The effects of polymer concentration, shear rate and temperature on the gelation time

of aqueous Silica-Poly(ethylene-oxide) “Shake-gels”

Harry Collini, Markus Mohr, Paul Luckham, Jiawen Shan, Andrew Russell

Department of Chemical Engineering, Imperial College London, Prince Consort Road, London, UK, SW7 2BB

AbstractHypothesisAqueous mixtures of silica and Poly(ethylene-oxide) (PEO) are known as “Shake-gels” due to the formation of reversible gels when subject to an applied force, such as shaking. This shear-thickening effect can be observed using a rheometer, via distinct and abrupt increases in the viscosity of the material. Preliminary experiments qualitatively showed that the time elapsed before this occurs, termed the gelation time, varied depending on the conditions used. This paper reports on a systematic study into the effects of polymer concentration, shear rate and temperature on the gelation time, to quantify any relationships that exist between the variables and develop understanding of the gelation mechanism and kinetics.

ExperimentsDifferent constant shear rates were applied to samples at various polymer concentrations and temperatures using a rheometer with concentric cylinder geometry.

FindingsThe gelation time varied significantly from several seconds to an hour or more and was exponentially accelerated by shear rate. A peak in gelation time occurred at medium polymer concentrations of 0.35 - 0.40% (25% silica) and at a temperature about 20 oC. Higher temperatures also exponentially accelerated the gelation time as kinetic effects dominated the thermodynamic and structural resistances to gel formation.

(195 words excluding headings)

Keywords: colloidal silica; polyethylene oxide (PEO); shake-gels; rheology; polymer coil expansion; gelation time.

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Graphical Abstract

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Introduction “Shake-gels” are aqueous polymer-colloid mixtures that exhibit reversible, discontinuous shear-thickening properties. When a force is applied, such as shaking, these colloidal mixtures transform into high viscosity gels (capable of holding their own weight), before returning to their initial liquid state when left to rest. A number of studies [1-16] have reported fluids displaying this phenomenon and they often comprise of relatively high molecular weight polymer, commonly polyethylene oxide (PEO), and a colloidal nanoparticle (usually silica or Laponite). However, this behaviour is only observed within specific concentration ranges of the two components: approximately 0.25-0.50 wt% PEO and 15-35 wt% Silica/Laponite, with variation across studies dependent on the grades of the materials used. Above the upper limit of these concentration ranges, irreversible permanent gels are observed, whilst at lower concentrations, the mixtures do not form gels or show only very weak thickening [1-3, 7-9].

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]

Much of the current literature has focused on the rheological properties of the gels in their gelled state or on the underlying molecular mechanism responsible for this shake gel behaviour [2-6, 8, 10, 11, 13, 15-17, 20]. Cabane et al,. (1997) [1] were one of the first to report the shake-gel phenomenon and proposed an underlying mechanism for the shear-thickening properties observed. This has since been investigated and generally accepted by several other studies, however, the language and terminology used when describing this mechanism between different authors, is inconsistent and can lead to confusion [1-20].

Here we attempt to clarify the mechanism in our own terms, based on our interpretation of previous literature (mostly based on the work by [1, 2, 7, 8, 18, 19]) as this will be used later to understand and explain our findings. Initially, under no applied shear, the polymer chains are coiled in their natural state with several silica particles adsorbed to them at different active sites along the chain (Fig 1(a)). The size and shape of these assemblies, along with the number of adsorbed silica particles per chain, are dependent on the properties and amounts of the materials used. The radius of gyration of the PEO, the diameter of the silica particles, the overlap concentration of the PEO chains and the resulting electrostatic repulsions between particles and colloids, along with the particle/polymer number ratio, all contribute to the initial equilibrium state.

Applying a shear force causes the polymer chains to linearly extend breaking some silica-PEO ‘bonds’. The extended PEO molecule now has more active adsorption sites available for further silica particles to adsorb. This results in the growth of the silica-PEO molecules into long chain “necklaces”. Each adsorbed silica particle also offers potential adsorption sites for other PEO chains, which leads to cross-linking and polymer bridging, resulting in very large, adsorbed silica-PEO 3D assemblies starting to form (Fig 1(b)).

