Residual order in amorphous dry films of polymerlatices: indications of an influence of particle interaction

Martin Evers a, Hans-Joachim Sch€oope a, Thomas Palberg a,*,Nico Dingenouts b, Matthias Ballauff b

a Institut f€uur Physik der Universit€aat Mainz, Staudinger Weg 7, D-55099 Mainz, Germanyb Polymer-Institut der Universit€aat Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe, Germany

Abstract

We report small angle X-ray scattering and atomic force microscopy measurements on macroscopically thick, dry

films of polymer latex particles. While the surface of dried droplets has long range order due to layering effects, the

overall bulk structure is amorphous. This holds for both low charge polymethylmetacrylate particles and for highly

charged polystyrene particles with additional stabilisation with sodiumdodecylsurfate. In the latter case, however,

considerable amounts of residual crystal-like order is observed.

� 2002 Elsevier Science B.V. All rights reserved.

1. Introduction

Colloidal spheres are well known to form bothamorphous and crystalline solids. For hard sphereinteractions the first order freezing transition isobserved at a packing fraction of UF ¼ 0:495 withmelting at UM ¼ 0:545 [1]. For charged spheresfreezing and melting are found at similar parti-cle number densities n ¼ 3U=4pa3, where a is theparticle radius [2], However, the (usually smaller)particles are not as closely packed. Rather they arekept apart by the long ranged screened Coulombrepulsion. As in both cases the centre–centre dis-tances are on the order of the wavelength of visiblelight, colloidal crystals have been intensively stud-

ied by light scattering and microscopy [3]. Athigher particle concentration glassy states are fre-quently observed. Hard sphere systems played aprominent role in establishing a mode couplingtheory of the glass transition [4] and are generallyconsidered a valuable model for fragile glassformers [5]. There the glass transition is observedat UG � 0:57. For charged spheres the situation isnot yet settled. A kinetic glass transition was ob-served by Beck et al. at U � 0:15 in a sample ofrather large polydispersity [6]. On the other handthere are claims that the strong tendency to crys-tallise observed for monodisperse samples mightalso lead to an amorphous state of piled crystalnuclei [7]. Further a low packing fraction ‘Wigner’glass is theoretically expected at high charge lowelectrolyte conditions [8,9].

In this report we are interested in the influenceof the interactions on structure of dry films of

Journal of Non-Crystalline Solids 307–310 (2002) 579–583

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* Corresponding author.

E-mail address: thomas.palberg@uni-mainz.de (T. Palberg).

0022-3093/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0022-3093 (02 )01489-8

colloidal spheres. Due to the evaporation processthe structure should become close packed. Thusone expects either random close packing (URCP ¼0:64) or crystalline structures (UFCC ¼ 0:74) in theidealised case. Of course, mixtures of both mor-phologies are possible as well as the formation ofcracks or voids. In general, the quench from themoderately concentrated dispersion to the dry filmis considered fast enough to mainly conserve thefluid order present in the initial state or to de-stroy any crystalline order due to shear forcesupon shrinking. Of more concern is the influenceof capillary forces which may lead to crack for-mation in the late stage of drying [10]. Further,upon falling dry, the interaction between thespheres might change drastically. For stericallystabilised hard spheres the Van der Waals attrac-tion shall dominate the dry state. This shouldalso hold for charged spheres where charges mayre-associated and/or the continuous phase is dis-rupted. In both cases Coulomb repulsion is dis-abled. As yet, no systematic investigation uponthis issue are, however, available. We thereforehere present preliminary investigations of the in-fluence of different stabilisation on the formationof amorphous dry films.

2. Experiments and results

In particular we compare the dried structuresformed from aqueous suspensions of sphericalparticles of comparable size and polydispersity butdifferent stabilisation (Samples A and B). In ad-dition, Sample C is of lower polydispersity butsame stabilisation as Sample B. Sample propertiesas determined from the small angle X-ray (SAXS)analysis are compiled in Table 1.

Samples were dialysed before drying. Drops ofapproximately 2 ml volume were placed on silicasubstrates. They were slowly dried at air underambient temperature over periods of several days.The starting packing fractions were around 0.4–0.5. We carefully checked that the drying condi-tions lead to reproducible results and no influenceof drying duration nor ambient air humidity wasnoticed.

