Rheological Study of the Gelation Kinetics of a Concentrated Latex

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Langmuir 2000, 16, 9627-9633

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Rheological Study of the Gelation Kinetics of a Concentrated Latex Suspension in the Presence of Nonadsorbing Polymer Chains J. L. Trompette* and C. Bordes Laboratoire de Ge´ nie ChimiquesUMR 5503, ENSIGC, 18 Chemin de la Loge, Toulouse 31078, France Received June 5, 2000. In Final Form: August 24, 2000

The gelation kinetics of a concentrated latex suspension in the presence of two nonadsorbing sodium carboxymethylcellulose polymer chains with different molecular weight has been investigated. The experimental results indicate that the presence of the polymer chains generates two concomitant and opposite effects on the gelation time. Providing excluded volume effects are predominant, the gelation time was found to decrease. When a critical value of the polymer volume fraction in the bulk phase was reached, the gelation time increased with concentration due to viscosity effects. Moreover, the dynamic rheological measurements were shown to exhibit the influence of the excluded volume effects on the fractal dimension of the growing aggregates of the gelified networks.

Introduction Colloidal stability has long been the subject of study from both a theoretical and experimental point of view.1-4 These investigations have primarily been motivated from a need to understand conditions for either the promotion or suppression of flocculation in both industrial and natural processes (froth flotation, wastewater treatment, paint formulation, etc.). Due to the specific properties of the emulsion polymerization process (nature and concentration of the used monomer units and surfactants), the production of spherical particles with well-controlled size distributions and surface characteristics (surface charge and hydrophobicity) can be achieved.5 The resulting latex particle suspensions were thus considered to be a suitable material for the testing of theoretical models. Furthermore, the improved understanding resulting from these models is expected to provide a better understanding of their behavior in various technological applications (adhesives, coatings, binders, etc.).6 In this context, many studies have been devoted to the specific aggregation mechanism referred to depletion flocculation. Typically, such flocculation has been studied with respect to dilute suspensions of latex particles in the presence of nonadsorbing dissolved polymer samples.7-18 * To whom correspondence should be addressed. (1) Tadros, Th. F. The Effects of Polymers on Dispersion Properties; Academic Press: London, 1982. (2) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions; Academic Press: London, 1983. (3) Hough, D. B.; Rendall, M. In Adsorption from Solution at the Solid/Liquide Interface; Parfitt, G. D., Rochester, C. H., Eds.; Academic Press: London, 1983; Chapter VI. (4) Koopal, L. K. In Coagulation and Flocculation; Dobias, B., Ed.; Marcel Dekker: New York, 1993; Chapter IV. (5) Daniels, E.; Sudol, E. D.; El-Aasser, M. S. Polymer Latexes: Preparation, Characterization and Applications; ACS Symposium Series 492; American Chemical Society: Washington, DC, 1992. (6) Gelbert, C. H.; Grady, M. C. Latex Technology. In Encyclopedia of Chemical Technology, 4th ed.; John Wiley and Sons: New York, 1995; Vol. 15, p 51. (7) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255. Asakura, S.; Oosawa, F. J. Polym. Sci. 1958, 33, 183. (8) Sperry, P. R.; Hopfenberger, H. B.; Thomas, N. L. J. Colloid Interface Sci. 1980, 82, 62.

