SHORT COMMUNICATION

Transition from thermodynamically stable solution to colloiddispersion state

Attila Borsos & Tibor Gilányi

Received: 4 November 2011 /Revised: 16 December 2011 /Accepted: 30 December 2011 /Published online: 17 January 2012# Springer-Verlag 2012

Abstract In this work, we investigated the transition betweensolution and dispersion state of the poly-N-isopropylacrylamidemicrogel latex. The aggregation state of the colloid system wasdescribed by applying the multiple chemical equilibriummodel. The model predicts that in the case of ordinarycolloid dispersions, formation of small equilibrium aggre-gates cannot be expected in the practically accessible concen-tration range. However, when the particle–particle attractionis small enough, then formation of finite size aggregates inequilibrium with the monomers may take place. To test themodel, the aggregation behavior of a temperature-sensitivesoft colloid dispersion (poly-N-isopropylacrylamide micro-gels) was investigated for which the attractive interactionscould be precisely controlled by the temperature of the sys-tem. The experimental results provide a support for the the-oretical predictions.

Keywords Colloid stability . Aggregation .

Poly(N-isopropylacrylamide) .Microgels . Soft particles

Introduction

The aggregation kinetics of the colloid particle systems hasattracted considerable attention over the past decades sinceits understanding is fundamental in many practical problemssuch as sedimentation, flotation, or the stability of manydrugs and food products [1]. Our current understanding ofcolloid stability is based on the pioneering work of Verweyand Overbeek [2] as well as Derjaguin and Landau [3]. The

Derjaguin and Landau, Verwey and Overbeek (DLVO) the-ory describes colloid stability in terms of the combinedeffect of attractive van der Waals forces and repulsive-double-layer forces acting between charged colloid par-ticles. The DLVO theory clearly presents that colloid dis-persions are not stable in a thermodynamic sense but theyexhibit kinetic stability due to the energy barrier actingbetween two approaching particles. Later, both theoreticalcalculations and experimental investigations have confirmedthat there are two possible types of aggregation indepen-dently from the nature of the colloid particles. These are thediffusion-limited cluster–cluster aggregation (DLCA) [4–6]and the reaction-limited cluster–cluster aggregation (RLCA)[7–9]. In the first case, DLCA, every collision leads toirreversible bond formation between the particles resultingin a strongly branched aggregate structure. In the case of theRLCA, only a fraction of the collisions results in aggregatesleading to the formation of more compact structures that hasa higher fractal dimension.

In the last decades, the aggregation of a wide range ofcolloid particles has been investigated in the literature andthe effect of various parameters (e.g., the effect of patch–charge attraction [10, 11], particle size [12], and ion-specificinteractions [13]) has been addressed. Recently, the stabilityand aggregation of soft nanoparticles gained significantattention. Stimuli responsive soft nanoparticles (e.g., poly(N-isopropylamide) (pNIPAm) microgels) are very promis-ing candidates in many applications ranging from dug de-livery to chemomechanical devices [14]. The large numberof investigations performed on pNIPAm microgels havebeen summarized in several excellent reviews [15–18]. pNI-PAm microgels can undergo a reversible volume phasetransition (VPT). The pNIPAm polymer has a lower criticalsolution temperature (LCST) at around 32 °C [19, 20].Below this temperature, the microgel particles are in a

A. Borsos : T. Gilányi (*)Laboratory of Interfaces and Nanosized Systems,Institute for Chemistry, Eötvös Loránd University,P.O. Box 32, 1117 Budapest, Hungarye-mail: gilanyi@chem.elte.hu

Colloid Polym Sci (2012) 290:473–479DOI 10.1007/s00396-011-2584-8

highly swollen state in aqueous environment resulting in athermodynamically stable solution of the microgel particles.However, when the temperature is raised above the LCST,the polymer network collapses expelling most of its watercontent and the system becomes an electrostatically stabi-lized dispersion of collapsed microgel particles. Rasmussonet al. studied the flocculation behavior of the pNIPAmmicrogel particles in the function of the ionic strength overthe temperature range of 25–60 °C [21]. They establishedthat at low NaCl concentrations, the latex is stable. At highersalt concentration, the system flocculates. The flocculationtemperature shifts to lower values with increasing salt con-centration. They concluded that the flocculation behavior ofthe pNIPAm could be interpreted by means of the reversibleflocculation model. Fernandez-Nieves et al. studied thestructure of the microgel particle aggregates. The aggrega-tion was observed above the critical coagulation electrolyteconcentration [22]. They found that the clusters have ahigher fractal dimension than in a typical diffusion-limitedcluster–cluster aggregation process.

