Fractal Aggregation in Relation to Formation and Properties of Particle Gels Aan myn ouders Promotoren: dr. ir. P. Walstra, hoogleraar in de zuivelkunde dr. B. H. Bijsterbosch hoogleraar in de fysische- en kolloidchemie Co-promotor: dr. T. van Vliet universitair hoofddocent in de levensmiddelen- natuurkunde JfJOSld' - 3 L.G.B. Bremer Fractal Aggregation in Relation to Formation and Properties of Particle Gels Proefschrift ter verkrijging van de graad van doctor in de landbouw- en milieuwetenschappen, op gezag van de rector magniflcus, dr. H.C. van der Plas, in het openbaar te verdedigen op woensdag 22 januari 1992 des namiddags te vier uur in de aula van de Landbouwuniversiteit te Wageningen 13r> : 5 52 £ ^ Table of Contents I Introduction 1.1 Generalintroductio n 1 1.2 Factors controlling gelation 4 1.3 Outline of this thesis 8 1.4 References 10 n Theory of Fractal Aggregation 2.1 Introduction 12 2.2 Computer simulations 14 2.3 The model 17 2.4 Some consequences of the model 20 2.4.1 The critical volume fraction 20 2.4.2 Permeability 22 2.4.3 Geometric structure and correlation function 24 2.4.4 Turbidity and (light)scatterin g 25 2.5 References 28 m Materials and methods 3.1 Materials 30 3.2 Preparation of the gels 32 3.3 Permeabilitymeasurement s 35 3.4 Determination of the geometry of the gel network 36 3.4.1 Confocal scanning laser microscopy 36 3.4.2 Correlation analysis 38 3.4.3 The grid method 39 3.5 Turbidity measurements ...42 3.5.1 The change in turbidity during aggregation 42 3.5.2 Turbidity measurements on gels 44 3.6 References 45 IV Formation and Geometric Structure of Particle Gels 4.1 Aggregation experiments 47 4.1.1 Caseinparticle s 47 B1BL10THEEK EXSDBOUWUNlVERSIim 5PAGEN1NGE0J Stellingen 1 Doordat percolatiemodellen voorbij gaan aan de beweeglijkheid van deeltjes en clusters en doordat de meeste modellen gebaseerd op de Smoluchowski-vergelijkingen geen rekening houden met de ruimtelijke opbouw van vlokken, resulteert het gebruik van deze modellen voor de beschrijving van gelvorming door deeltjes vaak in misverstanden en soms in onzin. Dit proefschrift 2 De door percolatiemodellen voorspelde algemene kritieke volumefractie beneden welke gelering niet mogelijk is, bestaat niet in het fractale model en wordt in de praktijk niet gevonden. Dit proefschrift, hoofdstukken 2 en 4, stelling 1 3 De bewering dat een gel alleen kan ontstaan indien de exponent, x, in de frequentieverdeling van het aantal deeltjes per cluster, N(n) <*=n _T, groter is dan 2 is onjuist. In de praktijk zal een monodisperse clustergrootteverdeling gelering juist in de hand werken. J.E. Martin and B.J. Ackerson, Phys. Rev. A, 31, 1180, (1985) Dit proefschrift, hoofdstukken 2 en 4, stelling 1 4 De halveringstijd, d.w.z. de tijd waarin het aantal deeltjes door vlokking is afgenomen tot de helft van het initiele aantal, wordt vaak ten onrechte vloktijd genoemd. Dit proefschrift, hoofdstuk 6, stelling 1 5 Volgens Kendall et al. streven clusters naar maximalisatie van hun vrije energie. K. Kendall, N. McN. Alford, W.J. Clegg and J.D. Birchall. Nature, 339, 130, (1989) 6 De hoeveelheid treinsegmenten van geadsorbeerde polymeer moleculen is gevoeliger voor de adsorptie-energie dan de staart- segmentdichtheid dat is. G.P. van der Beek, M.A. Cohen Stuart and T. Cosgrove, Langmuir, 7. 49, (1991) 7 De bijd rag e van texture profile analysis (TPA) aan een goede karakterisering van de mechanische eigenschappen van levensmiddelen is eerder negatief dan positief geweest. 8 In tegenstelling tot de moderne chemie kan men de fysische chemie de chemie van de toekomst noemen. W. Ostwald, Zeilschrift jur Physikalische Chemie, 1,1, (1887) 9 Een grote feitenkennis werkt remmend op het verrichten van onderzoek. 10 Het is onmogelijk om naar het verleden te reizen of in de toekomst te kijken. Iedereen kijkt in het verleden en reist naar de toekomst. 11 De regel dat je gewicht moet liggen onder het aantal kilo's verkregen door je lengte in meters in het kwadraat met 25 te vermenigvuldigen gaat uit van personen met een effectieve fractale dimensionaliteit van 2 en is dus oppervlakkig. 12 Reologische metingen met ondeugdelijke apparatuur zijn altijd "constant stress" experimenten. 13 Dit is een van de weinige stellingen over het oostblok die ten tijde van de promotieplechtigheid met zekerheid te verdedigen valt. Leon Bremer Fractal Aggregation in Relation to Formation and Properties of Particle Gels Wageningen, 22januari 1992 4.1.2 Polystyrene particles 48 4.1.3 Emulsions 53 4.1.4 Haematite particles 54 4.2 Permeability. 