However, from a fundamental point of view, very few studies have been concerned with the gelation process that might occur with concentrated systems in the presence of nonadsorbed polymer chains. For that purpose, the number of latex particles has to be large enough and the attractive interactions have to be predominant over the repulsive ones to allow the formation of a continuous pathway in the entire volume of the system, i.e., a gel network. Oscillatory measurements are known to be a suitable technique to study the transition from a sol state to a gel state of various gelling systems.19-21 Many previous rheological studies have focused on the formation of chemical gels resulting from cross-linking of vinylic monomer units22-24 or the formation of composite networks resulting from the bridging of solid particles by specifically adsorbed polymer chains.25-28 (9) Sperry, P. R. J. Colloid Interface Sci. 1982, 87, 375. (10) Fleer, G. J.; Scheutjens, J. M. H. M. Adv. Colloid Interface Sci. 1982, 16, 341. (11) Gast, A. P.; Hall, C. K.; Russel, W. B. J. Colloid Interface Sci. 1983, 96, 251. (12) Vincent, B.; Edwards, J.; Emmett, S.; Jones, A. Colloids Surf. 1986, 18, 261. (13) Prestidge, C.; Tadros, Th. F.; Colloids Surf. 1988, 31, 325. (14) Patel, P. D.; Russel, W. B. J. Colloid Interface Sci. 1989, 131, 201. (15) Snowden, M. J.; Clegg, S. M.; Williams, P. A.; Robb, I. D. J. Chem. Soc., Faraday Trans. 1991, 87, 2201. (16) Snowden, M. J.; Williams, P. A.; Garvey, M. J.; Robb, I. D. J. Colloid Interface Sci. 1994, 166, 160. (17) Ro¨hm, E. J.; Ho¨rner, K. D.; Ballauff, M. Colloid. Polym. Sci. 1996, 274, 732. (18) Ho¨rner, K.D.; To¨pper, M.; Ballauff, M. Langmuir 1997, 13, 551. (19) Winter, H. H.; Chambon, F. J. Rheol. 1986, 30, 367. (20) Durand, D. In Structure des Polyme` res et Me´ thodes d’Etudes; GFP series, 1990; Vol. 8. (21) Muller, R.; Ge´rard, E.; Dugand, P.; Rempp, P.; Gnanou, Y. Macromolecules 1991, 24, 1321. (22) Hodgson, D. F.; Amis, E. J. Macromolecules 1990, 23, 2512. (23) Martin, J. E.; Adolf, D. Annu. Rev. Phys. Chem. 1991, 42, 311. (24) Trompette, J. L.; Fabre`gue, E.; Cassanas, G. J. Polym. Sci.: Polym. Phys. 1997, 35, 2535. (25) Jones, D. A.; Leary, B.; Boger, D. V. J. Colloid Interface Sci. 1991, 150, 84. (26) Trompette, J. L.; Charnay, C.; Partyka, S. Langmuir 1998, 14, 4475. (27) Otsubo, Y. J. Colloid Interface Sci. 1999, 215, 99. (28) Oh, M. H.; So, J. H.; Yang, S. M. J. Colloid Interface Sci. 1999, 216, 320.

10.1021/la000786e CCC: $19.00 © 2000 American Chemical Society Published on Web 10/31/2000

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Trompette and Bordes

In contrast, the present study is focused on the dynamic rheological behavior of a concentrated latex particle suspension, in the presence of two sodium carboxymethylcellulose polyelectrolyte chains. These measurements may provide a good means to study the influence of the concentration of the polymer chains on the gelation time of the latex suspension.

the reagent (phenol-water with 80-20% w/w). After homogenization, the absorbance was measured at 485 nm using a double beam Shimadzu spectrophotometer. The amount adsorbed was evaluated from the difference between the initial concentration before adsorption (calibration curve) and that measured after adsorption equilibrium in the removed liquid phase.

Experimental Section

To study the gelation kinetics of a suspension of latex particles, the attractive forces acting on the particles have to be much greater than the repulsive forces. Furthermore, the number of particles has to be large enough to form a gel network. These two conditions may be achieved by using a concentrated latex sample in the presence of a sufficient amount of salt so as to significantly decrease the repulsive electrostatic forces between charged latex particles. However for a practical convenience, the salt concentration has to be chosen so as to enable the gelation process to be followed on a time scale that is suited to the rheological study technique. In addition, to avoid the possibility of specific bridging mechanisms with multivalent ions, the use of a monovalent salt is often recommended. It was thus decided to work with a latex suspension having a 0.24 particle volume fraction and in the presence of a 3.62 mol/L NaCl concentration. Typically, these conditions resulted in gelation times of less than 1 h. Latex and CMC Characteristics. The net interaction energy for two charged latex particles in dilute solution can be estimated from the DLVO model. For two particles of radius R separated by a distance D, this energy is given by30,31

