ��� ~��!1

; ð3Þ

where IN(q) denotes the nuclear scattering component in the

system. The other basic function, ~IIsðqÞ, describes the scattering

at the effective match point (� ~�� ¼ 0). It is determined by both

the residual nuclear scattering IN(q) and the magnetic scat-

tering IM(q) independent of the contrast:

~IIsðqÞ ¼ INðqÞ��� ~��¼0þ IMðqÞ: ð4Þ

Finally, the ~IIcsðqÞ contribution is a cross-function.

The best way to define the SLD �e is to use the solvent SLD

at the minimum in the �s dependence of the forward scattering

intensity I(0), which is found from the Guinier approximation

for the lowest q values,

IðqÞ ¼ Ið0Þ expð�q2R2g=3Þ; ð5Þ

where Rg is the apparent radius of gyration. Then, �e can be

directly related to an average particle SLD (Avdeev, 2007).

The important condition for equation (5), which determines

the approximation precision, is qRg < 1. If a Guinier analysis is

not possible for the determination of �e, the analogous �s

dependence of I(q) at any q point can be used (Avdeev, 2007).

However, the connection with the particle density in the

general case becomes very complicated.

The scattering invariants are expressed through the modi-

fied contrast as (Avdeev, 2007)

Ið0Þ ¼ nhV2c ið� ~��Þ2 þ nhV2

c iD; ð6aÞ

R2g ¼

hV2c R2

ci

hV2c iþ

A

� ~���

B

ð� ~��Þ2

� ��1þ

D

ð� ~��Þ2

� �; ð6bÞ

where n is the mean particle-number density, Vc and Rc are the

volume and radius of gyration of the equivalent particle shape

(particle with the effective unit SLD), and A, B and D are

parameters comprising information on the SLD distribution in

the particles and the polydispersity function [for definitions,

see Avdeev (2007)].

3. Results and discussion

We now explain the different stages of the experiment and

corresponding analyses. First, for both systems the initial

sample was diluted to a specific concentration (0.0043 and

0.0014 for ’m in Samples 1 and 2, respectively) with different

D2O content, �, in the carrier. This ensured that contrast

variation was performed for equivalent samples when varying

�. Next, the minimum in the � dependence of the scattering

intensity at certain values of q was associated with the effec-

tive match point. Thirdly, after the introduction of the modi-

fied contrast, separation of the modified basic functions was

carried out using scattering curves measured at different

contrasts. Fourthly, the solution of the corresponding system

of equations was checked experimentally by comparing the

obtained ~IIsðqÞ basic function with the scattering curves

measured around the effective match point. Finally, the ~IIcðqÞ

basic function was analysed. In particular, it was compared

with the scattering at � = 0, when the SLD of the surfactant

and PEG (for both, � ’ 0 � 1010 cm�2) is almost matched by

the scattering from light water (�H2O =�0.56� 1010 cm�2), so

only magnetite (�mag = 6.9 � 1010 cm�2) can be seen. Also, an

essential point is that at � = 0 the magnetic scattering can be

neglected as well, because of sufficiently high nuclear contrast

between magnetite and H2O (Gazeau et al., 2003; Avdeev et

al., 2006). Thus, at the final stage the scattering effect of the

H-containing components of the system is extracted from the

overall scattering.

The experimental SANS curves for the two samples with

different � are presented in Fig. 3. The changes in the char-

acter of the curves are similar in both cases. Fluids with a low

D2O content (below 30%) show mainly the signal from

magnetite. For higher D2O content the contribution from the

H-containing components becomes significant, which explains

particularly the appearance of a broad peak (band) in the

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962 Mikhail V. Avdeev et al. � Nanoparticle aggregates J. Appl. Cryst. (2010). 43, 959–969

Figure 3Changes in the SANS curves with contrast variation for (a) Sample 1 and(b) Sample 2. The per cent volume fraction of D2O in the solvent isindicated.

curves around q ’ 0.8 nm�1. At the same time, some specific

differences can be emphasized. First, the scattering from

Sample 1 is significantly larger on the absolute scale. It

resembles scattering from well defined particles, which is

reflected in the existence of the Guinier regime at low q

values. The corresponding Guinier plots are given in Fig. 4.