With continued applied shear, the polymer coils will further elongate, forming a reversible gelled state (Fig 1(c)). Here, the shear force has been continuously applied for a sufficiently long time for the PEO chains to extend and enough polymer bridging to occur, to form

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supra-molecular assemblies of sufficient size, leading to the formation of a gel network that extends throughout the fluid. These assemblies need to be large enough that the intermolecular forces between them are strong enough to hold their own weight and exhibit the high viscosity gel properties observed. Shake-gels are not observed at low particle or polymer concentrations as there is an insufficient amount of either component to form large enough supra-molecular assemblies.

The relaxation process and reversibility of the shake-gel phenomenon has been well-documented and the focus of several other studies [3, 5, 6, 8]. When the shear force is removed, the polymer chains desorb from the silica particles and the extended PEO chains contract back to their initial random coil state [7, 8, 18]. It has been shown by Pozzo and Walker (2004) that there is sufficient thermal energy at room temperature for the polymer-colloid adsorption bonds to break and for the relaxation process to occur [2].

Figure 1 . Schematic sketch of the molecular scale mechanism responsible for the observed shake-gel phenomenon. (a) shows the polymers and particles in their initial equilibrium state prior to applying a shear force. (b) shows how the

polymer chains extend and elongate under an applied shear allowing more silica particles to adsorb. (c) shows fully formed, polymer bridged supra-molecular assemblies once completely gelled and shows the complex, interconnected 3D structures

of the polymer-particles molecules in this state. *(Only to be reproduced in colour online)*

This study focuses specifically on the discontinuous, shear-thickening gelation transition of Shake-Gels. When a constant shear rate is applied to the system using a rheometer, it has been observed that an abrupt and significant increase in viscosity occurs. This corresponds to the gelation transition and has been confirmed by visual observation. Figure 2 is a typical plot of how the viscosity of a Shake-Gel changes under constant applied shear, as the gelation process occurs.

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Figure 2. Example of a Viscosity vs Time plot for a shake gel sample. The plot shows that the change from the initial liquid to gel state and the transitional gelation process is clearly visible when measuring the viscosity. This has been confirmed by

visual observations of the gel within the rheometer during constant shear rate tests. The gelation time is defined as the first point at which the viscosity starts to increase, identified here at 39s. *(Only to be reproduced in colour online)*

In this example, each datum point was measured for one second and the gel transition process, which is represented by a sharp, orders of magnitude increase in viscosity, occurred relatively quickly (within 10 seconds). The time at which this viscosity increase first occurs (39 s in this instance) is termed the gelation time. In Figure 2, the viscosity values associated with the gelled state of the Shake-Gels are lower than would be expected. The reason for this is that these values correspond to the effects of wall slip within the rheometer and therefore the true viscosity values of the gelled state are significantly higher. As a result, the viscosity readings after the initial gel formation are unreliable using this geometrical setup, however, this has been the focus of previous studies (references). Early experiments showed that the gelation time varied significantly and can be very long, in some instances over an hour. It has been observed from simple manual agitation of samples, that applying a larger force or shaking a sample more vigorously, results in faster and easier gel formation. The mode of applied shear, e.g. extruding the samples through a syringe, can also significantly affect the ease of gel formation [3]. Otsubo & Watanabe (1990) [21] reported that the polymer cross-linking rate in silica/polyacrylamide solutions is accelerated by shear.

Based on these observations, it was expected that the gelation time could be affected by shear rate and possibly by other factors. Previous literature has investigated and attempted to model the gelation of gelatin/water systems (e.g. [29], [30]). Understanding how the gelation time varies with various parameters may allow for similar models to be developed for shake-gel systems which can be used when designing gels for specific applications. Kawasaki and Kobayashi (2018) [28] briefly reported on the temporal changes in viscosity at three different shear rates and different pH values but did not specifically focus on the gelation time variations. This is the first systematic study probing the gelation transition

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process and the effects of shear rate, polymer concentration, temperature on the gelation time.

