Steric Interactions between Physically Adsorbed Polymer-Coated

Dec 2, 2006 - difficult. However, one can still estimate the form of the potential profile either .... combination of the hard potential plus a soft t...
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Langmuir 2007, 23, 475-481

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Steric Interactions between Physically Adsorbed Polymer-Coated Colloidal Particles: Soft or Hard? Dong Qiu,*,†,§ Terence Cosgrove,*,† and Andrew M. Howe‡ School of Chemistry, UniVersity of Bristol, Cantock’s Close, Bristol BS8 1TS, U.K., and Kodak European Research, 332 Cambridge Science Park, Milton Road, Cambridge CB4 0FW, U.K. ReceiVed August 3, 2006. In Final Form: September 26, 2006 The steric interaction potential between colloidal particles imparted by adsorbed polymer layers is directly related to their structure. Due to the complexity of these interfacial structures, the steric potential may behave differently at different interparticle separations. In this study, we proposed a combined model of the equivalent hard-sphere model (EHS) and the Hayter-Penfold/Yukawa model (HPY) to describe the steric potential due to adsorbed homopolymers on colloidal particles. The EHS potential describes the dense train/small-loop region and the HPY potential the more diffuse tail/long-loop region. The steric potential was extracted from the structure factors measured by small-angle neutron scattering (SANS). It was found that this combined model gave better agreement with experimental data than either of its component models alone. This study also shows that the adsorbed polymer layer in a good solvent partially collapses when the layers approach one another, which is also supported by an NMR solvent relaxation study.

Introduction Steric stabilization of colloidal particles can be imparted by adsorbed or grafted polymer chains on the surfaces of particles and this has been well-established in the literature.1-6 The pair potential plays a very important role in determining colloidal particle stability and the direct measurement of these interaction potentials between individual particles is challenging, especially for colloidal particles of diameter e100 nm where thermal fluctuations are significant and single-particle manipulation is difficult. However, one can still estimate the form of the potential profile either by measuring the interactions between macroscopic surfaces or by measuring some bulk property of colloidal dispersions from which the interparticle potential can be deduced. Techniques that have been used to probe the interparticle interactions include the following: the surface force apparatus (SFA),7 scanning force microscope (SFM),8-12 total internal reflectionmicroscope(TIRM),13-17 differentialelectrophoresis,18-21 * Authors to whom correspondence should be addressed. E-mail: [email protected]; [email protected]. † University of Bristol. ‡ Kodak European Research. § Current address: School of Physical Sciences, University of Kent, Ingram Building, Canterbury CT2 8JH, U.K. E-mail: [email protected]. (1) Ottewill, R. H. Ann. Rep. A 1969, 66, 183. (2) Napper, D. H. Ind. Eng. Chem. Prod. Res. DeV. 1970, 9, 467. (3) Napper, D. H. J. Colloid Interface Sci. 1977, 58, 390. (4) Vincent, B. AdV. Colloid Interface Sci. 1974, 4, 193. (5) Parfitt, G. D.; Peacock, J. Surf. Colloid Sci. 1978, 10, 163. (6) Tadros, Th. F. AdV. Colloid Interface Sci. 1980, 12, 141. (7) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 1, 975. (8) Tang, S. L.; Bokor, J.; Storz, R. H. Appl. Phys. Lett. 1988, 52, 188. (9) Weisenborn, A. L.; Hanama, P. K.; Albrecht, T. R.; Quate, C. F. Appl. Phys. Lett. 1989, 54, 2651. (10) Burnham, N. A.; Domingues, D. D.; Mowery, R. L.; Colton, R. J. Phys. ReV. Lett. 1990, 64, 1931. (11) Blackman, G. S.; Mate, C. M.; Philpott, M. R. Phys. ReV. Lett. 1990, 65, 2270. (12) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature (London) 1991, 353, 239. (13) Prieve, D. C.; Frej, N. A. Faraday Discuss. Chem. Soc. 1990, 90, 209. (14) Crocker, J. C.; Matteo, J. A.; Dirsmore, A. D.; Yodh, A. G. Phys. ReV. Lett. 1999, 82, 4352. (15) Biggs, S.; Dagastine, R. R.; Prieve, D. C. J. Phys. Chem. B 2002, 106, 11557. (16) Sharma, A.; Tan, S. N.; Walz, J. Y. J. Colloid Interface Sci. 1997, 191, 236.