The observed dependence of I(0) versus � is used to determine

the effective match point (Fig. 5). In Sample 2, a degree of

aggregation affects the curves, comparable to what is observed

in water-based ferrofluids with double steric stabilization

(Balasoiu et al., 2006; Wiedenmann et al., 2002; Avdeev et al.,

2006; Feoktystov et al., 2009). This is concluded from the

power-law behaviour of the scattering at low q values, which

points to the fractal-type organization of the aggregates

discussed below. The Guinier regime is not observed in the

initial parts of the curves for these aggregates, which means

that the aggregate size is beyond the instrument limit

D ’ 120 nm (the estimate is derived from the minimum

measured q value in accordance with the rule D ’ 2�/q). In

this case, the effective match point cannot be found in the

same way as for Sample 1. Nevertheless, as noted above its

choice for polydisperse systems is entirely arbitrary. To relate

it further to the structure of the observed aggregates, we use

the � dependence of the intensity at q = 0.09 nm�1, which is

also given in Fig. 5. As follows from the basic equation (1),

such dependence is of a parabolic type at any q point. The

effective match points found from the minima in Fig. 5 are

� = 0.395 and 0.446 for Samples 1 and 2, respectively. To

calculate the SLDs corresponding to these match points, we

use the SLDs of H2O and D2O (�D2O = 6.34 � 1010 cm�2) in

the expression

� ¼ ��D2O þ ð1� �Þ�H2O; ð7Þ

which gives � = 2.17 � 1010 cm�2 for Sample 1 and � =

2.55 � 1010 cm�2 for Sample 2. These values are used as the

effective mean SLDs in the definition of modified contrast

[equation (2)].

The dependence shown in Fig. 5 for Sample 1 was replotted

in the form of equation (6a) using the modified contrast. From

the corresponding parabolic fit, the D parameter of equation

(6) was found to be 0.265 � 1020 cm�4. In Fig. 6 we plot the

contrast dependence [equation (6b)] of the radius of gyration

R2g ’ ð� ~��Þ�1 for Sample 1. The resulting parameters of the

corresponding fit are given in the figure caption. The D

parameter was fixed at the value found earlier. One should

note that the obtained characteristic apparent radius of

gyration ðhV2c R2

ci=hV2c iÞ

1=2 = 12.9 (4) nm is significantly larger

than in ferrofluids based on organic non-polar solvents and

alcohols, where its typical values do not exceed 8 nm

(Aksenov et al., 2002; Avdeev et al., 2006, 2007; Avdeev, Bica et

al., 2009).

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J. Appl. Cryst. (2010). 43, 959–969 Mikhail V. Avdeev et al. � Nanoparticle aggregates 963

Figure 4Guinier plots for Sample 1 at different contrasts, with the correspondingapproximations (lines) according to equation (5).

Figure 5The change in scattering intensity I(0) for the two samples with varyingD2O content in the solvent. Effective match points corresponding tominima are indicated by vertical arrows.

Figure 6The squared apparent radius of gyration as a function of inverse modifiedcontrast for Sample 1 (points) and the fit according to equation (6b)(line). The resulting parameters are hV2

c R2ci=hV

2c i = 166.9 (45) nm2, A =

52 (16)� 1010 cm�2 nm2, B =�29.4 (2)� 1020 cm�4 nm2 and D = 0.265�1020 cm�4 (fixed).

To find the basic functions for Samples 1 and 2 from the

experimental curves obtained at various contrasts, the

following functional was minimized (Whitten et al., 2008):

�2 ¼1

N � 3

Xk

IkðqÞ � ~IIsðqÞ �� ~��k~IIcsðqÞ � ð� ~��kÞ

2~IIcðqÞ� �2

�2kðqÞ

;

ð8Þ

where Ik(q) and �k(q) are the experimental intensity and

error, respectively, for a point q at the kth contrast, and N is

the number of different contrasts in the experiment.

The resulting modified basic functions are given in Figs. 7

and 8. The obtained ~IIsðqÞ functions agree well with the resi-

dual scattering at the effective match points (Fig. 7), which

proves the consistency of the fit.

The basic function ~IIcðqÞ (Fig. 8a) reflecting the average

shape scattering differs greatly for the two samples in the

initial parts of the curve (q < 0.4 nm�1). It may be concluded

that there is a transition from well defined particles in the case

of Sample 1 to smaller particles and large aggregates in

Sample 2. The new aggregates can be associated with fractal

structures, which determine scattering of a power-law type

with an exponent of about �2.5. This corresponds to a mass

fractal dimension D = 2.5 (Schmidt, 1995). The behaviour of

the curves at high q values is similar and they show certain

types of bands. For comparison, in Fig. 8(b) the scattering

curve obtained at � = 0 (light water) is given. At low q values,

the character of the curves repeats those of the ~IIcðqÞ functions,

thus proving that magnetite particles mainly determine the

shape scattering. At high q values, the curves differ signifi-

cantly from the ~IIcðqÞ functions. In particular, the bands

disappear, which means that their origin is connected with

particles composed of H-containing components. As a result

of the well observed size effect at low q values in the case of

Sample 1, one can apply the indirect Fourier transform (IFT)