Experimental MaterialsThe shake-gels formulated and characterised in this work were comprised of polyethyleneoxide (PEO) and silica (LUDOX) particles. 2 wt% PEO (Sigma Aldrich, 900,000 g.mol-1, Batch#: MKBR1560V) stock solution was prepared via dissolution in deionised water. The silica concentration in all rheological samples was 25 wt%, which was measured directly from the stock solution of LUDOX®-TM50 (Sigma Aldrich; average diameter 25 nm; density = 2305 kg.m-3; Batch#: MKBV5538V). PEO was then added to samples (from the 2 wt% stock solution), with PEO concentrations varying from 0 to 0.8 wt% to allow for a phase diagram to be constructed. The solution was then made up to the total desired mass with deionised water. Final pH of the samples was in the range 9.5-10.0, consistent with those reported by Kawasaki and Kobayashi (2018) showing gel formation [28]. The samples were manually agitated to form gels and ensure a homogenous mixture was produced, before being left and allowed to relax back to their initial state for 12-24 hours before characterisation in the rheometer.

It is important to note that it was crucial to follow this procedure exactly, in order to obtain reproducible results. Deviating from this or using different batches of silica or PEO produced the same general trends but significant differences in the gelation (and relaxation) times were observed.

MethodologyAn Anton Paar MCR 302 Rheometer with concentric cylinder geometry (Anton Paar cc27 40884, diameter 26.66mm) was used for all rheological measurements, whilst RheoCompassTM software was used during analysis. 20 mL shake-gel samples were loaded into the rheometer cup and the software was initialised. Once a noticeably sharp and sudden increase in viscosity was visible, usually from approximately 20 mPa.s to 250 mPa.s, the rheological measurement was manually terminated, as this indicated gel formation had occurred.

The first test performed on each sample was a “critical shear rate” test. The shear rate was linearly increased from 1-2500 s-1 over a time period of 500 s, with gel formation usually occurring at a shear rate of approximately 1100-1250 s-1. The shear rate inducing gelation is referred to as the “critical shear rate” and gives an indication of how strong the gels are relative to one another. It should be noted that this is not a true “critical” value as gel formation will still occur at shear rates lower than this value, when undergoing constant shear rate-type tests for long time periods. For constant shear rate tests, a value approximately 100 s-1 less than the critical shear rate was applied to the sample and the data was accrued via viscosity-time plots. The viscosity was observed at a point density of 1 pt s-1 and the experiment was stopped once gel formation occurred at a specific gelation time. The temperature was controlled and adjusted via an internal water bath. This experiment was repeated at different shear rates, temperatures and PEO-silica compositions.

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Adsorption measurementsPolymer solutions of various concentrations were prepared and 10 mL of each polymer solution was poured into 50 mL centrifuge tubes. 5 mL of the LUDOX-TM50 suspension was then added into the polymer solutions; the pH of the solutions was measured and found to be in the range 9.6-10.0. The centrifuge tubes were sealed; placed onto a rotator and left rotating end-over-end gently for 16-24 hours. The samples were then centrifuged at 12000 rpm for 150 min. After this period, the equilibrium concentration of the supernatant solution was determined using the following spectrophotometric method.

The method consists of adding 0.25 mL of a freshly prepared KI-I2 solution (consisting of 1 g of I2 and 2 g of KI dissolved in 100 ml of distilled water) to 10 mL of the polymer solution. The absorbance is measured at 500 nm in the visible region using a Perkin Elmer 554 spectrophotometer. This technique was first described by Baleux [31] and used by others for determining the concentration of the PEO based polymers in adsorption experiments [32] [33]. Calibration curves were constructed in the polymer concentration range 0-40 ppm and values at higher PEO concentrations were determined by dilution.

The amount of PEO adsorbed on the LUDOX surface can be estimated using the following equation:

Γ=C i−C eqCLudox

(1)

where Ci is the initial polymer concentration within the sample, Ceq is the equilibrium concentration after adsorption and centrifugation, and CLudox is the concentration of the LUDOX in the suspension.