Materials. The copolymer latex studied here was a Rhoˆne Poulenc (France) product that was used as received. It was prepared by emulsion polymerization in aqueous phase from styrene and carboxylated butadiene monomers. The dried solids content was 50% w/w, and the density of the latex suspension was found to be 1.04 g/mL (corresponding to a 0.48 volume fraction of latex particles with a particle density of 1.08 g/mL). The average diameter and the zeta potential of a dilute suspension of latex particles (10-4 v/v) in deionized water at pH 6.5 were measured at both stationary levels in the cylindrical cell of a Zetasizer 5000 apparatus (Malvern Instrument). These values were found to be 160 nm and -37 mV, respectively. Two sodium carboxymethylcellulose (CMC) samples (identified as Walocel CRT 5G and 30G) were purchased from Bayer and used as received. The weight-average molecular weight (Mw) was given to be 55 000 for the 5G product and 95 000 g/mol for the 30G product. For both samples, the degree of substitution (DS) was quoted by the manufacturer to be in the range 0.65-0.95. Sodium chloride (NaCl) was a product of Prolabo (France), purity 99%. The distilled and deionized water was used as a solvent. Viscosity and Dynamic Rheological Measurements. The reduced viscosity and the apparent intrinsic viscosity of both CMC samples in 3.62 mol/L NaCl solution at 298 K were determined using an Ubbelhode capillary viscosimeter. The density and the time of flow (between the two reference marks on the capillary tube) of the solvent were found to be 1.1222 g/mL and 139.02 s, respectively. Measurements of the viscoelastic properties of the various samples were performed by using a Carri-Med CSL 500 rheometer in oscillatory mode. The experiments were carried out at 298 K with a cone-plate geometry (diameter, 40 mm; cone angle, 3°59′; gap, 119 µm) at three measuring frequencies 1, 1.5, and 2 Hz, with a maximum strain amplitude of 8%. The level of the strain was checked in order to ensure that all measurements were made within the linear viscoelastic regime. A controlled waterevaporation system was used for long time-dependent experiments. Latex Sample Preparation. The mixtures of latex and CMC samples for the rheological studies were prepared as follows. First, a known amount of CMC sample was dissolved in 5.5 M NaCl solution (corresponding to a given C polymer concentration). Then 3 mL of the resulting solution was added dropwise in a beaker containing 3 mL of a 48% v/v latex suspension (1.44 mL of solid particle phase + 1.56 mL of aqueous phase) under agitation during 1 min. Three milliliters of the resulting mixtures was then placed on the plate of the rheological device for the viscoelastic study, and the remaining 3 mL was poured into a 4 cm diameter glass beaker for a qualitative observation. Hence, for each sample studied, the latex particle volume fraction was 0.24 and the NaCl salt concentration in the aqueous phase was 3.62 M. The CMC polymer concentration in the available aqueous phase of the latex mixture was given by CP ) 3C/4.56 in g/mL. Adsorption Experiments. A volume of 1 mL of 48% v/v latex sample was added to 10 mL of 5.5 M NaCl aqueous solutions with CMC concentrations varying from 0 to 2 mg/mL for both 5G and 30G samples. The suspensions were stirred overnight at 298 K and then kept at rest for 1 day. According to a general method for analyzing carbohydrates,29 5 mL of concentrated sulfuric acid was added to a mixture containing 2 mL of the removed CMC aqueous solution after equilibrium and 100 µL of (29) Hoogendam, C. W.; De Keiser, A.; Cohen Stuart, M. A.; Bijsterbosh, B. H.; Batelaan, J. G.; Van der Horst, P. M. Langmuir 1998, 14, 3825.