procedure (Pedersen, 1997). The corresponding fitting curves

for Sample 1 are given in Fig. 8, while a comparison with the

observed p(r) functions is made in Fig. 9 and the values of the

fitted parameters are indicated. As a result, the difference

between the maximum sizes of the average particle and

magnetite is revealed and related to the effect of the surfac-

tant shell around the magnetite particles. Its thickness is

estimated from Fig. 9 to be about 2 nm (half of the difference

between the maximum sizes of the whole particle and the

magnetite component), comparable to the molecular length of

sodium oleate, which is about 2.1 nm according to the Tanford

(1972) formula. The observed relative difference between the

maximum sizes (Fig. 9) points to quite a strong interpenetra-

tion of the surfactant sublayers, because the magnetite parti-

cles are coated with a double layer of sodium oleate.

Usually, single particles of magnetite formed as a result of a

co-precipitation reaction satisfy well the log-normal size

distribution

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964 Mikhail V. Avdeev et al. � Nanoparticle aggregates J. Appl. Cryst. (2010). 43, 959–969

Figure 7Experimentally obtained ~IIsðqÞ basic functions for Samples 1 and 2,compared with the scattering curves at D2O contents close to the effectivematch points.

Figure 8(a) Experimentally obtained ~IIcðqÞ basic functions (shape scattering) forSamples 1 and 2, compared with (b) the curves at 0% D2O (scatteringfrom magnetite only). Solid lines for Sample 1 correspond to IFT fits.Solid lines for Sample 2 show power-type scattering with the indicatedexponents. The dashed line for the curve at 0% D2O in (b) shows thescattering from separate magnetite nanoparticles with radii distributedaccording to equation (9), R0 = 3.4 nm, S = 0.38.

DnðRÞ ¼ ½1=ð2�Þ1=2

SR� exp½� ln2ðR=R0Þ=2S2

�; ð9Þ

where R0 corresponds to the most probable radius and S

determines the distribution width. For example, such a Dn(R)

function has been observed for organic nonpolar (Aksenov et

al., 2002; Avdeev et al., 2007) and alcohol-based (Avdeev et al.,

2006) ferrofluids, where most of the magnetite particles were

shown to be in a separated (non-aggregated) state. In contrast,

here, for Sample 1 we fail in the direct modelling of the curve

at � = 0, after assuming a spherical shape for the magnetite

particles and applying equation (9). In Fig. 9 one can compare

the p(r) functions of the magnetite component and the whole

particle obtained in the given experiment and calculated

according to equation (9) with the typical parameters for

magnetite from previous work, R0 = 3.4 nm and S = 0.38, and

with the surfactant layer thickness estimated above (Avdeev et

al., 2006). This indicates that, in the case of Sample 1, we are

also dealing with a type of aggregate in the solution. They are

quite compact (aggregation number of about ten), which

determines the size observed in the SANS curves at low q

values. The fact that equation (9) does not hold for these

aggregates (with larger parameters R0 and S compared with

separate magnetite particles) can be explained by two reasons.

Firstly, if magnetite particles coated with surfactant form

aggregates, they are not in close contact, so, strictly speaking,

the spherical approximation of the magnetite component in

the aggregates is not valid. Also, for a low aggregation number

the effect of shape anisotropy can be significant, thus making

the aggregate shape very different from the spherical one. In

Fig. 9 some asymmetry is seen in the experimentally observed

p(r) functions. The effect of interaction between aggregates

(structure-factor effect) can be neglected because of the low

aggregate volume fraction, which is estimated to be below

0.01. Despite the major scattering contribution from the

aggregates in Sample 1, the presence of separate magnetite

particles coated with surfactant cannot be excluded.