In the previous investigations, the aggregation of themicrogel particles was induced by means of the additionof inert electrolytes and the microgel latex was treated as aclassical colloid dispersion. However, the fact that the pNI-PAm latexes form thermodynamically stable solutions of themicrogel particles at low temperature, which turn into col-loid dispersions above the LCST suggests the intriguingpossibility of equilibrium aggregate formation in the transi-tion temperature range. The aim of our work was to inves-tigate the possibility of finite size equilibrium aggregateformation in colloid dispersions. To achieve this goal, weapplied the multiple chemical equilibrium model to describethe particle aggregation. As it will be discussed, the modelindicated the possibility of finite size equilibrium aggregateformation. To test the model prediction, we also investigatedthe aggregation of pNIPAm particles that gave us the uniquepossibility to tune the attractive interaction among the par-ticle by varying the swelling of the microgel network.

Materials and methods

Preparation of monodisperse microgel latex For the prepa-ration of the pNIPAm N-isopropylacrylamide (NIPAm),methylene bisacrylamide (BA), ammonium persulfate(APS), and dodecylbenzenesulphonic acid sodium salt(DBANa) were used. The chemicals were provided byAldrich and were used for the preparation without furtherpurification. Our procedure was based on a modifiedmethod developed by Wu et al. [23] for the preparation ofmonodisperse pNIPAm microgel particles. Dissolved in190 ml of distilled water were 2.85 g NIPAm monomer,129 mg of BA, and 46 mg DBANa. The temperature of the

reactor was kept at 80 °C and the solution was intensivelystirred. In order to remove oxygen, nitrogen gas was purgedthrough the solution for 30 min. Then, 2 ml of a 2.80 wt.%aqueous APS solution (56 mg) was added to the solution,followed by intensive stirring for 4 h. The pNIPAm latexwas purified from unreacted monomers and surfactant bydialysis against distilled water for 4 weeks and by ultrafil-tration with Vivaflow 200 flip-flop filter.

Dynamic light scattering measurements The dynamic lightscattering measurements were performed by means of aBrookhaven dynamic light scattering equipment consistingof a BI-200SM goniometer and a Bi-9000AT digital corre-lator. An Omnichrome (model 543) argon–ion laser operat-ing at 488 nm wavelength and emitting vertically polarizedlight which used as the light source. The signal analyzer wasused in the real-time “multi-tau” mode. The time axis islogarithmically spaced over a time interval ranging from0.1 μs to 0.1 s in this mode and the correlator used 218time channels. The pinhole was 100 μm. The measurementswere performed at 90 scattering angle. Prior to the measure-ments, the microgel samples were cleaned of dust by filter-ing through a 0.8 μm pore size-sintered glass filter. Theintensity–intensity time–correlation functions were mea-sured (homodyne method) and then converted to the nor-malized electric field autocorrelation functions by means ofthe Siegert relation. The autocorrelation functions were an-alyzed by the cumulant expansion methods. The measuringcell and connections to the thermostat were specially insu-lated from the environment to keep constant temperaturewithin ±0.01 °C during the measurements.

Application of the multiple chemical equilibrium modelfor the microgel aggregation

It has been generally accepted that the stability of thecolloid particle systems is of kinetic nature and theaggregates of colloid particles grow unlimitedly leadingto macroscopic phase separation of the system on aproperly chosen time scale. In this contribution, we aimat investigating the possibility of the formation of equi-librium colloid aggregates. To address this problem, firstwe formulated a multiple chemical equilibrium model, inwhich the colloid aggregates grow (or shrink) in a step-wise manner by capturing or dissociating colloid particlesone by one (see Table 1.).

The particles (P) are treated as compact uniform spheres.Each particle–particle contact within an aggregate is char-acterized by ΔG00−kTlnK0 binding energy and it is sup-posed that the interaction between two particles isindependent from the presence of the others. Thus, the totalfree energy change of the aggregate formation with k

474 Colloid Polym Sci (2012) 290:473–479

particle–particle contacts is ΔG0,tot0k ΔG0. In Table 1, thescheme of the dimer and trimer formation is given. Onlyone particle–particle contact is possible in dimers. If theaggregation number is 3, then the number of contacts maybe 2 (chain-like) and 3 (triangle-like). With further increas-ing aggregation number (m), the number of the possiblecontacts (k) in the aggregate may increase by one (chain-like attachment), two (triangle-like attachment), or three(tetrahedron-like attachment) contacts on the addition of anew particle.