Results and Discussion

VT(D) ) VvdW(D) + Vrep(D)

(1)

such that the attractive interaction energy is given by

VvdW(D) ) -AR/12D

(2)

where A is the Hamacker constant for solid particles in the suspending medium. As the exact value was not known for the studied copolymer latex sample, the value of 2.3 × 10-20 J corresponding to that of polystyrene particles in water30 was taken in a first approximation. In the literature, the Hamacker constant for various polymeric solids in water is generally found to be of the same order of magnitude.30 So that it can be assumed that the extent of the attractive force is similar. R is 80 × 10-9 m and D is expressed in m. The repulsive interaction energy is given by

Vrep(D) ) 32π0R(kBT/e)2γ2 exp(-κD)

(3)

where 0 represents the total electric permittivity of the suspending medium (80 × 8.8 × 10-12 C2/(J m)), kBT is the thermal energy (4.11 × 10-21 J at 298 K) and e is the electronic charge (1.6 × 10-19 C). The term γ is given by

γ ) tanh(zeψ0/4kBT)

(4)

where z is the valence of ion (here z ) 1 for NaCl salt). The surface potential (ψ0) is identified in a first approximation with the experimentally measured zeta (30) Hiemenz, P. C. Principles of Colloid and Surface Chemistry, 2nd ed.; Marcel Dekker: New York, 1986. (31) Behrens, S. H.; Semmler, M.; Borkovec, M. Prog. Colloid Polym. Sci. 1998, 110, 66.

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potential (ζ ) -37 mV). Finally the reciprocal of the Debye length is given by

( ) ( e2

κ)

∑i F∞izi2

1/2

)

)

1/2

3

2

(2 × 10 )e NACNaCl

0kBT

0kBT

(5)

where F∞i is the number density of each type of ion in the bulk phase (number of ions/m3), NA is the Avogadro number, and CNaCl is the salt concentration in molarity unit (here 3.62 × 103 mol/m3). Substituting the appropriate numerical values of the physical constants into eq 1 gives the following:

8.67 × 10-29 + D -19 4.45 × 10 exp((-3.26 × 109)CNaCl1/2D) (6)

VT(D) ) -

It can be shown that in the range 1 < CNaCl < 4 M, VT(D) is always negative for D < 500 nm. This indicates that within the experimental conditions studied the attractive regime is always predominant. Although the above relation is valid in the case of dilute suspensions, it can be assumed that the same trends hold for more concentrated systems. The transition from a stable to a coagulated suspension in dilute system occurs over a narrow range of electrolyte concentrations and the critical coagulation concentration (ccc) for a given salt may be evaluated. Its determination is based on two conditions that have to be fulfilled:30

VT(D) ) 0 and

dVT(D) )0 dD

(7)

It can be shown that the derived expression for the ccc in the case of a symmetrical (z-z) electrolyte in water is given by30

ccc ) 3.9 × 10-39

γ4 A2z6

(8)

where the ccc is expressed in mol/L. Substituting the appropriate numerical values of the physical constants into the above expression yields for the ccc a value of about 0.1 mol/L for NaCl salt. This result indicates that within the experimental conditions used, the 3.62 M NaCl concentration is well above the expected value of the ccc. The formation of particle aggregates (flocs) was effectively found to occur in dilute suspensions of latex particles in 3.62 M NaCl solution, but it is a kinetic phenomenon and not instantaneous. To make a comparison with the case of pure water and to ensure that the measurements were performed on individual particles, the zeta potential of a freshly prepared dilute suspension of latex particles (10-4 v/v) in 3.62 M NaCl solution was measured. Its value was found to be -21 mV, in contrast with -37 mV in the case of pure water. These results confirm the expected trend that the presence of salt ions contributes to a decrease in the electric potential at the plane of shear. This, in turn, indicates a decrease in the extent of the diffuse layer (the value of 1/κ), and thus also a reduction in the repulsion between colloidal particles. It enables the particle aggregates to form, and these may lead to a gelation process in the case of much more concentrated systems. In the presence of nonadsorbing polymer molecules (i.e., depletion flocculation), it has previously been shown7,9