For Sample 2 the aggregate effect is more explicit than for

Sample 1. The IFT procedure does not give stable smooth

solutions for the p(r) functions, since the maximum size is

undetermined. The characteristic size of the magnetite parti-

cles composing the aggregates can be derived from the scat-

tering at 0% D2O (Fig. 8b). A specific break at q = 0.42 nm�1

gives the characteristic radius Rchar ’ 7.5 nm, which is

comparable to the similar radius of magnetite in organic non-

polar ferrofluids with stabilization by oleic acid (Avdeev et al.,

2007). In SANS experiments on polydisperse particles, this

parameter (Rchar) is a weighted radius of the type Rchar =

(hRV2i/hV2i)1/2, where V is the particle volume and angle

brackets h . . . i denote the average over the particle-size

distribution function. Using the typical parameters for

magnetite nanoparticles indicated above for the Dn(R) func-

tion, one obtains Rchar = 7.6 nm. The model curve showing the

scattering from single particles with these parameters is given

for comparison in Fig. 8(b). Thus, we can conclude that the

basic units of the fractal aggregates in Sample 2 are single

magnetite particles. The change in the basic structural units is

also reflected in a decrease in the total scattering intensity.

Compared with Sample 1, the magnetite concentration in

Sample 2 is about three times less, which is not enough to

explain the more than ten times decrease in the scattering for

0% D2O (Fig. 8b). Since the contrast factor for magnetite and

its content are the same for both samples, this decrease is

mainly because of the change in the characteristic particle

volume. The non-aggregated particles in the initial fluid, the

possible presence of which was mentioned above, are the most

probable basic units in the new large branched aggregates. We

suppose that the added PEG replaces the first surfactant on

the surface of these particles, which decreases their stability

and initiates the growth of new aggregates.

We relate the bands above q ’ 0.3 nm�1 in the ~IIcðqÞ func-

tions to micelles of free sodium oleate in the solvent. At the

highest q values the two functions differ by only a factor

showing that the micelle concentration is about 30% higher in

Sample 2 than in Sample 1. Additionally, the contribution

from the micelles is more significant in the case of Sample 2,

when the scattering from the magnetite particles decreases. In

this case, the Guinier region for the micelles is well resolved.

In Fig. 10 this is treated by IFT, taking into account the power-

law scattering at low q values. If a spherical shape is assumed

for the micelles, the resulting radius of gyration of the micelles,

Rgmic = 1.59 (5) nm, gives R = 2.05 nm according to the well

known equation R2gmic ¼ ð3=5ÞR2. The obtained value corre-

lates well with the molecular length of sodium oleate. This

conclusion is confirmed by comparing the ~IIcðqÞ basic function

with the experimentally observed and properly rescaled scat-

tering from a 1% solution of free sodium oleate (Fig. 10),

which shows the presence of micelles. The parameter Imic(0) =

0.021 (1) � 10�20 cm3 can be used to estimate the volume

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J. Appl. Cryst. (2010). 43, 959–969 Mikhail V. Avdeev et al. � Nanoparticle aggregates 965

Figure 9Functions p(r) for Sample 1, as a result of IFT fits to the ~IIcðqÞ function(shape scattering) and the scattering intensity at 0% D2O (scattering frommagnetite only). Functions are calibrated to unity. The resulting values ofthe characteristic radius of gyration are Rg = 12.9 (1) nm for the ~IIcðqÞfunction and Rg = 11.6 (1) nm for the scattering intensity at 0% D2O. Themodel p(r) functions based on the Dn(R) function of the type given inequation (9) are shown for single magnetite particles and forhomogeneous particles where the surfactant shell is taken into account.

fraction, ’mic, of the surfactant in the micelles. For this purpose

we use the equation

Imicð0Þ ¼ nmicV2mic ¼ ’micVmic; ð10Þ

where nmic and Vmic are the micelle concentration and volume,

respectively. From equation (10) we have ’mic = Imic(0)/Vmic =

0.0058, which corresponds to 5.8 mg ml�1 (we assume the

specific density of sodium oleate to be �1.0 g ml�1). Taking

into account the difference in the ~IIcðqÞ functions at high q

values, one obtains for Sample 1 ’mic = 0.0045, or 4.5 mg ml�1.

In both cases, these concentrations significantly exceed the

critical micelle concentration (CMC) for sodium oleate of

2 mM or about 0.6 mg ml�1, corresponding to free surfactant

in the non-associated state in solution.

From the comparison of the effective match points of the

two samples, we conclude that the addition of PEG increases

the relative content of magnetite in the aggregates. For

Sample 1, by definition of the effective match point (Avdeev,

2007) one has

�e ¼ h�V2c i=hV

2c i; ð11Þ

where the mean particle SLD, �, is different for various

particles in the solution and the brackets h . . . i again denote

the average over the polydispersity function. Nevertheless,

with good precision we can relate equation (11) to the

aggregate SLD only, since the contribution from the micelles is

negligible. In fact, from equation (10) we have Imic(0) =

0.017 � 10�20 cm3 for the micelles in Sample 1, which is

negligibly small compared with the analogous parameter for

the aggregates [Ic(0) = 20 � 10�20 cm3]. As a first approx-

imation, one can neglect the polydispersity in equation (11).