osmotic pressure,22,23 rheology,24,25 and scattering methods.26-32 Small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) are especially suitable for concentrated colloidal dispersions because of their short wavelengths and their ability to penetrate matter. Recently, we have successfully measured the pair potentials in concentrated silica and polystyrene colloidal dispersions using SANS and SAXS.30-32 In the scattering methods, the correlation between colloidal particles is reflected by a structure factor term, S(Q), which can be tracked back to the effective pair potential through solving the Ornstein-Zernike integral equations.33 In this process, model potentials are normally required. Potentials are referred to as either “soft” (change gradually with interparticle separation) or “hard” (change abruptly with interparticle separation). Steric potentials arising from short chains have been treated as a hard potential34 and those imparted by adsorbed long-chain polymer layers have been treated as “soft” potentials, which may take the functional form of either an exponential decay30 or a power law decay.35 Theoretical predictions show that the profile of the (17) Biggs, S.; Prieve, D. C.; Dagastine, R. R. Langmuir 2005, 21, 5421. (18) Velegol, D.; Anderson, J. L.; Garoff, S. Langmuir 1996, 12, 4103. (19) Anderson, J. L.; Velegol, D.; Garoff, S. Langmuir 2000, 16, 3372. (20) Holtzer, G. L.; Velegol, D. Langmuir 2003, 19, 4090. (21) Holtzer, G. L.; Velegol, D. Langmuir 2005, 21, 10074. (22) Costello, B. A.; Kim, I. T.; Luckham, P. F. J. Chem. Soc., Faraday Trans. 1990, 86, 3693. (23) Costello, B. A. de L.; Kim, I. T.; Luckham, P. F.; Tadros, Th. F. Colloids Surf., A 1993, 77, 55. (24) Tadros, Th. F.; Liang, W.; Costello, B.; Luckham, P. F. Colloids Surf., A 1993, 79, 105. (25) Buscall, R.; Goodwin, J. W.; Hawkins, M. W.; Ottewill, R. H. J. Chem. Soc., Faraday Trans. 1 1982, 78, 2889. (26) Ottewill, R. H.; Rennie, A. R.; Johnson, G. D. W. AdV. Colloid Interfaces Sci. 2003, 100-102, 585. (27) Douglas, C. B.; Kaler, E. W. Langmuir 1994, 10, 1075. (28) Zulauf, M.; Hayter, J. B. J. Phys. Chem. 1985, 89, 3411. (29) Penfold, J.; Staples, E.; Tucker, I. J. Colloid Interface Sci. 1997, 185, 424. (30) Qiu, D.; Dreiss, C. A.; Cosgrove, T.; Howe, A. M. Langmuir 2005, 21, 9964. (31) Qiu, D.; Cosgrove, T.; Howe, A. M.; Dreiss, C. A. Langmuir 2006, 22, 546. (32) Qiu, D.; Cosgrove, T.; Howe, A. M. Langmuir 2006, 22, 6060. (33) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids, 2nd edition; Academic Press: London, 1986. (34) Ramakrishna, S.; Gopalakrishnan, V.; Zukoski, C. F. Langmuir 2005, 21, 9917. (35) Likos, C. N.; Vaynberg, K. A.; Lowen, H.; Wagner, N. J. Langmuir 2000, 16, 4100.

10.1021/la062294t CCC: $37.00 © 2007 American Chemical Society Published on Web 12/02/2006

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polymer layers normal to the interface is closely related to the interparticle steric potential.36 When homopolymer chains are adsorbed to a colloidal particle surface, different conformational sequences appear at the interface, commonly referred to as trains, loops, and tails.37 Scaling theory predicts that there are three domains in the adsorbed polymer profile normal to the interface. In the proximal region the segment density is constant, while in the central and distal regions the density decays with a power law and an exponential form, respectively.37-40 Different regions are thus expected to have different degrees of “softness” or “hardness”. Trains, because of their close contact with the surface, are effectively incompressible and thus increase the effective hard-sphere size of the particle. The potential corresponding to loops may be soft or hard, depending on their length and density and the particular interaction potentials obtained. Tails, being considerably more dilute, are more likely to be soft. Therefore, some of these characteristics could be incorporated into the hardsphere core and some into the soft tail. This means that a combination of the hard potential plus a soft tail (which we refer to as the “combined model”) may describe the steric interactions better than either a single soft or hard potential. The Hayter-Penfold/Yukawa potential (eq 1) was used to describe the soft part of the potential because in the mean-spherical approximation,41 it gives an analytical expression for the structure factor42