that there is an additional contribution to the attractive force between neighboring colloidal particles when the effective diameter of the polymer coils exceeds the distance between the particles (particularly in good solvent conditions). In this case, the macromolecules are excluded from the interparticle region since their presence in this restricted space would give rise to a loss of configurational entropy resulting in a free-energy increase. In the majority of earlier studies, it was often necessary to add nonionic surfactants in order to provide a protective layer that prevented the adsorption of neutral polymer chains. In the current study, a polyanion such as sodium carboxymethylcellulose (CMC), with a charge of the same sign as the latex particles in solution, was used since it has a large extension in solution and thus promotes significant exclusion effects. In previous studies devoted to the behavior of concentrated aqueous silica dispersions in the presence of nonadsorbed polyelectrolyte chains,15,16 it was shown that CMC was much more efficient in promoting phase segregation than other polyanions (such as sodium polystyrene sulfonate). This was ascribed to the uneven charge distribution and the relatively stiffness of rodlike CMC chains. It was thus recognized that CMC chains could give rise to high depletion forces since they could form an anisotropic liquid phase.16,32 Viscosity Properties of CMC Aqueous Solutions. It is well-known that sodium carboxymethylcellulose behaves as a polyanion in aqueous solution and that it possesses the characteristic properties of polyelectrolytes33 (i.e., specific correlation between their size and shape with the ionic strength). In aqueous systems of low or moderate salt concentrations, the polymer chain adopts an expanded conformation in order to minimize the electrostatic repulsion between the carboxylated groups carried by the polymer segments. With a decrease of the polymer concentration, the screening of the charges is decreased and the repulsion between the segments increases the expansion of the chains. This gives rise to large excluded volume effects, and the reduced viscosity is found to increase with dilution. However, as the polymer concentration increases, the excluded volume effect of a chain becomes progressively screened and the expansion of the chains decreases to give an ideal dimension.34 Then, the reduced viscosity is found to increase due to the increasing number of polymer chains in the system (as the polymer volume fraction). As a result, the curves are characterized by the presence of two distinct behaviors.34 It was shown in the literature,35,36 that the apparent intrinsic viscosity of polyelectrolyte chains and hence their apparent size occupied in the bulk phase were decreased in the presence of increasing amounts of monovalent salt. With increasing the density of counterions, the charges carried along the polymer chains become progressively screened. For very high salt concentrations, depending on the DS of the sample, they may be completely screened by the counterions so that the macromolecule can be assumed to be neutral.33,34 In the present study, with a 3.62 M NaCl concentration, it can be expected that the polyelectrolyte chains are at least significantly screened. As an indication, the zeta potential of a solution of the 30G sample at a concentration of 10-4 g/mL measured in deionized water and in a 3.62 (32) Flory, P. J. Macromolecules 1978, 11, 1138. (33) Oosawa, F. Polyelectrolytes; Marcel Dekker, Inc.: New York, 1971. (34) Champetier, G. Chimie Macromole´ culaire; Hermann, ed.; Paris, 1972; Vol. II. (35) Ait-Kadi, A.; Carreau, P. J.; Chauveteau, G. J. Rheol. 1987, 31, 357. (36) Takahashi, A.; Nagasawa, N. J. Am. Chem. Soc. 1964, 86, 543.

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Figure 1. (a) Variation of the reduced viscosity as a function of the concentration of the 5G sample in 3.62 M NaCl aqueous solution at 298 K. (b) Variation of the reduced viscosity as a function of the concentration of the 30G sample in 3.62 M NaCl aqueous solution at 298 K.

M NaCl solution was found to be -19 and -4 mV, respectively. Figure 1 shows the variation of the reduced viscosity of the CMC samples as a function of the polymer concentration in 3.62 M NaCl solution at 298 K. From both these figures, the extrapolation to zero concentration of the observed linear regime allows the determination of the apparent intrinsic viscosity [η] of the polymer chains at salt concentration studied.35,36 This is justified by the fact that the conformation (or size) of the chains remains the same. As it can be seen, the values obtained for 5G and 30G samples in 3.62 M NaCl solution at 298 K are 165 and 218 mL/g. Therefore, the corresponding value of the radius of the equivalent hydrodynamic sphere, Rh, is found to be 11 and 15 nm respectively.18 In addition, the concentration at the overlap threshold CP*, for which the density of polymer chains is large enough to allow individual chains to overlap and entanglements to occur,35 may be approximated by the relation CP* ) 1/[η]. This