Taking into account the SLDs of magnetite and surfactant, the

volume fraction of magnetite in the aggregates of Sample 1 is

0.31.

In Sample 2, the effective match point is defined in a way

that differs from equation (11), but some conclusions about

the mean SLD of the aggregates in this case can also be made.

Again, the contribution from the micelles can be neglected.

Then, one can see that the character of the initial parts of the

SANS curves (Fig. 3b), i.e. the power-law decrease, does not

change with contrast, which means that in the region corre-

sponding to the aggregates the curves differ approximately by

only the contrast factor. In fact, if one plots the contrast

dependence of the scattering intensity [I(q) versus �] at

different q points, for each point one obtains a parabolic-type

curve. It can be seen that the position of the dependence

minimum (�0) changes slightly for the first ten points over the

measured q interval. This means that the value �0 = 0.45

obtained above corresponds to the mean SLD of the aggre-

gates. To good precision, the SLD of the new component in the

aggregates, i.e. PEG inclusion, is the same as for sodium

oleate. Again, after neglecting the polydispersity in equation

(11), one obtains a value for the volume fraction of magnetite

in the aggregates of Sample 2 of about 0.37. It is reasonable to

assume that PEG replaces some part of the adsorbed surfac-

tant and forms new (but thinner) shells around the magnetite

particles, which explains the lower content of the H-containing

component in the aggregates and is in agreement with the

increase in free surfactant in Sample 2. In turn, this assumes

that the PEG is adsorbed onto the magnetite in a flat config-

uration, as shown for other types of interfaces with mercury

(Mota et al., 1994; Tronel-Peyroz et al., 1983) and silica (Dijt et

al., 1990).

PEG adsorption on magnetite is confirmed by IR spectro-

scopy (Fig. 11) and DSC (Fig. 12). Fig. 11 clearly demonstrates

PEG coating of magnetite from a comparison of the IR

spectra for pure sodium oleate and PEG before and after

adsorption on magnetite. The absorption bands at 1560 cm�1

correspond to asymmetric stretching of the carboxylate group

of the oleate anions. The bands at 1462, 1447 and 1425 cm�1

(usual for organic compounds) are caused mainly by the CH2

and CH3 groups from both oleate and PEG; before adsorption

they are narrow, but after adsorption they overlap, so a wide

band is observed. The band at 1113 cm�1, which appears

mainly as a result of the C—O stretching vibration of poly-

ether, proves the presence of PEG. Magnetite itself also shows

a band at 584 cm�1. In Fig. 12, typical DSC traces of the

considered systems are given. It is seen that the glass transition

temperature (corresponding to the peak position) in the

curves of pure PEG (about 320 K) is shifted to lower values

for the mixed systems, which is an indication of PEG

adsorption. The peak splitting shows the presence of non-

adsorbed PEG in the solution.

As far as the aggregate sizes are concerned, it can be seen

that the SANS data are in agreement with the results of SEM

and PCCS analysis. Additionally, the applied contrast varia-

tion makes it possible to draw conclusions about the inner

structure of the aggregates. Such a complementary aspect in

investigations of complex systems containing aggregates of

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966 Mikhail V. Avdeev et al. � Nanoparticle aggregates J. Appl. Cryst. (2010). 43, 959–969

Figure 10The experimentally obtained ~IIcðqÞ basic function for Sample 2. Differentscattering levels are indicated, corresponding to two different kinds ofparticles. The solid line shows a fit to the curve, which takes into accountthe power-law type scattering from aggregates (low q values) andscattering from micelles (high q values). The basic function is comparedwith the scattering from 1% solutions of free sodium oleate (SO) andPEG in D2O scaled with the appropriate contrast factor.

various types is quite important. For example, the increase in

aggregate size after the introduction of PEG observed here in

SEM and PCCS could easily be interpreted as the formation of

a PEG shell around the magnetite particles, with a thickness of

about the full length of the polymer, whereas in fact (as has

been shown from the SANS study presented here) this is not

the case.