Using the multiple chemical equilibrium model, the con-centration of an aggregate having an aggregation number mand particle–particle contact k can be given as (see alsoTable 1.):

xm ¼ Kk0 x

m1 : ð1Þ

In a system, in which equilibrium aggregate formationtakes place, the concentration of small aggregates (e.g.,dimers) must be significant compared to the concentrationof the individual particles, while the concentration of largeaggregates must converge to zero:

x2=x1 ¼ K0x1 >> 0 ð2aÞand

xm=x1 ¼ Kk0x

m�11 ���������!m ! 1

0: ð2bÞIf as an upper limit for the large aggregate formation, the

formation compact aggregates is assumed (maximum num-ber of particle–particle contacts) then it is straightforward toshow that

xm=x1 ¼ K30x1

� �mif m ! 1 ð3Þ

Equation 3 indicates that Eq. 2b can be fulfilled if K30x1<1.

This means that for a given value of K0, the formation of

equilibrium aggregates of finite size can take place when theequilibrium monomer concentration becomes small enough(x1 < K�3

0 ). Taking into account thatKo exponentially increaseswith increasing binding energy (K0 ¼ expð�ΔG0=kTÞ ) it isevident that finite size aggregates could be observed experimen-tally only in systems where the binding energy has a limitedvalue.

In the case of colloid dispersion, the attractive interactionenergy between two spherical particle of diameter d at H(<<d) separation distance of the surfaces is approximated as[24]

VH ¼ � AHd

24Hð4Þ

where, AH is the effective Hamaker constant. In the case ofordinary, condensed colloid particles, the Hamaker constantis so large that the attractive interaction acting between twocolloid particles in close contact gives rise to unlimitedaggregation even at extreme small particle concentrations.To achieve equilibrium aggregate formation, in principlethis problem could be overcome if the attractive interaction(the effective Hamaker constant) could be decreased be-tween the colloid particles. While this is not possible forordinary colloid particles, stimuli-responsive microgels of-fer a unique possibility to tune the strength of the attractiveinteraction between the microgel particles. Since the effec-tive Hamaker constant is proportional to the square of thepolymer segment density of the microgel particles it isstraightforward to show that the swelling of the microgelparticles gives rise to the following variation of the effectiveHamaker constant [25]:

AH ¼ AH ;odh;odh

� �6

ð5Þ

where, the “o” index indicates the collapsed state of themicrogel particles and the hydrodynamic diameter (dh) isthe particle diameter. This means that the binding energybetween two microgel particles can be tuned from a valuecharacteristic for ordinary colloids (collapsed state) to aclose to zero value (swollen state) by controlling the swell-ing of the microgel particles. This implies that by control-ling the microgel swelling, equilibrium aggregation may beachieved.

Experimental results

To experimentally investigate the aggregation behavior ofstimuli responsive microgels, pNIPAm microgels wereprepared with the classical precipitation polymerizationmethod. In Fig. 1, the dh of the pNIPAm microgel particles,measured by dynamic light scattering, is plotted against the

Table 1 Structure of the aggregates in the case of dimer and trimerformation

Colloid Polym Sci (2012) 290:473–479 475

temperature. The measurements were carried out at 0.05%microgel latex concentration in both salt-free medium and1 mM La(NO3)3 solution.

In salt-free medium, the pNIPAm latex shows the well-known volume phase transition. The hydrodynamic diameterof the particles strongly decreases with increasing tempera-ture at around 34 °C (volume phase transition Temperature,VPTT) where the particles lose the majority of their watercontent [26] and the hydrodynamic diameter tends to aconstant value of about 140 nm. This hydrodynamic diame-ter represents the completely collapsed state of the individuallatex particles. In the investigated temperature range, thesalt-free microgel system was found to be practically mono-disperse (the cumulant analysis yielded 0.02±0.01 for thesecond cumulant).