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Results & DiscussionPhase diagramA phase diagram for the silica and PEO materials used in this work was constructed prior to experimental work. The diagram (Figure S-1 in the supplementary material) shows the concentration limits separating the regions in which clear shake-gels formed (central region, purple circles) exhibiting the reversible gelation properties; strong permanent gels (green squares) which do not relax back to their liquid state after gelation and mixtures which do not form gels at all (dark grey diamonds). Shake-gels formed at silica concentrations between 14.5 – 30 wt% and at PEO concentrations of 0.05 - 0.60 wt%. Below these concentrations no obvious gels were formed and above these concentrations strong permanent gels were produced. Other studies have produced similar diagrams showing this intermediate region in which shake-gel formation occurs and our results are generally in agreement with previous work, allowing for some variation due to the exact type, size and shape of the different materials used [1-3, 7-9]. Based on the phase diagram, it was decided that mixtures with a constant silica concentration of 25 wt% and a PEO concentration of between 0.25-0.50 wt% would be examined in further detail as these concentrations produced clear, unambiguous shake-gels in the central region of the phase diagram.

Polymer Adsorption Isotherms

Figure 3 - Adsoption Isotherms at 25 OC for PEO on Silica at pH 5, pH 9 and pH 10.

The adsorption isotherms for the adsorption of PEO on silica at pH 5, pH 9 and pH 10 is given in Figure 3. At pH 9, a high affinity type adsorption isotherm with a plateau value of 0.38 mg m2 is observed. This is a rather low value, indeed at pH 5 the adsorbed amount was found to be 0.5 mg m2. At pH 10, there is some observed PEO adsorption reaching a maximum of 0.16 mg m2. At pH 11, no PEO adsorbed onto the silica. These results are in agreement with several studies [ [19], [28], [34], [35]] the recent studies by Kawasaki & Kobayashi (2018) [28] who report increased PEO adsorption on silica at lower pH. Thus at the pH at which shake gels are formed in this study (between 9.5-10.0) the adsorption of the PEO onto the

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silica is relatively weak. These results are also in agreement with the work of Gage et al, [35] who studied the adsorption of silica nanoparticles onto PEO brushes using neutron scattering and found that the mass of silica nanoparticles adsorbed at pH 11 was zero but increased as the pH decreased. Further agreement with an earlier study of Van der Beek and Cohen Stuart [34] who studied the adsorbed layer thickness of PEO with a molecular mass of 270,000 at different values of pH. They found that the adsorbed layer thickness was approximately constant up to pH 10.5, but then dropped to zero at pH 11.0. It is surprising that there is such a strong pH dependence for the formation of shake gels, given that the isoelectric point of silica is around pH 2. At pH 9.5, there will still be some silanol groups on the silica surface which have the potential for hydrogen bonding, but these would be expected to be low in number. We speculate that under shaking or in simple shear or extensional flow, these hydrogen bonds could break and the reform bringing about the formation of the gel as described by the gelation mechanism.

Effect of PEO Concentration on Gelation TimeThe effect of varying the PEO concentration, at constant silica concentration, on the gelation time of shake-gels was studied. The PEO concentrations of the samples used ranged between 0.25 and 0.50 wt% at a silica concentration of 25 wt%. Figure 4 plots the average gelation times of multiple samples against PEO concentration at a constant shear rate of 1600 s-1 and a temperature of 15 oC.