To summarize, the proposed model of the PEG addition

effect is illustrated qualitatively in Fig. 13. The initial fluid

(Sample 1) consists of single magnetite nanoparticles (coated

with a double layer of sodium oleate) and small aggregates

thereof. The free surfactant excess in the solvent required for

stabilization results in the formation of micelles of non-

adsorbed surfactant. The added PEG (Sample 2) replaces to

some extent the surfactant on the accessible surface and

modifies the shell around the magnetite, leaving its thickness

approximately the same. However, the separate particles in

Sample 2 are not stable and form new fractal-type aggregates.

The initial aggregates also develop and sediment during the

preparation, thus explaining the lower volume fraction of

dispersed magnetite in Sample 2. The possible non-adsorbed

PEG affects the scattering only slightly compared with the

other components. In Fig. 10 the maximum possible influence

is demonstrated by comparing the ~IIcðqÞ function with the

experimental scattering curve from a 1% solution of free PEG

in D2O, properly rescaled by the contrast factor. This last

curve is consistent with the similar SANS data for PEG of

various molecular masses (Rubinson & Krueger, 2009;

Rubinson et al., 2008).

It is important to note that the aggregate exchange seen

here is not observed under the same experimental conditions

if the amount of added PEG is half that in the experiments

described above. The results of the SANS measurements in

this case are very close to those obtained for Sample 1, while

DSC shows PEG adsorption. Thus, the higher PEG content in

the modified sample determines the higher rate of the

observed aggregate exchange.

Finally, the temperature stability of the studied fluids must

be mentioned. As was shown previously (Avdeev et al., 2006),

a temperature increase (to 343 K) strongly affects secondary

aggregation in water-based ferrofluids with steric double

stabilization and leads to its distortion. In the given case, full

temperature stability in both samples is observed up to 343 K.

This is concluded from the fact that the curves corresponding

to different contrasts do not show significant changes with

increasing temperature. Thus, the fluids studied here are

characterized by stronger interactions between particles in the

aggregates.

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J. Appl. Cryst. (2010). 43, 959–969 Mikhail V. Avdeev et al. � Nanoparticle aggregates 967

Figure 12DSC traces of the systems considered.

Figure 11IR spectra of pure sodium oleate, pure PEG and magnetite/PEGcomposite particles from Sample 2. Spectra have been shifted verticallyfor convenience.

Figure 13Schematic representation of the PEG effect on the structure of the water-based ferrofluid magnetite/sodium oleate. PEG replaces sodium oleate tosome extent on the accessible surface, which results in the formation of anew shell (shown conventionally in the right-hand part as homogeneousgrey rings around the magnetite particles) and initiates the appearance ofnew fractal-type aggregates with a size of more than 120 nm and fractaldimension of 2.5. Initial compact aggregates (size �40 nm) develop aswell and are removed during the preparation. Micelles of sodium oleateare present in both samples.

4. Conclusions

The structures of a water-based ferrofluid with magnetite

stabilized by sodium oleate and its mixture with PEG have

been revealed by the contrast-variation technique in small-

angle neutron scattering experiments. In particular, the addi-

tion of PEG leads to reorganization of the aggregate structure

compared with the initial ferrofluid. Notably, a type of

exchange of packed and comparatively small aggregates

(about 40 nm) with developed and large aggregates (above

120 nm) is observed, which is caused by the adsorption of PEG

on the magnetite particles. Aggregates in both kinds of

ferrofluids are stable with respect to time and temperature

increase (343 K).

The possibilities of the modified basic functions approach

for polydisperse and superparamagnetic systems have been

demonstrated using the analysis of nonhomogeneous multi-

scale structures. It has been shown that, despite the complex

nature of the systems studied, the method allows one to judge

reliably the different scattering contributions. Firstly, the

nuclear scattering is well separated from the magnetic scat-

tering. The shape scattering can then be compared with the

scattering from the different components of the system, which

provides an additional independent analysis of the inner

structure of colloidal particles in ferrofluids. As a result,

important conclusions can be drawn with respect to the scat-

tering from the basic units of the ferrofluid and their aggre-

gates, as well as to micelles of non-adsorbed surfactant.

This work was performed within the framework of the

Helmholtz–RFBR project (grant No. HRJRG-016). The work

was also partially supported by project Nos. VEGA 0077,

APVV-0509-07 and APVV-99-02605, by the Slovak Academy

of Sciences within the framework of CEX-NANOFLUID, and

by implementation of the Operational Research and Devel-

opment Programme provided by the European Regional

Development Fund, project Nos. 26220120021 and 262022005.