U(w) ) 2RHPYU0 exp[-(w - 2RHPY)/κ]/w

(1)

where w is the distance from the center of a reference particle. In this model, the particle radius (RHPY), the volume fraction (φHPY), and the depth (U0) and decay constant (κ) of the potential are needed to calculate the structure factor. As a simple approximation, the equivalent hard-sphere potential is used to describe the hard part, where only the effective hard-sphere radius (REHS) and effective hard-sphere volume fraction (φEHS) are essential for simulating the structure factors.43 The parameters describing the effective hard-sphere characteristics REHS and φEHS are related to the colloidal particle hard-sphere radius (RHS) and volume fraction (φP-HS) by

φEHS )

( )

REHS 3 ‚φP-HS RHS

(2)

φP-HS can be measured by evaporation of the solvent in the sample (φP) and RHS can be measured by TEM or a scattering technique. Therefore, to calculate φEHS, only REHS needs to be found; however, we still leave φP-HS and RHS floating in the fitting process to achieve the best agreement between the theoretical predictions and the experimental data. Experimental Section Materials. A colloidal suspension of narrow size distribution silica particles was kindly supplied by Clariant (France) and was used as received. The particles have a mean diameter of 28.0 ( 0.2 nm measured by SANS, 28.4 ( 0.3 nm by SAXS, and 27 ( 2 nm by TEM. The suspension, product name 30R25, was supplied with a solid content of 30 wt %, a density of 1.2 g‚mL-1, and a pH of (36) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions; Academic Press: London; 1983. (37) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. In Polymers at interfaces; Chapman & Hall: London, 1993. (38) Ishinabe, T. J. Chem. Phys. 1982, 76, 5589. (39) Eisenriegler, E.; Kremer, K.; Binder, K. J. Chem. Phys. 1982, 77, 6296. (40) de Gennes, P. G.; Pincus, P. J. Phys. Lett. 1983, 44, L-241. (41) Lebowitz, J. L.; Percus, J. Phys. ReV. 1966, 144, 251. (42) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. (43) Ashcroft, N. E.; Lekner, J. Phys. ReV. 1966, 45, 33.

9. The counterion was sodium and the Na2O content was less than 0.2 wt % in total, according to the manufacturer. Poly(ethylene oxide) (PEO) of 97400 g‚mol-1 molecular weight was purchased from Polymer Labs (UK) with a quoted polydispersity of 1.02 and was used as received. Sample Preparation. 1. Samples for SANS. The stock silica colloid was mixed with a PEO/D2O solution, stirred for at least 24 h, and then diluted with D2O and H2O to yield various dispersions with different volume fractions. The PEO added to the dispersions would give an adsorbed amount of 0.27 mg‚m-2 assuming all polymer chains were adsorbed. The full coverage of this silica by PEO was found to be above 1.0 mg‚m-2 by NMR solvent relaxation and PCS. Little non-adsorbed polymer is expected to be present in the samples as the isotherms for this narrow molecular distribution polymer have high affinity so the added amount approximates well to the actual surface coverage and the two parameters are used interchangeably in the discussion. Although the samples were below full polymer coverage, they were sterically stable in 20 mM sodium chloride even for the most concentrated sample (0.16 silica particle volume fraction). Salt was used to screen the electrostatic interactions. This gives a Debye screening length of approximately 21.2 Å at 298 K. The ratio of D2O/H2O was adjusted to give an H2O volume fraction of 0.83 in the solvent, which corresponded to a scattering length density of 0.63 × 10-6 Å-2. At this contrast, the adsorbed polymer is invisible to neutrons (layer-contrast-matched). 2. Sample for 1H SolVent Relaxation NMR. The samples were made following the same procedure for neutron scattering samples but were dispersed in H2O. Three series of PEO concentrations were used to give different levels of steric repulsions: added amounts were 0.27, 0.54, and 0.93 mg‚m-2. These samples gave hydrodynamic adsorbed PEO layer thicknesses of 4.5 ( 0.2, 7.5 ( 0.3, and 10.5 ( 0.5 nm, respectively, as measured by PCS. MilliQ water and bare silica dispersions at various volume fractions were also measured as controls. Samples with different PEO surface coverage at a silica volume fraction of 0.01 were used to study the adsorption behavior of PEO. Measurement. 1. SANS Measurement. The SANS measurements were performed on D22 at the ILL, Grenoble, France, using 1 mm path-length quartz Hellma cells equilibrated at 298 K. Neutrons of 8 Å wavelength were used. The detector distance was 17.5 m and the collimation distance was 17.6 m. The Q-resolution with this setup is 10% (∆Q/Q). The resultant Q range extended from 0.002 to 0.035 Å-1. Two million neutron counts were collected for each measurement to give good statistics. 2. 1H SolVent Relaxation NMR Measurement. 1H spin-spin relaxation time measurements were performed on a Bruker MSL 300 MHz NMR spectrometer using the CPMG pulse sequence.44,45 4096 data points were taken with an 180° pulse spacing of 4 ms. All the relaxation functions were single component as the solvent is in fast exchange between the bulk and the interface. Signal averaging (typically 16 scans) and receiver phase cycling were employed to reduce errors from random noise and possible DC offsets. Data Treatment. All the SANS data were reduced and calibrated following the standard procedures used on D22. At this contrast condition (layer-contrast-matched), only the scattering from the silica particles is visible. The form factor, which is determined by the shape of the silica particles, does not change with volume fraction. Hence, the structure factors, S(Q), can be obtained from the measured scattering spectra by26,31 S(Q) )