Trompette and Bordes

corresponds to concentrations of 6.1 and 4.6 mmol/L for sample 5G and 30G, respectively. Adsorption Tests. At this point the question arises as to whether the CMC chains could be adsorbed on the surface of the latex particles and thus lead to aggregation through a bridging mechanism.1 To clarify this point, adsorption experiments were carried out according to the method described in the Experimental Section. As polyelectrolyte adsorption is known to be enhanced at high ionic strength,29 the experiments were performed using a NaCl concentration of 5.5 mol/L. For the experimental conditions described previously, a latex surface of approximately 17 m2 was thus in contact with 10 mL of a CMC solution of variable concentration. After equilibration at rest, the latex particles were observed to be progressively collected at the top of the samples due to the high density of the aqueous salt solution. In this case, the latex particles would form a gel phase (see Figures 2 and 3). It can also be seen in Figure 2 that the presence of the CMC chains seems to cause a more pronounced effect on this segregation behavior. As the latex particles separated from the aqueous phase, it was possible to analyze a solids-free sample of the aqueous phase. As an indication, no difference was observed in the scattering behavior of the liquid phase relative to the sample 0 without polymer and that of a 5.5 M NaCl solution. Within the range of polymer concentration considered (up to 2 mg/mL), the experimental measurements indicated that no adsorption of both CMC samples was found to occur. This may be ascribed to the hydrophilic nature and also to the weak residual charge (as suggested by the previously electrophoretic measurements) of the CMC chains, preventing them from adsorbing on the hydrophobic and negatively charged latex surface. Therefore, it is concluded that CMC addition contributes to favor a phase segregation of the latex particles. Dynamic Rheological Study of Latex Mixtures. As the objective of this study is to investigate the influence of the polymer concentration on the gelling behavior of the concentrated latex suspension, the storage modulus G′ (measuring the solidlike elasticity of the material) and the loss modulus G′′ (measuring the viscous flow properties of the material) were determined in oscillatory measurements during the sol-gel transition. Hence, for a given polymer concentration, the variation of the storage and the loss modulus as a function of time was followed at three frequencies, 1, 1.5, and 2 Hz, and with the same

Figure 2. Mixture of 1 mL of latex (48% v/v) and 10 mL of 5.5 M NaCl aqueous solutions of the 5G sample at concentrations of 0, 0.5, 1, and 2 mg/mL, after 1 h at rest.

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Figure 3. Mixture of 1 mL of latex (48% v/v) and 10 mL of 5.5 M NaCl aqueous solutions of the 5G sample at concentrations of 0, 0.5, 1, and 2 mg/mL, after 1 day at rest.

Figure 4. (a) Variation of the viscoelastic parameters as a function of time at 1 Hz for the 5G sample at a concentration of 1.34 × 10-3 g/mL: G′ ([); G′′ (O). (b) Variation of the viscoelastic parameters as a function of time at 1 Hz for the 30G sample at concentration of 1.34 × 10-3 g/mL: G′ ([); G′′ (O).

torque value (10 µN m), allowing nondestructive conditions to be applied. The period of individual measurements was fixed at 3 s, and the interval between consecutive measurements was 100 s. As an example, the variation of the viscoelastic parameters in the presence of the same CMC concentration, CP ) 1.34 × 10-3 g/mL, for 5G and 30G samples has been shown in Figure 4 for a frequency of 1 Hz. The trends obtained are similar for each polymer. At the beginning the storage modulus is very low but increases with time so indicating the formation of latex particle clusters. During the gelation process, G′ increases more significantly than G′′ and becomes definitively greater after the crossover. The value of the storage modulus is expected to be directly proportional to the growing density of aggregated particles participating in the formation of clusters.13,23