The research was also supported by the European Commis-

sion under the 6th Framework Programme through the Key

Action ‘Strengthening the European Research Area’,

Research Infrastructures, contract No. RII3-CT-2003-505925,

GKSS, Germany.

References

Aksenov, V., Avdeev, M., Balasoiu, M., Rosta, L., Torok, G., Vekas,L., Bica, D., Garamus, V. & Kohlbrecher, J. (2002). Appl. Phys. A,74, s943–s944.

Avdeev, M. V. (2007). J. Appl. Cryst. 40, 56–70.Avdeev, M. V., Aksenov, V. L., Balasoiu, M., Garamus, V. M.,

Schreyer, A., Torok, Gy., Rosta, L., Bica, D. & Vekas, L. (2006). J.Colloid Interface Sci. 295, 100–107.

Avdeev, M. V., Bica, D., Vekas, L., Aksenov, V. L., Feoktystov, A. V.,Marinica, O., Rosta, L., Garamus, V. M. & Willumeit, R. (2009). J.Colloid Interface Sci. 334, 37–41.

Avdeev, M. V., Bica, D., Vekas, L., Marinica, O., Balasoiu, M.,Aksenov, V. L., Rosta, L., Garamus, V. M. & Schreyer, A. (2007). J.Magn. Magn. Mater. 311, 6–9.

Avdeev, M. V., Dubois, E., Meriguet, G., Wandersman, E., Garamus,V. M., Feoktystov, A. V. & Perzynski, R. (2009). J. Appl. Cryst. 42,1009–1019.

Avdeev, M. V., Mucha, B., Lamszus, K., Vekas, L., Garamus, V. M.,Feoktystov, A. V., Marinica, O., Turcu, R. & Willumeit, R. (2010).Langmuir, 26, 8503–8509.

Balasoiu, M., Avdeev, M. V., Aksenov, V. L., Hasegan, D., Garamus,V. M., Schreyer, A., Bica, D. & Vekas, L. (2006). J. Magn. Magn.Mater. 300, e225–e228.

Bica, D., Vekas, L., Avdeev, M. V., Balasoiu, M., Marinica, O., Stoian,F. D., Susan-Resiga, D., Torok, G. & Rosta, L. (2004). Prog. ColloidPolym. Sci. 125, 1–9.

Bica, D., Vekas, L., Avdeev, M. V., Marinica, O., Socoliuc, V.,Balasoiu, M. & Garamus, V. M. (2007). J. Magn. Magn. Mater. 311,17–21.

Brusentsov, N. A., Brusentsova, T. N., Filinova, E. Yu., Jurchenko,N. Y., Kupriyanov, D. A., Pirogov, Yu. A., Dubina, A. I.,Shumskikh, M. N., Shumakov, L. I., Anashkina, E. N., Shevelev,A. A. & Uchevatkin, A. A. (2007). J. Magn. Magn. Mater. 311, 176–180.

Butter, K., Hoell, A., Wiedenmann, A., Petukhov, A. V. & Vroege,G.-J. (2004). J. Appl. Cryst. 37, 847–856.

Cebula, D. J., Charles, S. W. & Popplewell, J. (1983). J. Magn. Magn.Mater. 39, 67–70.

Dijt, J. C., Cohen Stuart, M. A., Hofman, J. E. & Fleer, G. J. (1990).Colloids Surf. 51, 141–158.

Feoktystov, A. V., Bulavin, L. A., Avdeev, M. V., Vekas, L., Garamus,V. M. & Willumeit, R. (2009). Ukr. J. Phys. 54, 266–273.

Gazeau, F., Boue, F., Dubois, E. & Perzynski, R. (2003). J. Phys.Condens. Matter, 15, s1305–s1334.

Grabcev, B., Balasoiu, M., Bica, D. & Kuklin, A. I. (1994).Magnetohydrodynamics, 30, 130–134.

Grabcev, B., Balasoiu, M., Tirziu, A., Kuklin, A. I. & Bica, D. (1999).J. Magn. Magn. Mater. 201, 140–143.

Hajdu, A., Tombacz, E., Illes, E., Bica, D. & Vekas, L. (2008). Prog.Colloid Polym. Sci. 135, 29–37.

Harris, J. M. & Zalipsky, S. (1997). Editors. Poly(ethylene glycol):Chemistry and Biological Applications, p. 489. Washington, DC:American Chemical Society.

Hoell, A., Kammel, M., Heinemann, A. & Wiedenmann, A. (2003). J.Appl. Cryst. 36, 558–561.