Figure 4. Average gelation time (s) vs PEO concentration (wt%) at a shear rate of 1600 s-1 and a temperature of 15 oC for shake gels with PEO concentrations between 0.25-0.50 wt% with a pH of 9.5-10.0. *(Only to be reproduced in colour

online)*

At 0.25 wt% gelation occurred very quickly, typically between 3-10 seconds. Given the scale used in Figure 4, this is not very clear, however it is important to note that clear and distinct non-zero gelation times were observed. As the polymer concentration was increased, the

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gelation times also increased up to 0.35 wt% and 0.40 wt%, where the gelation time appeared to reach a maximum. Shake-Gels at these PEO concentrations produced stronger gels that had a higher resistance to gel formation, shown by the longer gelation times. Further increases in PEO concentration decreased the gelation time and gel formation became easier to induce. At 0.5 wt% the gelation times were again very fast, but non-zero, similar to the results obtained at 0.25 wt%. At both these concentrations, the gelation times appeared to be independent of shear rate and temperature. A quadratic trend line was fitted to the data to help visualise the trends observed. Figure S-2 of the supplementary material includes additional data from several experiments at different temperatures. The plot shows the same trends observed here. The quadratic trend lines fitted to the data show the peak in gelation time appears to occur at a PEO concentration of 0.35 - 0.40 wt%.

These results suggest that there is some concentration at which shake-gels exhibit a maximum strength and resistance to gel formation. Yan et al (2016) investigated the effect of changing the particle concentration on the zero-shear viscosity of silica-PEO shake-gels [2]. However, their results were discussed in terms of the particle/polymer number ratio. They found that the zero-shear viscosity increased up to a maximum, at which point the PEO chains were completely saturated by the silica particles. After this point, adding more silica and increasing the particle/polymer ratio reduced the zero-shear shear viscosity. In this work, the polymer concentration was increased and thus the particle/polymer ratio decreased, as summarised in Table 1. Yan et al used particle/polymer ratios of between 3.4 – 20.2 with a maximum zero-shear viscosity at 13.4. The ratios used in this work are of similar magnitude, and the slight differences can be attributed to the different amounts and properties of the materials used across the two studies.

Table 1. Particle/Polymer number ratio for the PEO concentrations used in the experiments, at a constant silica concentration of 25 wt%.

PEO Concentration (wt%) Particle/Polymer Number Ratio (25 wt% Silica)

0.25 7.90.30 6.60.35 5.70.40 5.00.45 4.40.50 4.0

Yan et al discuss the similarity between the zero-shear viscosity and the shear-thickening behaviour of silica-PEO mixtures and suggest that the two are closely related. The zero-shear viscosity represents the static structure and behaviour whilst the shear-thickening behaviour represents the dynamic structure of the shake-gels. Both static and dynamic behaviour have shown peaks in their measurements at medium particle/polymer ratios. In the current study, an inverse relationship between the particle polymer ratio and shear-thickening behaviour was observed. Initially, the polymer chains were over-saturated with silica particles, however as the polymer concentration increased, the particle/polymer ratio values decreased, with an observed peak in the gelation time occurring at a PEO concentration between 0.35-0.40 wt% (a particle/polymer ratio between 5.7–5.0) Based on the conclusions made by Yan et al, this should correspond to the polymer concentration at

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which the particle saturation is reached, for the materials used in this study. The gelation time indicates the behaviour of the dynamic, shear-thickening gelation process and the similarity between the gelation time peak observed in our work, and the peak in zero-shear viscosity obtained by Yan et al, provides further support to their suggested link between the static and dynamic structures proposed [2]. At low polymer concentrations (high particle/polymer ratios) the polymers are over-saturated with silica particles. When a shear force is applied and the polymer chains begin to extend and elongate, opening up more adsorption sites, there is a high probability of the sites being occupied by a free silica particle. This results in rapid growth of the polymer-colloid assemblies to the size required for gelation and so a low gelation time is observed. As the polymer concentration is increased and the particle/polymer ratio approaches the medium saturation value, there are fewer free silica particles available to occupy the adsorption sites and so assembly formation becomes more dependent on polymer bridging than simple particle adsorption. The reduced probability of this occurring, due to the lack of excess of free silica particles, results in a longer gelation time as more time is required for the assemblies to grow to a sufficient size via polymer bridging. When the concentration was further increased and the polymers were under-saturated with silica particles, the probability of a free adsorption site being occupied by another polymer chain, or a polymer bridge to another silica particle, increases and the decrease in gelation time is observed. Under these conditions, the assemblies form faster through a greater extent of polymer bridging rather than particle adsorption. We propose that the peak in gelation time observed at the saturation ratio is due to these two mechanisms of assembly formation competing with each other.