I(Q)int × φni I(Q)ni × φint

(3)

where I(Q) is the absolute scattering intensity, φ is the particle volume fraction, and the subscripts “int” and “ni” stand for interacting system (where the effect of layer-layer interactions can be seen in the data) and noninteracting system (where the effect of interactions is not (44) Carr, H. Y.; Purcell, E. M. Phys. ReV. 1954, 94, 630. (45) Meiboom, S.; Gill, D. ReV. Sci. Instrum. 1958, 29, 688.

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Table 1. Parameters Obtained from Fitting the Structure Factors to the EHS Model φP φP-HS φeff RHS/Å REHS/Å δEHS/Å χ2

0.06 0.06 ( 0.01 0.13 ( 0.01 155.0 ( 0.5 199.0 ( 0.5 44.0 ( 0.7 11.7

0.11 0.11 ( 0.01 0.22 ( 0.01 155.0 ( 0.5 194.0 ( 0.5 39.0 ( 0.7 1.8

Table 3. Parameters Obtained from Fitting the Structure Factors to the Combined Model

0.16 0.16 ( 0.01 0.29 ( 0.01 155.0 ( 0.5 188.0 ( 0.5 33.0 ( 0.7 1.4

Table 2. Parameters Obtained from Fitting the Structure Factors to the HPY Model (Radius of Silica Particle Was Fixed at 155.0 Å) φP U0/kT κ/Å χ2

0.06 2.29 ( 0.04 67.7 ( 0.8 9.5

0.11 3.56 ( 0.16 62.7 ( 2.0 15.2

( ) -t T2

(4)

and the specific relaxation rate constants (R2sp) were calculated from T2s46-48 R2sp )

T20 - T2 T2

0.06 0.09 ( 0.01 179.7 ( 1.6 1.04 ( 0.08 51.1 ( 2.6 24.7 ( 3.1 19.5 ( 2.0 44.5 ( 3.7 1.8

0.11 0.21 ( 0.01 190.9 ( 1.2 0.47 ( 0.07 24.8 ( 2.4 35.9 ( 2.4 5.4 ( 1.0 40.4 ( 2.6 0.9

0.16 0.29 ( 0.01 187.3 ( 1.0 0.39 ( 0.11 21.3 ( 2.7 32.3 ( 2.0 4.1 ( 1.3 36.1 ( 2.4 0.8

0.16 4.56 ( 0.0.27 52.2 ( 2.1 19.6

seen). In the latter case, the suspension is either very dilute or the interactions have been screened. In the system studied here, the dispersion with a volume fraction of 0.01 could be fitted with a spherical form factor without any contribution from a structure factor and is therefore taken as a non-interacting system. However, a detailed analysis of the particle form factor is not essential as it cancels out by the division. The polydispersity (described by a log-normal distribution of particle size) suggested by SAXS was 0.07, indicating a near monodisperse nature (please see the Supporting Information). In the fitting to the EHS model, all parameters were left floating, and the parameters returned with the best agreement with the experimental data were accepted (Table 1.). In the fitting to the HPY model, RHS and φP-HS obtained from the fits to the EHS model were used and fixed in the fitting process since in this model we assume that there was no contribution to the particle size and volume fraction from the adsorbed polymer layer, while U0 and κwere left floating to achieve the best fit (Table 2.). In the fitting to the combined model, again, all parameters were left floating to achieve the best fit. φeff is the volume fraction of the hard sphere part including the particles themselves and the hard part of the adsorbed polymer layers (analogous to φeff in the EHS model); RHPY is the particle size used to control the soft potential and it is the same as the REHS in the combined model for the hard sphere part (Table 3.). The spin-spin relaxation time constant (T2) was extracted from the measured magnetization (M) relaxation decay curves by fitting the data to a single-exponential decay M(t) ) M(0) exp

φP φeff RHPY ) REHS/Å U0/kT κ/Å δEHS/Å δHPY/Å δeff/Å χ2

(5)

where T20 is the relaxation time constant of a reference sample.