After drying the drop was removed and thebottom surface inspected by atomic force micro-scopy (AFM). Usually some triangular order wasobserved indicating the formation of fcc crystalswetting the charged silica substrate with (1 1 1). Asthe presence of a flat wall may induce layering andfavour crystallisation we carefully checked thatthis order formation is restricted to a small re-gion of only few layers off the wall by studyingthe transition from ordered mono-layers to amor-phous multi-layer samples [11].

In this study we restrict ourselves to bulkamorphisation. The dried samples are powderedand subjected to SAXS measurements. Details ofthe apparatus [12] and the experimental proce-dures were recently given elsewhere [13,14]. Fol-lowing the theoretical treatment of D’Aguannoand Klein [15], we discuss structure formation interms of a measurable structure factor SMðqÞ ¼IðqÞ=nI0ðqÞ, where q is the scattering vector. It re-sults from a comparison of intensities IðkÞ mea-sured at the finite particle number density n in thedried state and I0ðkÞ measured dilute suspendedsample at vanishing n. Fig. 1(a) and (b) shows theobtained SMðkÞ and fits for polydisperse hardspheres according to Percus–Yewig–Vrij theory[16,17].

A good overall agreement is observed showingthat indeed the overall bulk structure is amor-phous. For Sample A deviations are observed forthe depth of first and second minimum and for theposition of the second minimum. For Sample Cthe experimental peak width significantly exceedsthe expectation. This is even more pronouncedfor the more polydisperse Sample B, where in ad-dition the formation of a distinct shoulder featureis observed on the high q side of the principlepeak. We note that its position corresponds to theposition of the (2 0 0) Bragg reflection of an fcc

Table 1

Sample properties as obtained from SAXS analysis

Sample Material Diameter

(nm)

Polydis-

persity

Final pack-

ing fraction

A PMMA 71 0.12 0.59

B PS/SDS 67 0.11 0.62

C PS/SDS 104 0.048 0.66

580 M. Evers et al. / Journal of Non-Crystalline Solids 307–310 (2002) 579–583

crystal. We suspect a similar feature to be presentfor Sample C which, however is not properly re-solved in the shown measurement. We further notethat with decreased polydispersity the height of themain peak increases and its width decreases. Datacould, however, not be fitted with scattering func-tions for polydisperse fcc crystalline structures norfor fcc nano-crystals [18]. Since the particle radiusand the polydispersity had been determined beforefrom measurements of dilute samples, the only freefitting parameter was the packing fraction of thespheres in the powder grains. Results are compiled

in Table 1. The final packing fraction increasesfrom 0.59 for Sample A to 0.66 in Sample C. Thelatter value is larger than expected for randomclosed packing. Together with the observations onSMðqÞ this suggests the presence of some residualcrystalline order in the system.

To further explore this point we performedAFM measurements on powder splinters of thedried drops which were embedded in epoxy resin.We note that without statistical analysis these mayonly give a guideline for structural interpretation.For this reason we here only show a single exampleand refer the reader to a forthcoming paper for amore complete analysis. Fig. 2 shows an examplerecorded on Sample C. The sample appears tohave some degree of symmetric six and fourfoldsymmetric co-ordination (centre, lower left). Par-ticles are rather close packed, but the surface isstrongly corrugated (the grey scale spans 200 nm).Some degree of longer ranged bond orientationalorder is present, but not at all perfect. The stackingof planes is not visible in this image but was ob-served in other splinters of Samples B and C.Also for Sample B we observed the presence of

Fig. 1. Measurable static structure factors SM ðqÞ versus scat-tering vector q (a) respectively qD (b), where D is the particle

diameter (cf. Table 1). Symbols: (closed squares): Sample A;

(open triangles): Sample B; (open squares): Sample C. Lines are

the best fits obtainable with Percus–Yewig–Frij theory for

polydisperse hard spheres. Note the shoulders on the high k side

of the principle peaks in Fig. 1(b) suggesting the presence of

residual crystalline order in Sample B.