55 4.3 Confocal scanning laser microscopy 60 4.4 Turbidity measurements 71 4.5 References 76 V Rheological Properties of Particle Networks 5.1 Introduction 77 5.2 The modulus ofgel swit h stretched strands 81 5.2.1 Introduction 81 5.2.2 Themode l 82 5.2.3 Extensional deformation 87 5.3 On the fractal nature of acid casein gels 89 5.3.1 Introduction 89 5.3.2 Theory 91 5.3.3 Materials and methods 95 5.3.4 Results 97 5.3.5 Discussion 99 5.3.6 Appendix 102 5.4 Rheological behaviour of gels of polystyrene particles 105 5.4.1 Introduction 105 5.4.2 Materials and methods 105 5.4.3 Results 107 5.4.3.1 Formation and ageing of the gels 107 5.4.3.2 Strain sweep measurements 109 5.4.3.3 Dynamic moduli versus frequency Ill 5.4.3.4 Dynamic moduli versus volume fraction 112 5.4.4 Discussion 114 5.5 References 119 VI Aggregation Kinetics Relatedt o the Observation of Instability 6.1 Introduction 121 6.2 Diffusion limited aggregation 123 6.3 Complications 125 6.3.1 Floesinstea d ofsmoot h spheres 125 6.3.2 Interactions between particles 128 6.3.3 Polydispersity 130 6.3.4 The effective volume fraction 131 6.3.5 Velocity gradients 133 6.3.6 Sedimentation 135 6.4 Some aggregation times 138 6.5 Reaction limited aggregation 147 6.6 Floe break up and rearrangements 151 6.7 Conclusions 154 6.8 References 157 VH Factors DisturbingGelatio n andAlterin g Gel Structure 7.1 Introduction 159 7.2 Gravity 159 7.2.1 Effects of sedimentation and creaming 159 7.2.2 Collapse of the network under its own weight 163 7.2.3 Changes of the Theological properties of the gel 165 7.3 Velocity gradients 168 7.4 Rearrangements 170 7.4.1 Rearrangement of clusters of colloidal particles 170 7.4.2 Rearrangements after gelation, microsyneresis 175 7.6 References 180 General Reflections and Suggestions for Further Research 181 List of symbols 184 Some terms and abbreviations used in this study 188 Summary 189 Samenvatting 194 Curriculum vitae 200 Nawoord 201 I Introduction 1.1 General introduction To gel or not to gel, that is the question on which this work is meant to give the clue. Sometimes aggregation of colloidal particles leads to a gel, and sometimes to a sediment. In spite of the tremendous importance of this difference, not in the last place for industrial purposes, still not much is known about the factors determining whether a system containing colloidal particles will gel or not. In general, aggregation leads to rather irregular-shaped aggregates which, potentially, may completely occupy the available volume, leading to a gel. Factors like sedimentation, velocity gradients in the aggregating dispersion and rearrangements of the floes may, however, disturb this process. The ability to gel varies widely among different colloidal systems. Plastic fats (fat crystals in oil) and pulp particles in beverages like orange juice [1], gel at very low concentrations whereas emulsions seldom form a gel unless their volume fraction exceeds about 0.2. The term 'gel' has traditionally been used rather loosely for various combinations of substances. Gels formed by the aggregation of particles may be mentioned as one of them, but even within this group, the gel properties vary widely as may be illustrated by comparing two members of this group; orange juice and silica gel! Another group of gels is constituted by networks consisting of long, flexible macromolecules, partially cross- linked by covalent bonds, microcrystalline domains, entanglements or other linkages. These gel types have traditionally been subject to more extensive studies, which resulted in the classical theory of gelation of Flory [2] and Stockmayer [3], and in percolation theories [4]. These theories have also been applied to particle networks [5 - 7] and they are even successful in fitting experimental results. For being successful it is, however, necessary to introduce some misty factors like a critical volume fraction (corresponding to a percolation threshold) and appropriately chosen polyfunctional structural elements [7]. For gels that are formed by the aggregation of particles the critical volume fraction is mainly dependent on the accuracy of the measurement and on factors like 1 convection currents in the sample. Consequently, the use of these theories does not contribute to a better understanding and insight in the formation of a particle network. A third group of gels is composed of fairly small, amphiphilic molecules which may associate into a gel. These types of gels are well ordered and also called liquid crystalline phases. A concentrated dispersion of (electrostatically) repulsive colloidal particles, may also be classified in this group because it exhibits a similar, well ordered structure. In this gel type the particles are not connected geometrically, but there is strong repulsive interaction which leads to a high packing density of the 'effective' hard-spheres whose interaction size is considerably larger than the particle geometrical size [8, 9]. Due to this huge variety of gels it is difficult to give a general definition of a gel [10].