For the 5G CMC sample at concentrations of 0, 4 × 10-4, 9.7 × 10-4, and 2.7 × 10-3 g/mL, parts a-d of Figure 5 show that the gelation time was taken as that corresponding to the crossover of the curves representing the variation of tan δ ) G′′/G′ as a function of time at the three measuring frequencies.22,23,35 The same procedure was applied for the 30G sample. From these measurements, the variation of the gelation time as a function of the polymer concentration in the aqueous phase for both CMC samples is plotted in Figure 6. As can be seen, the trends are similar for both CMC samples and are characterized by a marked change. The gelation time is found to decrease at first and to begin to increase after a given polymer concentration has been reached. However, for higher polymer concentrations, the gelation time was found to decrease again. This result is in contrast with observations made during qualitative tests since gelation was not found to occur for such polymer concentrations; a rather viscous mixture was obtained. In the absence of any polymer chain, the gelation time was found to be 2624 s in 3.62 M NaCl aqueous solution. The gelation mechanism of the bare concentrated suspensions is ascribed to the formation of growing particle aggregates resulting from a significant reduction of the repulsive interaction between the constitutive latex particles. Moreover, by comparing the results for 5G and 30G samples (see Figure 6), it can be observed that for the 5G sample (i.e., the lower molecular weight) the polymer concentration corresponding to the minimum gelation time is greater. It corresponds to concentrations of 9.7 × 10-4 and 6.1 × 10-4 g/mL for the 5G and 30G samples, respectively. For both CMC samples, an interesting point is that the polymer concentration at this lowest gelation time seems to correspond to the same polymer volume fraction. Indeed, considering that the size occupied by the polyelectrolyte chains in the bulk phase corresponds to the volume of the equivalent hydrodynamic sphere (previously determined), the polymer volume fraction, φP, is related to the polymer concentration, CP, through

φP )

CP 4 πRh3NA 3 Mw

(9)

Substituting by the appropriate numerical values, one obtains φP ) 0.059 and 0.055 for 5G and 30G samples, respectively, which is rather similar.

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Figure 5. Variation of the loss tangent as a function of time for the 5G sample at concentrations of 0 (a), 4 × 10-4 (b), 9.7 × 10-4 (c), and 2.7 × 10-3 (d) g/mL, at three measuring frequencies: 1 (0), 1.5 ([), and 2 Hz (O).

predominant over the other. When the polymer chains are added in the system, the viscosity in the bulk phase increases but it is not the predominant effect. As the polymer chains do not adsorb on the negatively charged surface of the latex particles, they experience in the aqueous phase mutual excluded volume effects and promote depletion flocculation. This results in aggregate formation which, in turn, leads to segregation due to their own properties.16,32 As a result when the polymer concentration increases, there is a supplementary reduction in the available volume to the latex particles, so that the latex particles may be regarded as being concentrated in a more restricted volume. The latex particles can thus form a continuous pathway in a shorter time. The CMC polymer chains thus act as a catalyst for the gelation process in this concentration domain. This mechanism prevails as long as the concentration of polymer chains in the aqueous phase is not greater than a critical volume fraction, corresponding to an average value of about 0.057.By use of the viscosity model for a dilute suspension of spheres30 (here the polymer chains with the same size), the corresponding value of the relative viscosity in the bulk phase is given by

η/η0 ) 1 + 2.5φP ≈ 1.14 Figure 6. (a) Variation of the gelation time as a function of the 5G concentration. (b) Variation of the gelation time as a function of the 30G concentration.

As in the case of depletion flocculation, it is suggested that the system may be considered as being composed of two pseudophases:13 a floc phase constituted by the particle clusters and an aqueous phase containing the polymer chains that have been expelled from the vicinity of approaching particles. However in the present case, the number of particles in the floc phase is sufficient to result in the formation of a gel structure. The experimental results suggest that both excluded volume (or segregating) and viscosity effects can be assumed to occur simultaneously, but according to the CMC volume fraction in the aqueous phase, one effect is

(10)

When more polymer chains are added, the viscosity of the aqueous phase still increases in the latex mixture and the excluded volume effects are no longer predominant. The diffusion of the individual latex particles and the dynamics of the growth of particle aggregates are significantly reduced, so that the gelation time is found to increase with polymer concentration. When the polymer concentration becomes relatively high, the aqueous volume of the latex mixture is occupied by the compact CMC chains. The polymer chains then experience overlapping and entanglements when the polymer concentration reaches the CP* concentration in the aqueous phase. As can be seen in Figure 6 for concentrations greater than the expected CP* values for both CMC samples, the gelation time was found to