Effect of Shear Rate on Gelation TimeThe applied constant shear rate was varied between 500-1200 s -1 for shake-gel samples with PEO concentrations of 0.30-0.45 wt% at 25 °C. Gels with a PEO concentration of 0.25 wt% and 0.5 wt% were not examined as these gels showed very fast gelation times, regardless of shear rate or temperature. Figure 5 shows the plot of viscosity against time at different shear rates for one shake-gel with a PEO concentration of 0.45 wt%. After the initial gelation occurred, the measurement was manually terminated to display the results clearly.

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Figure 5. A viscosity (mPa s) against time (s) plot for a shake-gel sample of 0.45 wt% PEO and 25 wt% silica with a pH of 9.5-10.0 at 25 °C at different constant shear rates, obtained using an Anton Paar MCR 302 rheometer. The large vertical spikes

in viscosity indicate gel formation and the gelation time. Point density was 1 pt/s. *(Only to be reproduced in colour online)*

Increasing the shear rate decreased the gelation time and when the applied shear rate was high enough (≥ 1100 s-1), the gels formed almost instantaneously. At lower shear rates (≤ 600 s-1), the samples formed gels at times of ≥ 40 minutes. Preliminary experiments observed that some samples required over an hour at low shear rates before gelation occurs. This behaviour was unexpected so further work into the kinetics of the polymer-bridging gelation mechanism is required to fully explain this. Some samples, not included in Figure 5, were rheologically characterised at very low shear rates (300–400 s -1) and gel formation did not occur within 2 hours. A minimum shear rate may exist, below which, the rate of particle-polymer desorption caused by thermal energy, exceeds the adsorption and polymer bridging rate induced by the applied shear, therefore preventing gelation from occurring. Figure 6 shows the gelation times plotted as a function of applied constant shear rate for several different shake-gel samples of varying PEO concentration.

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Figure 6. Gelation Time (s) vs Shear Rate (s-1) for 4 samples of different PEO concentrations all with a pH of 9.5-10.0. All samples showed exponential decreases in gelation time with increased shear rate however the gradients varied

significantly depending on the individual concentration and critical shear rate (CSR) of the sample at 25 oC. *(Only to be reproduced in colour online)*

Figure 6 shows the gelation time plotted as a function of applied constant shear rate for four shake gel samples of different PEO concentrations. The 0.45wt% sample (yellow triangles) corresponds to the sample shown in Figure 5. It can be seen from Figure 6 that the gelation time shows an exponential decrease with increasing shear rate; the trend lines shown are exponential fits to the data. The gradients of the fitted exponential trend lines vary with the PEO concentration and the critical shear rate (CSR) of the sample due to the differences in gel strength. Samples with a PEO concentration of 0.35 wt% showed the largest gradient and were significantly more resistant to gel formation than other samples with different PEO concentrations. As previously discussed, 0.35 wt% is close to the PEO concentration at which peak gelation time occurs and the gels exhibit the maximum resistance to gel formation. Hence, a steeper gradient was observed at this PEO concentration when varying the shear rate. The remaining samples all showed similar trends but different gradients. Gels with higher CSRs took longer to gel and resulted in steeper exponential gradients. The difference in the CSR values of these samples is likely to be caused by experimental error when originally formulating the gels, however, it can be seen that the critical shear rate can have a significant impact on the shake-gel behaviour and the gelation time, and thus it is an important parameter to measure initially.