Results 1. Structure Factors. With use of eq 3, the structure factors for the concentrated colloidal dispersions were obtained from the SANS measurements and are shown in Figure 1. The peaks of the structure factors move to higher Q with increasing volume fraction of the silica particles, indicating a decrease in the (46) van der Beek, G. P.; Cohen Stuart, M. A.; Cosgrove, T. Langmuir 1991, 7, 327. (47) Barnett, K. G.; Cosgrove, T.; Vincent, B.; Sissons, D. S. Macromolecules 1981, 14, 1018. (48) Nelson, A.; Jack, K. S.; Cosgrove, T.; Kozak, D. Langmuir 2002, 18, 2750.

Figure 1. Structure factors of layer-contrast-matched PEO-coated 30R25 colloidal particle dispersions in the presence of 20 mM NaCl. Symbols: experimental data on the volume fraction of 0.06 (O), 0.11 (0), and 0.16 (3); lines are the fit based on the EHS model (dashed lines), the HPY model (dotted lines), and the combined model (solid lines).

interparticle distance, as expected. The amplitude of the peak in the structure factor also increases with volume fraction, which reflects an increase in the interparticle coherence.34 2. Equivalent Hard-Sphere Model. The structure factors were first fitted to the equivalent hard-sphere model (dashed lines in Figure 1). All the fits are acceptable. The parameters obtained are presented in Table 1. It can be seen that the volume fractions obtained from the fits (φP-HS) are very close to those independently measured by the solvent evaporation method (φP). The hard-sphere radius (RHS) is very consistent for different volume fractions (155 ( 0.5 Å), which indicates that RHS does not depend on the interparticle correlations; however, it is larger than the value of 140 Å obtained from directly fitting the form factor for the 0.01 volume fraction sample.30 The discrepancy of size measured by form factors and structure factors was also observed for silica colloidal dispersions without adsorbed polymer layers.31 This small increase in size may be caused by ignoring the polydispersity when simulating the structure factors.31 Polydispersity decreases the amplitude of the structure factor, especially the first peak,49-51 which has the same effect as increasing the particle size when keeping the volume fraction constant, and because polydispersity was not taken into account in fitting the structure factors, the particle size obtained was expected to be slightly larger (10% larger in this case). However, in this article, all the dimensions compared were obtained from the fitting of structure factors; therefore, we can overlook this difference. As expected, the effective hard-sphere radius (REHS) (49) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983, 261, 1022. (50) Kotlarchyck, M.; Chen, S. H. J. Chem. Phys. 1983, 79, 2461. (51) Ginoza, M.; Yasutomi, M. Mol. Phys. 1998, 93, 399.

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Figure 2. Effective layer thickness (δeff) obtained from the fits to the EHS model (O) and the combined model (0).

Figure 3. Interparticle potentials given by the HPY model for PEOcoated silica colloidal dispersions at the volume fraction of 0.06 (solid line), 0.11 (dashed line), and 0.16 (dotted line).

is larger than the hard-sphere radius (RHS) due to the presence of the adsorbed polymer layer. Assuming this difference is caused by the presence of the adsorbed polymer layer, one can estimate the equivalent hard sphere layer thickness (δEHS) by

δEHS ) REHS - RHS

(6)