Gelation Kinetics of a Concentrated Latex Suspension

decrease, which was at variance with the qualitative observation. It may be suggested that in such cases the system is composed of particle clusters that are isolated and separated from one another by a pseudonetwork of entangled polymer chains. This prevents aggregation of the particle clusters and thus constitutes a gel structure. It may explain the reason the gelation time was found to become very long and also why, for very high polymer concentrations, the gelation was not observed. From the point of view of the rheological measurements, the elastic contribution due to the entanglements between the constitutive polymer chains may correspond effectively to the characteristics of the formation of a gel network at the studied frequencies.21 Hence, the rheological measurements become inaccurate when the polymer concentration is greater than the CP* value. Most of the experimental and theoretical studies of rheological dynamic properties of various cross-linking systems have focused on determining the frequency dependence of G′ and G′′ in the vicinity of the sol-gel transition. These measurements have indicated that at the gel point the following relations are valid:20,23,37

G′ ∼ G′′ ∼ ωn and

tan δ )

G′′ nπ ) tan G′ 2

( )

(11)

The values of n obtained experimentally were compared with those theoretically predicted by different models of the sol-gel transition to elucidate the growth of the network structure by using the fractal scaling concept. As already seen in Figure 5, the variations of the loss tangent have been presented as a function of time for four characteristic concentrations relative to the curve displayed in Figure 6a for the 5G sample. The gelation time (tg), the loss tangent at the gel point, and the corresponding value of the fractal n exponent are reported in Table 1. The n values are found to increase as the gelation time decreases up to the minimum gelation time, corresponding to the critical polymer volume fraction, and to decrease with time thereafter. The same trend was observed in the case of the 30G sample. According to the framework of the fractal model of Muthukumar,38 the n exponent can be related to the fractal (37) Nystro¨m, B.; Walderhaug, H.; Hansen, F.; Lindman, B. Langmuir 1995, 11, 750. (38) Muthukumar, J. J. Chem. Phys. 1985, 83, 3161.

Langmuir, Vol. 16, No. 24, 2000 9633 Table 1. Experimental Values of the Gelation Time, the Loss Tangent at the Gel Point, and the Corresponding Calculated Fractal n Exponent, for Four Characteristic Concentrations of the 5G Sample in the Latex Mixture concn (g/mL)

gelation time, tg (s)

loss tangent, tan δ

exponent value, n

0 4 × 10-4 9.7 × 10-4 2.7 × 10-3

2624 1541 865 1812

0.95 1.14 1.76 1.10

0.48 0.54 0.67 0.53

dimension df of the gelling system and it was shown that they have an opposite sense of variation.37,38 As such, the results indicate that the fractal dimension df of the gelling system decreases with the polymer concentration up to the critical volume fraction and then increases. This suggests that the way the constitutive aggregates occupy the offered gelation volume is influenced by the presence of the polymer chains. With an increase of the polymer concentration and as long as the excluded volume effects are predominant, the available gelation volume is reduced. Hence, the growing aggregates of latex particles may be assumed to form more rapidly and with a preferential direction, thus allowing the gelation to be obtained in shorter times. When the excluded volume effects are no longer predominant and the viscosity of the aqueous phase increases significantly after the critical volume fraction, the kinetics of the cluster formation is reduced and the particle aggregates may be expected to form in a more random way. Conclusions The experimental results were shown to highlight the role played by the balance between the forces resulting from the excluded volume and viscosity effects on the gelation time of a concentrated latex suspension, in strong correlation with the volume fraction of the nonadsorbing polymer chains in the system. As long as the excluded volume effects were predominant, the polymer chains were found to act as a catalyst for the gelation of the studied latex suspension and to decrease the fractal dimension of the growing clusters. Acknowledgment. The authors are grateful to the Rhoˆne-Poulenc Society for supplying the latex sample.

LA000786E