Fig. 2. AFM image of Sample C. The frame size is approxi-

mately 2:5� 2:5 lm2. Note that traces of fourfold and sixfold

co-ordination order are visible in several isolated regions; e.g. in

centre and the lower left. The height range comprises 200 nm

and the surface appears slightly corrugated.

M. Evers et al. / Journal of Non-Crystalline Solids 307–310 (2002) 579–583 581

crystal-like order restricted to small regions ofspace. Maximum extensions of these were esti-mated to be on the order of 103–105 particles.While this is approximately the same value as inSample C, Sample B crystal-like regions appearedeven more corrugated and distorted. In additionstacking faults were readily visible in some regions[11]. From this qualitative analysis we concludethat most of the splinters investigated containedsmall regions of distorted and stacking faultedcrystal-like order. Sample C was found somewhatmore ordered than Sample B. But in neither casetrue long range crystalline order was observed. Incontrast, Sample A did not show evidence of shortrange crystalline order.

3. Discussion and conclusion

Under reproducible identical drying conditionsSample A of low charge forms fully amorphousstructures with a mean packing fraction of UA ¼0:59, while Samples B and C of high charge andadditional stabilisation by SDS form overallamorphous structures with a significant amount oftiny (103 particles) crystal-like regions. There lar-ger packing fractions are observed. The smallcrystal-like regions, however, are strongly dis-torted, corrugated or cracked. AFM analysis sug-gests to interpret the shoulder observed in themeasurable static structure factor as indicative forresidual crystal-like order. We use the term crystal-like to stress that local symmetry coordinationdoes not imply the formation of long range order.Rather such regions are separated by others oflocal disorder.

We like to discuss three points shortly. First, thedifference between the structures formed in A andB cannot be traced back to the influence of poly-dispersity, as both samples show similar size andsize distributions. Only the increase of order fromSamples B to C of identical stabilisation can becorrelated with decreasing polydispersity.

This, secondly, leaves us with the influence ofstabilisation as possible reason for the observeddifference. We first discuss Sample A. It is chargedin the suspended state. Upon evaporation theconcentrations of spheres and ionic impurities in-

crease. This leads to an increased (self-) screeningof the Coulomb repulsion. As the water evaporatescompletely, Coulomb interactions are disabled ei-ther due to re-association of charges and/or dis-ruption of the continuous phase. Thus in bothcases Van der Waals forces should become oper-ative. At the same time, particles should be pinnedto each other upon first surface contact.

Samples B and C carry larger charges. FurtherSAXS evaluation yields the presence of a 1nm thicksurfactant shell in both wet and dry state. SDS isphysisorbed rather than chemisorbed and thussome surfactant should be present also in solution.Upon evaporation its concentration increases.Accordingly capillary forces should be reduced andscreening further enhanced. On the other side thesurface layer will act as steric stabilisation. Its ex-tension is shorter than the estimated range of Vander Waals attraction (decaying as r�3 for spheres)of some 3 nm. It nevertheless may effectively reducethis attraction and thus also allow for some mo-bility of spheres even in the last stage of evapora-tion. Both conditions will leave the particles withmore space and time to rearrange before beingdriven into contact and being immobilised.

Finally our investigation demonstrates the use-fulness of complementary data from real and re-ciprocal space. SAXS data showed with statisticalsignificance the presence of qualitative differencein the overall amorphous structure. AFM datahelped in developing some imagination of thesource of such difference. In fact, careful analysissuggests some direct measures of amorphicity, likecoordination number fluctuations, layer corruga-tion amplitude and wavelength, or stacking faultdistribution. It now would be very interesting toquantify such measures. Then model structurescould be generated numerically. Fourier trans-formed and compared to measured SMðqÞ, as hasbeen already done for nano-crystals and polydis-perse crystals [18].

Acknowledgements

It is a pleasure to thank A. Hexemer, M.Stamm, H.Richter and T. Schimmel for stimulat-ing discussions of our and their AFM results. This

582 M. Evers et al. / Journal of Non-Crystalline Solids 307–310 (2002) 579–583

work was financially supported by the DFG (SFB262, TP D20) the MWFZ, Mainz and the BMBF(Grant no. 03N6500).

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