At room temperature, the pNIPAm microgel latex is athermodynamically stable solution, i.e., the water is a goodsolvent of the polymer. The overall interaction between theswollen microgel particles is repulsive which is reflected inthe positive value of the second virial coefficient (B208.5×10−7 mol cm3 g−2) [27]. Raising the temperature above theVPTT, the particles collapse in a narrow temperature rangeforming more compact microgel particles with small watercontent [26]. This results in a significant increase of thepolymer segment density within the particles. It is expectedthat around the VPTT, the state of the system changes fromsolution to colloid dispersion as a consequence of the in-creased attractive dispersion forces acting between the par-ticles (Eq. 5). Above 33 °C despite the increased attractiveinteractions, the pNIPAm latex does not coagulate but formsa kinetically stable colloid dispersion as a result of therepulsive double-layer forces acting between the collapsed

microgel particles due to the small amount of negativecharges originating from the persulfate initiator used in thesynthesis. According to the classical DLVO theory, thecolloid stability decreases with increasing ionic strength ofthe medium due to the screening of the electrostatic inter-actions. The collapsed latex particle system undergoes fastcoagulation in the presence of an inert electrolyte at aconcentration above the critical coagulating electrolyte con-centration (ccc).

In order to find the temperature where the state of thelatex changes from thermodynamically stable solution tokinetically stable dispersion, the electrostatic interactionsbetween the particles should be eliminated. NaCl is notsuitable to screen the electrostatic interactions because itsccc value is around 0.1 M [22] and at such a high concen-tration, the salt has a large effect on the solvent quality (thecollapse of the particles can be induced with a high amountof NaCl even at room temperature). Therefore, 1 mM La(NO3)3 was chosen to screen the electrostatic interactions,because its ccc value falls into very low concentration range(0.1 mM).

In 1 mM La(NO3)3 solution, the size of the particlesdecreases with increasing temperature up to 34 °C, similarlyas in the case of the salt-free medium (see Fig. 1). A shift inthe dh(T) function can be observed indicating a little influ-ence of the salt on the solvent properties even at this smallconcentration. At 34.1 °C, the measured apparent hydrody-namic diameter sharply increases due to the aggregation ofthe pNIPAm particles (the turbidity of the system and theapparent particle size increases with the time). At this crit-ical temperature, the individual particles are considerableshrunken but their size does not reach the fully collapsedstate (140 nm).

The narrow temperature range where the transition of thesystem from thermodynamically stable solution to a colloiddispersion state takes place was further studied. In Fig. 2,the apparent hydrodynamic diameter is plotted in the func-tion of the time (t) at constant latex concentration at differenttemperatures. The measurements were very sensitive to thefluctuation of the temperature; therefore, the temperaturewas kept at constant value within ±0.01 °C by speciallyinsulating the measuring cell from the environment.

Raising the temperature from 34.1 °C to 34.2 °C, thelatex starts to aggregate and the mean hydrodynamic diam-eter increases to a higher value. The cumulant analysis ofthe dynamic light scattering measurements indicates that thesystem becomes polydisperse. However, the hydrodynamicsize does not diverge with time but tends to a constant valueas it is indicated in Fig. 2. In another experiment, thetemperature was changed from 34.2 °C to 34.3 °C, whichresulted in further increasing average hydrodynamic size,which again leveled off at a constant value. However, whenthe temperature was raised again with 0.1 °C (to 34.4 °C),

Fig. 1 Hydrodynamic diameter (dh) of the poly(N-isopropyl acrylamide)microgel particles against the temperature in salt-free medium andin 1 mM La(NO3)3 solution. The microgel concentration is 0.05%(grams dry latex/100 ml percent)

476 Colloid Polym Sci (2012) 290:473–479

the hydrodynamic diameter sharply increased and after asufficiently long time, the latex macroscopically coagulated.Adjusting the temperature back to 34.3 °C, the mean size ofthe microgel particles decreases back to its original constantvalue measured at this temperature. It can be concluded fromthese measurements that the transition of the latex from solu-tion to dispersion state takes place in the temperature rangebetween 34.1 °C and 34.4 °C. In this transition range, thepNIPAm particles form small equilibrium aggregates.

To gain further insight into the formation of equilibriummicrogel aggregates of limited size, the effect of latex con-centration on the particle aggregation has also been investi-gated (Fig. 3). With increasing latex concentration, the sizeof the aggregates profoundly increases, which results in a

decrease of the temperature where equilibrium aggregateformation can be observed (to 34.1 °C from 34.2 °C) anda decrease of the temperature where unlimited aggregationand macroscopic phase separation takes place. These obser-vations also provide a firm support for the formation thesmall equilibrium microgel aggregates in the investigatednarrow transition temperature range.