The exponential decay trends observed on all samples can be explained through an analogous relationship to the Arrhenius equation (Equation (1)). [22]

k=Ae−( ERT ) (1)

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Where k is the rate constant, A is a pre-exponential factor, E is the activation energy of the reaction, R is the universal gas constant and T is the absolute temperature. The Arrhenius equation is derived from collision theory and explains that increasing the temperature of a reaction increases the kinetic energy and movement of the particles within the reaction mixture, resulting in more collisions and a higher rate of reaction. We hypothesise that in the case of the silica-PEO shake-gels, increasing the shear rate (rather than the temperature, as was the case of the Arrhenius equation) also increases the movement of the colloidal polymer-particle entities within the system. This results in an increased internal kinetic energy within the shake-gels, increasing the rate of the linear expansion of the PEO chains and formation of both silica and polymer-bridging adsorption bonds. The increased rate of these processes at high shear rates contribute to a faster formation of the assemblies and a faster gelation time. We also propose that there may be some analogous “gelation energy” term that must be reached before gelation occurs and that this is responsible for the long gelation times observed at low shear.

It was observed that samples tested at low shear rates (<800 s -1) showed a slight increase in viscosity of approximately 2-3 mPa.s before the increase in viscosity associated with gel formation occurred. This suggests that an intermediate stage exists in the gelation process, where the polymer bridged assemblies are beginning to form on the molecular scale but the gels still exhibit macro liquid properties. We propose that these intermediate particle-polymer assemblies are larger than those in the initial state and have stronger intermolecular forces between them resulting in a slightly higher viscosity. However, these forces are insufficient to hold the weight of the intermediate assemblies as they do in their fully-gelled state. This slight increase in viscosity and intermediate gelation phase is also expected to occur at higher shear rates, however due to the increased applied shear, the liquid-gel transition was too fast for this to be observable. This is shown clearer in Figure S-3 of the supplementary material which is a restricted plot focusing on the time period prior to gelation for the sample tested at 700 s-1.

These results show a clear trend between the applied shear rate and the gelation time which can be used in kinetic modelling of the gelation transition process. However, as mentioned previously, the mode of shear can have a significant effect upon the ease of gel formation and so the gelation times observed here may not be applicable to other situations. Despite this, we expect the overall trends to still be observed in different geometries.

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Effect of Temperature on Gelation Time Constant shear rate tests at 1000 s-1 were performed on samples at temperatures between 2.5 - 40 oC. Figure 7 shows the gelation times of these experiments plotted against temperature. The cloud point temperature of PEO has been reported to be in the range of 90-95 oC [36] and was therefore assumed not to have affected the results.

Figure 7. Gelation Time (s) vs Temperature (C) for two shake-gel samples with PEO concentrations of 0.45 wt% and a pH of 9.5-10.0 at a constant shear applied shear rate of 1000/s for the temperature range 2.5-40C. *(Only to be reproduced in

colour online)*

Initially, as the temperature of the samples was increased, the gelation time increased somewhat and reached a maximum at approximately 15 - 20°C. Further increase of the temperature to room temperature and higher resulted in a decrease in the gelation time. These results contradicted the expected trend and our initial thoughts. The temperature at which the maximum peak in gelation time occurred varied slightly depending on the sample. The decrease in gelation time observed at temperatures above room temperature follows a reasonably well fitted exponential decrease; the same trend observed when increasing the shear rate. This can be seen from the trend lines fitted to the higher temperature region of both samples shown in Figure 7. These results suggest that increasing temperature and shear rate can be considered to have a similar effect on the gelation kinetics, as they increase the kinetic energy and the rate of movement of particles within the system, resulting in an increased rate of polymer-bridged assembly formation and thus a faster gelation time. The results provide some indication of the gelation mechanism as a function of temperature that can be used when modelling or predicting shake gel behaviour or kinetics.

It has been widely reported that aqueous PEO exhibits polymer coil shrinkage with increased temperature [23-27]. Hammouda and Ho (2007) [26] report the correlation length (proportional to the radius of gyration) of PEO in deuterated water, determined from small