Hong, R. Y., Ren, Z. Q., Han, Y. P., Li, H. Z., Zheng, Y. & Ding, J.(2007). Chem. Eng. Sci. 62, 5912–5924.

Jacrot, B. (1976). Rep. Prog. Phys. 39, 911–953.Jo, S. & Park, K. (2000). Biomaterials, 21, 605–616.Massart, R., Dubois, E., Cabuil, V. & Hasmonay, E. (1995). J. Magn.

Magn. Mater. 149, 1–5.Mota, A. M., Simoes Goncalves, M. L., Farinha, J. P. & Buffle, J.

(1994). Colloids Surf. A, 90, 271–278.Odenbach, S. (2002). Editor. Ferrofluids. Magnetically Controllable

Fluids and Their Applications, Lecture Notes in Physics, Vol. 594,pp. 233–251. Berlin: Springer-Verlag.

Pedersen, J. S. (1997). Adv. Colloid Interface Sci. 70, 171–210.Rubinson, K. A. & Krueger, S. (2009). Polymer, 50, 4852–4858.Rubinson, K. A., Stanley, C. & Krueger, S. (2008). J. Appl. Cryst. 41,

456–465.Schmidt, P. W. (1995). Modern Aspects of Small-Angle Scattering,

edited by H. Brumberger, pp. 1–56. Dordrecht: Kluwer AcademicPublishers.

Shen, L., Laibinis, P. E. & Hatton, T. A. (1999). Langmuir, 15, 447–453.

Shen, L., Stachowiak, A., Fateen, S.-E. K., Laibinis, P. E. & Hatton,T. A. (2001). Langmuir, 17, 288–299.

Stuhrmann, H. B. (1995). Modern Aspects of Small-Angle Scattering,edited by H. Brumberger, pp. 221–253. Dordrecht: KluwerAcademic Publishers.

Sun, C., Lee, J. S. H. & Zhang, M. (2008). Adv. Drug Deliv. Rev. 60,1252–1265.

research papers

968 Mikhail V. Avdeev et al. � Nanoparticle aggregates J. Appl. Cryst. (2010). 43, 959–969

Tanford, C. (1972). J. Phys. Chem. 76, 3020–3024.Timko, M., Koneracka, M., Kopcansky, P., Tomori, Z., Vekas, L.,

Jozefczak, A., Skumiel, A., Radenovic, A., Dietler, G., Bystrenova,E. & Lita, M. (2004). Indian J. Eng. Mater. Sci. 11, 276–282.

Tomasovicova, N., Koneracka, M., Kopcansky, P., Timko, M. &Zavisova, V. (2006). Meas. Sci. Rev. 6, 32–35.

Tronel-Peyroz, E. T., Raous, H. & Schuhmann, D. (1983). J. ColloidInterface Sci. 92, 136–153.

Vekas, L., Avdeev, M. V. & Bica, D. (2009). Nanoscience and itsApplications in Biomedicine, edited by D. Shi, ch. 25, pp. 645–704.Berlin: Springer-Verlag and Tsinghua University Press.

Vekas, L., Bica, D. & Avdeev, M. V. (2007). China Particuology, 5, 43–49.Vorobiev, A., Major, J., Dosch, H., Gordeev, G. & Orlova, D. (2004).

Phys. Rev. Lett. 93, 267203.

Whitten, A. E., Cai, S. & Trewhella, J. (2008). J. Appl. Cryst. 41, 222–226.

Wiedenmann, A. (2001). Physica B, 297, 226–233.Wiedenmann, A., Hoell, A. & Kammel, M. (2002). J. Magn. Magn.

Mater. 252, 83–85.Xu, H., Yan, F., Monson, E. E. & Kopelman, R. (2003). J. Biomed.

Mater. Res. Part A, 66, 870–879.Yoon, T. J., Kim, J. S., Kim, B. G., Yu, K. N., Cho, M. H. & Lee, J. K.

(2005). Angew. Chem. Int. Ed. 44, 1068–1071.Zhang, Z., Berns, A. E., Willbold, S. & Buitenhuis, J. (2007). J. Colloid

Interface Sci. 310, 446–455.Zhao, J., Meerwinck, W., Niinkoski, T., Rijillart, A., Schmitt, M.,

Willumeit, R. & Stuhrmann, H. B. (1995). Nucl. Instrum. MethodsPhys. Res. Sect. A, 356, 133–137.

research papers

J. Appl. Cryst. (2010). 43, 959–969 Mikhail V. Avdeev et al. � Nanoparticle aggregates 969