δEHS decreases with an increase of the particle volume fraction, indicating that the adsorbed polymer layers collapse when two particles approach each other (Figure 2). 3. Hayter-Penfold/Yukawa (HPY) Potential. The equivalent hard-sphere model only considers the excluded volume effect. When the stabilizing layer is thin and dense, for example with short grafted chains, the interaction potential is expected to be hard;33 however, for physically adsorbed long polymer chains, the interparticle interactions are expected to become somewhat “soft”, due to the presence of more flexible distal tails and long loops. The structure factors were also fitted to a soft potential model, HPY model (Figure 1, dotted lines). The particle size and volume fraction obtained from the EHS model were used in the HPY model and two other parameters: the strength, U0, and decay constant, κ, of this potential were allowed to vary to reach the best agreement with the experimental data (Table 2). The fits are not very satisfactory, especially at high Q. However, the results do show that the steric potential becomes stronger and in shorter range with the increase of particle volume fractions (Figure 3). This agrees with our previous findings.30 4. Combined Model. As discussed before, the structure factors for the PEO-coated silica dispersions were fitted to the combination of the EHS and HPY potential (combined model). The combined model gave a better agreement with the experimental data than the EHS model and the HPY model alone. The relative goodness of the fits can be judged from the fit in Figure 1 (solid lines) and the resultant χ2 values. For the combined model, the particle size (RHPY), volume fraction (φeff), and the potential strength (U0) and decay constant (κ) are all allowed to vary to achieve the best fit. The resultant parameters obtained are presented in Table 3. The potential is divided into two parts: the hard part and the soft part (Figure 4). When calculating the interparticle separation, the hard-sphere radius, RHS, and volume fraction, φP-HS, from fits to the EHS model were used because they represented the core silica particles.31 The success of this model supports the idea that there are different regions in an adsorbed polymer layer at interfaces. As discussed above, segments of adsorbed polymer at an interface may take different conformations: trains, loops, and tails. Trains

Figure 4. Interparticle potentials given by the combined model for PEO-coated silica colloidal dispersions at volume fractions of 0.06 (solid line), 0.11 (dashed line), and 0.16 (dotted line).

and small loops are denser and less compressible; hence, they can be effectively incorporated into the “hard” part. Large loops and tails are less dense and can be more easily compressed; the steric interactions arising from this part will show some degree of “softness”. Consequently, the effective volume fraction (φeff) of the particles in the combined model should also include the contribution from the closely attached polymer segments (the hard part). In the fitting process, the volume fraction (φeff in Table 3) and particle size (RHPY in Table 3) are independent parameters but φeff in the combined model can also be calculated in a similar way to that in the EHS model by eq 2, where REHS ) RHPY in the combined model. The calculated φeff values are in good agreement with those obtained from the data fitting (Figure 5), which also justifies the validity of this model. The thickness of the hard part (δEHS) can be calculated following the same method used for the EHS model (eq 6). It is worth noting that in the combined model, the thickness of the hard part first increases from 24.7 Å (0.06 volume fraction) to 35.9 Å (0.11 volume fraction), and then decreases to 32.3 Å (0.16 volume fraction) (Table 3). This will be discussed later. 5. Structure of the Adsorbed PEO Layers by the 1H Solvent Relaxation NMR. First, the adsorption of PEO on silica colloidal dispersions was studied by 1H NMR solvent relaxation (Figure

Polymer-Coated Colloidal Particles Steric Interactions

Figure 5. Effective hard-sphere volume fractions (φeff) for the combined potential model given by fitting (O) and by calculation according to eq 2 (0) at different volume fractions.

Figure 6. R2sp of PEO-coated silica colloidal particles as a function of PEO surface coverage (added amount of polymer). (The volume fraction of silica particle was fixed at 0.01.)

6). In this case, bare silica dispersion at the volume fraction of 0.01 was used as reference. It can be seen that, with the increase of PEO surface coverage, R2sp increases, indicating more “trains” exist at the surface and the “trains” density reaches a maxim at a PEO surface coverage of around 1.0 mg‚m-2. This is expected as the adsorption of homopolymer at a finite coverage cannot lie completely flat; however, with more polymer chains adsorbed, the “train” density can increase further.37 With the increase of silica particle volume fraction, the interparticle separation decreases and interactions between different adsorbed polymer layers can take place. The repulsion between these layers may affect the structure of the layers. As mentioned before, R2sp is sensitive to adsorbed polymer segments in train conformations.37 Therefore, if the repulsion is strong enough, the density of trains could change for example by collapsing loops and such a change may be reflected in the NMR solvent relaxation. R2sp should increase linearly with the increase of the PEO-coated particle concentration and any deviations from this could give information on this collapse. Four series of silica dispersions were studied. They were bare silica and silica with PEO concentrations corresponding to surface coverages of 0.27, 0.54, and 0.93 mg‚m-2 which were all below the critical surface coverage for the maximum train density (Figure 6). The results are shown in Figure 7. Pure water from the same batch was used

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Figure 7. R2sp of silica colloidal dispersions as a function of silica particle volume fraction at different added PEO: concentrations of 0 mg‚m-2 (O), 0.27 mg‚m-2 (4), 0.54 mg‚m-2 (0), and 0.93 mg‚m-2 (3).