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angel neutron scattering experiments and show that in the dilute region (less than 0.7% PEO) the correlation length decreases as temperature increases over the temperature range 10-80 OC. It should be noted that the PEO used in their study has a molecular weight of 41,500 g.mol-1, however they propose a correlation that is applicable to other molecular weights and their results are applicable for our materials. In the shake-gel mixtures, this polymer coil expansion at lower temperatures allows for a larger number of silica particles to adsorb to the PEO chains, forming larger molecules in the initial state. This suggests that the polymer-bridged assemblies are initially partially formed and, under applied shear, a lesser extent of polymer chain expansion and polymer bridging is required to form assemblies of sufficient size for gel formation. This is further supported by the observed increase in initial viscosity at lower temperatures shown in Table 2 which shows the initial viscosity of a shake-gel sample at different temperatures. When the gel is cooled to low temperatures (below 10 °C) a higher initial viscosity is observed than for gels at higher temperatures (≥ 15 °C). The large, polymer-bridged supra-molecular assemblies that form due to the expanded polymer chains at lower temperatures, have stronger intermolecular forces between them resulting in a higher viscosity. This proposed state is similar to the intermediate gelation state discussed previously, where slight increases in viscosity were observed at lower applied constant shear rate prior to gel formation. These data suggest that at higher temperatures, kinetic effects from the extra thermal energy dominate the thermodynamic and molecular resistances caused by the increased polymer coil shrinkage and the more compact initial molecules.

Table 2 - Initial viscosities of a 0.45wt% PEO shake-gel sample at different temperatures

Temperature (oC) Initial Viscosity (mPa.s)5 14.5

10 12.815 11.820 11.825 11.930 11.9

It should be noted that temperature also affected the visual appearance of the gels. Gels formed at room temperature were opaque and had a white colouration with a slightly wet and soft texture. Gels formed at higher temperatures (e.g. 40 °C) were optically more translucent with a stickier and more gelatinous texture that adhered more to the rheometer probe as it was removed. Images of shake gels at different temperatures can be found in Figure S-4 of the supplementary material. Saito et al. (2010) [5] showed that the optical properties of shake-gels were determined by structural changes in the polymer-bridged assemblies. We expect that the reduced radius of gyration of the polymer coils caused by the higher temperatures is responsible for the optical differences observed. This suggests that at higher temperatures, kinetic effects from the extra thermal energy dominate the thermodynamic and molecular resistances caused by the increased polymer coil shrinkage and the more compact initial molecules.

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ConclusionsWe have demonstrated that when Silica-Poly(ethylene-oxide) (PEO) Shake-gels are subject to a constant applied shear, there is a clear and distinct time period before the mixtures change from their liquid to gelled state. This is accompanied by a change in the viscosity of several orders of magnitude, indicative of the gelation process. Previous work investigating the rheological properties and structures of Shake-gels have commonly examined the rheo-response against the magnitude of the applied shear [1-6, 11, 13, 15, 17, 18, 20, 28]. Only Kawasaki and Kobayashi (2018) [28] had previously reported on the temporal change in viscosity for the gelation process and briefly showed that the applied shear rate and pH of the mixtures can affect the time at which gels form.

The conditions used in constant shear rate tests have a significant effect on the gelation time, varying from seconds to an hour in some of our experiments. In some instances, no liquid to gel transition was observed within the experimental timeframe. The effects of shear rate, polymer concentration and temperature on the gelation time were investigated further. It was found that increasing the shear rate decreased the gelation time and was described well with an exponential trend fit, suggesting the gelation process is dependent on the amount of kinetic energy and particle movement within the system. A peak in gelation time was observed at medium polymer concentrations which corresponded to the saturation concentration based on analogous work by Yan et al., (2014) [2]. A peak in gelation time was observed near room temperature (approximately 15 - 20 0C) and decreased at both higher and lower temperatures. These relationships determined in this work provide a kinetic foundation for the development of predictive models of the gelation time, analogous to work done by Tobitani & Ross-Murphy (1997) [29] and Normand et al., (2000) [30], which are necessary when designing gels for specific applications.

Conflict of InterestThe authors declare no competing financial interest.

Acknowledgements We would like to thank Ann-Sophie Chevalier and Prof Francisco José Martínez Boza for their preparatory work on the rheological properties of these systems and for continuing useful discussions. Andrew Russell would like to thank the EPSRC and Syngenta for their financial support towards his postgraduate studies.

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