Discussion

Since the average hydrodynamic size of the small aggre-gates depends on both the aggregation number and theshape of the aggregates, a direct quantitative comparison

Fig. 2 The apparenthydrodynamic diameters atdifferent temperatures infunction of the time afterchanging the temperature insteps. The pNIPAmconcentration is 0.025% in1 mM La(NO3)3 solution

Fig. 3 The apparenthydrodynamic diameter againstthe time at different pNIPAmconcentrations andtemperatures in 1 mM La(NO3)3 solution

Colloid Polym Sci (2012) 290:473–479 477

of the theoretical and experimental results would require theformulation of a detailed hydrodynamic model. To avoidthese difficulties, we restrict our analysis to a qualitativecomparison.

Taking into account the geometrically possible aggregatestructures, the total concentration of the particles in thesystem can be expressed in the following form:

x0 ¼X1

m¼1

mxm ¼ x1 þ 2K0x21 þ

X1

m¼3

mX3m�6

k¼m�1

Kk0x

m1 ð6Þ

where, xo is the total concentration of the particles (expressedin monomer mole fraction units). On the bases of Eq. 6,the different mean aggregation numbers can be calculatedas a function of the particle–particle interaction energy(ΔG00−kTlnK0) at constant latex concentrations (x0). Forexample, the z-average aggregation number that can becompared to the measured z-average hydrodynamic sizeis given as:

hmiz ¼P

m3xmPm2xm

ð7Þ

The z-average aggregation number can be determined bymeans of Eqs. 4, 5, and 7. However, these calculationswould require an arbitrary choice of the particle–particledistance (H) for the bound particle pairs that could give riseto large uncertainties. To avoid this ambiguity, we solvednumerically Eq. 6 for the experimentally investigated latexconcentration range in the function of K0. These calculationssuggest that aggregates forms in detectable amount if ΔG0

reaches the value of −20 kT independently from furtherassumptions. Below this ΔG0 value, only individual par-ticles are present in the system, i.e., the aggregation numberm≈1. Exceeding this value, the mean aggregation numberrapidly increases and at about −24 kT, the aggregationnumber tends to infinity. On the other hand, experimentallythe aggregation starts between 34.0 °C and 34.1 °C indicatingthat the interaction energy reaches the −20 kT value at thisnarrow temperature range. Thus, by setting ΔG00−20 kT at34.0 where the hydrodynamic diameter of the individualmicrogel particles is dh,34 the theoretical and experimentalresults correspond to each other with about 1 kT uncertainty.Combining Eqs. 4 and 5 and using ΔG00−20 kT at 34.0 °Cthe following relation can be derived

ΔG0ðTÞ ¼ �20dh;34dhðTÞ

� �5

ð8Þ

where, dh,34 is the hydrodynamic diameter of the latex particleat 34.0 °C. The ΔG0(T) function was calculated by means ofEq. 8 as a function of the temperature and the result is plottedin Fig. 4. The experimental hydrodynamic size dh(T) functionmeasured in salt-free medium was used in these calculationsdisregarding the minor effect of the lanthanum nitrate on the

individual particle size. The figure shows that as expected theparticle pair interaction energy changes strongly around thevolume phase transition temperature of the pNIPAm.

In Fig. 5, the results of the model calculations are pre-sented by plotting the z-average aggregation number againstthe particle pair interaction energy. xo was calculated usingthe experimental weight concentration and the molar massof the particles determined earlier for the investigated latexby static light scattering [27]. In line with the experimentalobservations, the model calculation predicts that smallaggregates form in equilibrium with the monomers only ina narrow temperature range at which the transition fromstable solution to colloid dispersion state of the latex takesplace. At constant temperature, the degree of aggregation

Fig. 4 The change of the particle–particle interaction energy of thepNIPAM microgel particles with the temperature

Fig. 5 The z-average aggregation number of the microgel particlesagainst the particle pair interaction energy at different latex molefractions

478 Colloid Polym Sci (2012) 290:473–479

increases and the critical temperature range shifts to smallervalues with increasing latex concentration. With further in-crease of the temperature in the critical range, the meanaggregation number tends to infinity resulting in the phaseseparation of the system. The chemical equilibrium modelpresented above predicts the formation of macroscopiccolloid crystals at m→∞ limit in ideal case. In practice,colloid crystal formation cannot be realized on a practicaltime scale, because non-equilibrium fractal structures form.