as the reference and the silica particle volume fraction was normalized to that of water (silica/water). As expected, the presence of colloidal particles enhanced the R2sp and the adsorbed polymer provided an extra enhancement. The R2sp increases linearly with the increase of volume fraction of silica particles except for the series with the highest PEO coverage which instead shows a turn up at volume fraction of around 0.06. For bare silica particles, R2sp is expected to be linear with silica particle volume fraction as a result of increase of the interfacial area as has been found for various colloidal systems studied previously.46-48 As already shown above, when the silica volume fraction is over 0.06, steric repulsion takes place. However, for the series with a PEO concentration corresponding to 0.27 mg‚m-2, the interaction between adsorbed layers does not show any significant effect on R2sp. This indicates that although there are repulsions between adsorbed layers, these repulsions do not affect the structure of the proximal part or “trains”. Changes in the proximal part may be evident when the repulsion between the layers increases, which can be realized either by increasing the volume fraction or by increasing the layer thickness. In this study, we chose the latter as the former approach can lead to aggregation when the volume fraction is too high. In the silica series with a PEO concentration corresponding to 0.54 mg‚m-2, however, still no significant effect was found. For the silica series with the highest PEO concentration (0.93 mg‚m-2), a turn up was found at around a volume fraction of 0.06. This implies that the PEO-coated silica particles become more efficient in enhancing R2sp and hence suggests that the fraction of PEO segments in “train” conformation has increased as a result of the increased interlayer repulsions. The layer thicknesses for the samples corresponding to 0.27, 0.54, and 0.93 mg‚m-2 added polymer are 4.5 ( 0.2, 7.5 ( 0.3, and 10.5 ( 0.5 nm, respectively, as measured by PCS. The average surface-to-surface interparticle separations are around 297, 191, and 136 Å for the volume fraction of 0.06, 0.11, and 0.16, respectively. Therefore, it is expected that the interlayer repulsion in the series with the 0.93 mg‚m-2 sample would be much stronger, leading to an increase in PEO segments in train state.

Discussion 1. Steric Potentials. As expected, the combined model which considers both the hardness and softness of the steric potential

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imparted by the physically adsorbed long polymer chains gives the best agreement with the experimental data. However, it is surprising that the simplest potential model, EHS, also gives a good agreement, which suggests that, in certain cases, the EHS model can be used to describe the experimental data. The “soft” potential (HPY) itself, however, does not provide a satisfactory description of the steric interactions especially at high Q, which corresponds to a shorter distance in real space. This suggests that the “hard” part of the steric potential plays a more dominant role in determining the interparticle correlations, especially upon close approaches between colloidal particles. These three models all suggest that the adsorbed polymer layers collapse with the increase of colloidal particle volume fraction which agrees with previous findings.30,52 The current work also agrees with the findings by neutron reflectometry where it was shown that the adsorbed polymer layer on a flat surface collapsed under compression in a good solvent media.53 2. Effective Layer Thickness of Adsorbed Polymers. The combined model and the EHS model itself can both describe the steric potentials well; therefore, it is reasonable to expect that these two models have some degree of similarity. The effective layer thickness (δeff) of the adsorbed polymer can be measured independently by other methods, for example, PCS.54-58 In the EHS model, δeff is equal to δEHS and can be obtained by eq 6. In the combined model, the effective layer thickness should be the sum of the hard part (δEHS) and the soft part (δHPY). Taking the softness of the HPY potential into account, and following the procedure Barker and Henderson used to calculate the effective range of the soft potential,59 the contribution of the soft part to the effective layer thickness could be calculated by

δHPY ) 1/2 ×

∫d

∞

[1 - exp(-U(w)/kT)] dw

(7)

EHS

The total effective thickness of the layer in the combined model is

δeff ) δEHS + δHPY

(8)

The results of these calculations are presented in Figure 2 and Table 3. It can be seen that δeff given by these two models are indeed very similar; however, the combined model does systematically give larger values. This is expected because of the presence of distal polymer segments. It can also be seen that the adsorbed polymer layers collapse with increasing the silica particle volume fraction. The hydrodynamic layer thickness for the same PEO adsorbed on the same batch of silica particles at the same adsorbed amount was measured by PCS to be about 4.5 ( 0.2 nm, which is very close to the effective layer thickness (δeff) for the dispersion at the volume fraction of 0.06. At this concentration, the interparticle interaction is not so strong and therefore the layer thickness is expected to be close to that of the noninteracting system (PCS result). However, when the volume fraction increases, the (52) Greenwood, R.; Luckham, P. F.; Gregory, T. Colloids Surf., A 1995, 98, 117. (53) Cosgrove, T.; Luckham, P. F.; Richardson, R. M.; Webster, J. R. P.; Zarbakhsh, A. Colloids Surf,. A 1994, 86, 103. (54) van der Beek, G. P.; Cohen Stuart, M. A. J. Phys. 1988, 49, 1449. (55) Cohen Stuart, M. A.; Waajen, F. H. W. H.; Cosgrove, T.; Vincent, B. Macromolecules 1984, 17, 1825. (56) Killmann, E.; Maier, H.; Baker, J. A. Colloids Surf. 1988, 31, 51. (57) Garvey, M. J.; Tadros, Th. F.; Vincent, B. J. Colloid Interface Sci. 1976, 55, 440. (58) Kato, T.; Nakamura, K.; Kawaguchi, M.; Takahashi, A. Polym. J. 1981, 13, 1037. (59) Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 14.

adsorbed polymer layers start to repel each other (good solvent conditions) and the effective layer thickness decreases. Based on the PCS results, it would appear that the steric interactions in this system are rather weak as the interparticle separations are more than twice the dynamic layer thickness. The existence of steric interactions also implies there are distal tails in the adsorbed PEO layers which cannot be detected by PCS even though the measurement is hydrodynamic in origin47 but still affecting the interparticle interactions. As shown above, in the combined model, the thickness of the hard part first increases from 24.7 Å (0.06 volume fraction) to 35.9 Å (0.11 volume fraction), and then decreases to 32.3 Å (0.16 volume fraction) (Table 3). Taking into account the particleparticle separation, this may be interpreted as follows: when the particle volume fraction increases, particles get closer and the repulsion between the adsorbed polymer layers causes large loops and tails to shrink and become denser, which contributes to the hard part of the potential (volume fraction from 0.06 to 0.11). As the volume fraction increases further, the thickness of the hard part may still decrease because of further compression (volume fraction from 0.11 to 0.16); however, the change between volume fraction of 0.11 and 0.16 is not obvious within the error. The soft part, due to the collapse of large loops and tails, becomes weaker and shorter ranged (Figure 4). The change of the adsorbed polymer structure by repulsion is also supported by NMR solvent relaxation and neutron reflectometry.53 NMR results showed that, for this series of PEO-coated silica samples (0.27 mg‚m-2), the structure of the train state was not affected by the interparticle repulsion, but it can be influenced when the repulsion is very strong (0.93 mg‚m-2). That however also suggests that the hard part is not exclusively comprised of “trains”. The NMR results also suggest that no desorption took place when two adsorbed polymer layers approach eachother as the R2sp is linear with respect to the silica concentration. 3. Relative Contribution of the Hard Part and Soft Part of the Potential. From the χ2 values, it can be seen that the combined model gave the best fit for almost all particle concentrations, followed by the EHS model, and the worst fit was the HPY (Yukawa) model; this justifies the use of the combined model. The relative contributions of the hard part and the soft part can also be determined qualitatively: at a volume fraction of 0.06, both the HPY and EHS models are not satisfactory, indicating that the hard part and soft part both play important roles. However, the soft part contributes slightly more since the χ2 is smaller than that for the EHS. At volume fractions of 0.11 and 0.16, the EHS model is close to the combined model, which suggests that the hard part dominates the potential. This agrees with the finding in this paper that the adsorbed layers compress each other and collapse, which renders the potential harder when the particle volume fraction increases.

Conclusions The structure factors for PEO-coated silica colloidal dispersions were measured experimentally by small-angle neutron scattering (SANS). The steric interparticle interactions were modeled by both the equivalent hard-sphere model (EHS), Hayter-Penfold/ Yukawa potential (HPY), and their combination (the combined model). The combined model gave the best agreement with the experimental data and also revealed more details of the structure of the adsorbed polymer layers. The effective adsorbed polymer

Polymer-Coated Colloidal Particles Steric Interactions

layer thicknesses given by the combined model and EHS model were in good agreement with that independently measured by PCS. In the combined model, the hard part was related to the closely attached trains and small loops while the soft-sphere part was related to the loosely attached tails and large loops. This study also shows that, with the increase of the particle volume fraction, the adsorbed polymer layers collapse as a result of the interparticle repulsion. This structural change in the adsorbed

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polymer layers is supported by the solvent relaxation NMR results. Acknowledgment. We thank the ILL for providing neutron beam time and Dr. Ralf Schweins for his help with the SANS measurements. D.Q. acknowledges Kodak for funding through the Eastman Fellow Award and Unilever for a postdoctoral fellowship. LA062294T