Conclusions

An equilibrium thermodynamic model was derived todescribe the aggregation state of colloid dispersions. Themodel was based on the multiple chemical equilibriumconcept to describe the particle aggregation. It predicts theexistence of three characteristic concentration ranges of thedispersion at any given particle–particle interaction energy.In the dilute concentration range, the system contains prac-tically only individual colloid particles. With increasingconcentration, first, small equilibrium particle aggregatesform, which is followed by unlimited aggregation and phaseseparation with further concentration increase. Experimen-tally, the transition between the different states of a colloidsystem can be observed only if the particle–particle interac-tion energy is sufficiently small, because otherwise thecolloid system is in equilibrium in the phase separated stateeven at extremely low particle concentrations. To test themodel predictions, we investigated the aggregation of pNI-PAm particles that gave the unique possibility to tune theattractive interaction among the particles by varying theswelling of the microgel network. The observed experimen-tal results are in good agreement with the theoreticalprediction providing a firm support for the formation ofequilibrium particle aggregates of finite size.

Acknowledgment This work was supported by the HungarianScientific Research Fund (NKTH-OTKA K68027 and OTKA K68434).

References

1. Myers D (1999) Surfaces, interfaces and colloids: principles andapplications, 2nd edn. Wiley, New York

2. Verwey EJW, Overbeek JTG (1948) Theory of the stability oflyophobic colloids. Elsevier, Amsterdam

3. Derjaguin B, Landau L (1941) Theory of the stability of stronglycharged lyophobic sols and of the adhesion of strongly chargedparticles in solutions of electrolytes. Acta Physico Chemica URSS14:633

4. Witten TA, Sander LM (1981) Phys Rev Lett 47:14005. Witten TA, Sander LM (1983) Phys Rev B 27:56866. Ball RC, Bradly RM, Rossi G, Thompson BR (1985) Phys Rev

Lett 55:14067. Ball RC, Weitz DA, Witten TA, Leyvraz F (1987) Phys Rev Lett

58:2748. Meakin P, Family F (1987) Phys Rev A 36:54989. Meakin P, Family F (1988) Phys Rev A 38:2110

10. Sadeghpour A, Seyrek E, Szilagyi I, Hierrezuelo J, Borkovec M(2011) Langmuir 27:9270

11. Finessi M, Sinha P, Szilagyi I, Popa I, Maroni P, Borkovec M(2011) J Phys Chem B 115:9098

12. Rentsch S, Pericet-Camara R, Papastavrou G, Borkovec M (2006)Phys Chem Chem Phys 8:2531

13. Wang D, Tejerina B, Lagzi I, Kowalczyk B, Grzybowski BA(2011) ACS Nano 5:530

14. Varga I, Szalai I, Mészaros R, Gilányi T (2006) J Phys Chem B110:20297

15. Saunders BR, Vincent B (1999) Adv Colloid Interface Sci 80:116. Nayak S, Lyon L (2005) Angew Chem 44:768617. Hoare T, Pelton R (2008) Curr Opin Colloid Interface Sci

13:41318. Pich A, Richtering W (2011) Advances Polym Sci 234:119. Heskins JE, Guillet J (1968) Macromol Sci Chem A2 8:144120. Shild HG, Tirrell DA (1990) J Phys Chem 94:435221. Rasmusson R, Vincent B (2004) React Funct Polym 58:20322. Fernández-Nieves A, Fernández-Barbero A, Vincent B, de las

Nieves FJ (2001) Langmuir 17:184123. Wu C, Zhou SQ, Auyeung SCF, Jiang SH (1996) Angew Makromol

Chem 240:12324. Hunter RJ (1993) Foundations of Colloid Science, vol 1. Chapt. 4.

Clarendon, Oxford25. Snowden MJ, Marston HJ, Vincent B (1994) Colloid Polym Sci

272:127326. Varga I, Gilányi T, Mészáros R, Filipcsei G, Zrínyi M (2001) J

Phys Chem B 105:907127. Gilányi T, Varga I, Mészáros R, Filipcsei G, Zrínyi M (2000) Phys

Chem Chem Phys 2:1973

Colloid Polym Sci (2012) 290:473–479 479