Langmuir 1992,8, 464-468
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Investigation of the Interaction Forces of Polymer-Coated Surfaces Using Force Balance, Rheology, and Osmotic Pressure Results B. A. de L. Costello and P. F. Luckham* Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW7 2BY, United Kingdom
Th. F. Tadros ICI Agrochemicals, Jealott’s Hill Research Station, Bracknell, Berkshire RG12 6EY, United Kingdom Received February 20, 1991.I n Final Form: November 12,1991 The forces between layers of poly(methy1methacrylate)/poly(12-hydroxystearic acid) comb copolymer adsorbed on macroscopic (mica) surfaces have been measured. Results show that the interaction energy increases monotonically and approximately exponentially with decreasing surface separation, with the force commencing at a surface separation of -24 nm. Comparisonshave been made with rheological and osmotic pressure data for latices stabilized by adsorbed layers of the same copolymer taken from the literature. The osmotic pressure data agree reasonably closely with the macroscopically measured forces, although due to the increased sensitivity of the surface forces apparatus, a softer, longer range interaction was observed. The general form of the rheological data is similar to the results obtained in the surface force experiments; however, the elastic moduli predicted from the force data are more than an order of magnitude greater than those experimentally determined. This implies that the models used to make the comparison do not hold at the high volume fractions used.
Introduction Nonaqueous dispersions are of considerable academic and industrial Such dispersions are frequently stabilized by polymers attached (either by physical adsorption or chemical grafting) to the surfaces of the dispersed particles. For fundamental studies one of the most commonly used model nonaqueous dispersions is poly(methy1methacrylate) (PMMA) spheres dispersed in a high-boiling aliphatic liquid medium. Almost invariably the stabilizer used has been a comb (graft) copolymer with a PMMA or similar backbone and poly(l2-hydroxyoctadecanoic acid) (poly(l2-hydroxystearic acid), PHSA) side chains. There is now an extensive body of work in the literature devoted to the investigation of the properties of these model dispersions. Much of this work has been carried out by Ottewill and co-~orkers,~7~ who have used light and neutron scattering to obtain structure factors for the dispersions at low and intermediate concentrations, and from those calculated their osmotic pressures. The same group had previously measured osmotic pressures using a pressure cell? and Doroszkowski and Lambourne have measured a similar property, namely, the surface pressure of a monolayer of particles spread at the oil/
* To whom correspondence should be addressed. (1) Barrett, K. E. J. Dispersion Polymerization in Organic Media; Wiley: London, 1975. (2) Croucher, M. D.; Milkie, T. H. J. Chem. Soc., Faraday Trans. 1 1983, 76, 261. (3) Vincent, B.; Edwards, J.; Emmett, S.; Croot, R. Colloids Surf. 1988,
31, 267. (4) Livsey, I.; Ottewill, R. H. Colloid Polym. Sci. 1989, 267, 421. (5) Markovic, I.; Ottewill, R. H.; Underwood, S. M.; Tadros, Th. F. Langmuir 1986, 2, 625. (6) Cairns, R. J. R.; Ottewill, R. H.; Osmond, D. J. W.; Wagstaff, I. J. Colloid Interface Sci. 1976,54, 51.
water interfa~e.~ In addition Strivens has made a systematic and detailed study of rheological properties*1° of these systems. One important property which has not been measured directly is the force between two particles as a function of their separation; in practice, of course, the particles are too small to handle and the forces too small to detect. It is possible to circumvent this difficulty, however, and these forces may be determined indirectly by measuring the forces between macroscopic bodies bearing the adsorbed comb copolymers. However, this method requires a specialized apparatus which is not available in most laboratories. A less quantitative method that can be applied for obtaining the interaction force between particles in a dispersion is to measure a bulk property such as its rheology or osmotic pressure. One important piece of information that these types of measurement can produce is the onset of interaction between adsorbed or grafted polymer layers. A t present there is no rigorous theory that may be applied to convert the information obtained from bulk measurements to force/distance profiles. However, it is possible to compare the trends of the results obtained from the various techniques, and this is the object of the present paper. For any comparison to be meaningful, the mode and amount of adsorption of the stabilizing polymer on the substrate should be the same in each case. It is difficult for this to be established withcertainty, but for a dispersion to be stable the copolymer must be formulated and the medium selected such that the backbone is insoluble and (7) Doroszkoweki, A.; Lambourne, R. J.Polym. Sci., Part C: Polym. Symp. 1971,34, 253. (8)Strivens, T. A. Colloid Polym. Sci. 1983,261, 74. (9) Strivens, T. A. Colloid Polym. Sci. 1987, 265, 553. (10) Frith, W. J.; Strivens, T. A.; Mewis, J. J. Colloid Interface Sci. 1990, 139, 55.
0743-7463/92/2408-0464$03.00/00 1992 American Chemical Society
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Interaction Forces of Polymer-Coated Surfaces
the side chains are soluble. These conditions have been met in all the cases discussed here, and it is therefore highly likely that the copolymer adsorbs in a similar way throughout, presumably as a monolayer with the backbone (PMMA) adhering to the substrate surface and the side chains (PHSA) extending into the medium. Although it is not possible to say with certainty that the amount of adsorbed polymer is the same in all cases, the similarity of the adsorbed layer thicknesses does tend to support this assumption. Several expressions have been derived which relate force to separation for surfaces bearing terminally attached polymers, most notably those of de Gennes, using a "blob" model and scaling theory," and Milner,12using a continuum mean field theory. Unfortunately Milner's expression requires the insertion of solution characteristics of the homopolymer such as the radius of gyration and osmotic pressure, which are not available for PHSA. Ideally de Gennes' expression also requires the radius of gyration, from which the layer thickness of the adsorbed polymer is calculated, but it may be used with the latter inserted as a parameter as we shall do here.
io3
lo2
10'
e 100
0
10
20
0
Distance, D / nm
Experimental Section Materials. The stabilizing polymer used was a comb copolymer consisting of a PMMA backbone with grafted PHSA side chains, supplied by IC1 Paints Division Ltd., Slough. The molecular weight of the copolymer,M,,was about 20 000. The side chain molecular weight, M., was 1600 (i.e., degree of polymerization -5). The backbone to side chain ratio was 1:lby weight. The medium used was analytical grade decalin (decahydronaphthalene) supplied by Aldrich ltd., Gillingham, Dorset, redistilled and dried over calcium hydride (decalin refractive index, nDzo,1.4750, boiling point 190 "C, density 896 kg m-3). Measurement of t h e Forces between Mica Surfaces. The surface forces apparatus and the procedure used have been described in detail elsewhere,13J4and only a summary will be presented here. Two molecularly smooth mica sheets, 1-3 pm thick, were partially silvered on the underside and attached with molten glucose to the curved surfaces of cylindrical section glass formers. These formers were then placed mutually perpendicular in a crossed cylinder geometry with the mica surfaces facing each other. The upper former was rigidly fixed, while the lower one was attached to a moveable cantilever spring of known spring constant, K (4100 N m-l). A beam of collimated white light was passed perpendicularly through the mica sheets. The partial silvering permits 10% transmission of visible light, and a series of interference fringes (fringes of equal chromatic order, FECO) were therefore formed. These fringes are observed in a spectrometer (0.5-m path length with a 32 A mm-l diffraction grating) and the wavelengths measured with a micrometer eyepiece calibrated against a Hg/Cd source. The cantilever spring was moved through a series of motors, to an accuracy of 0.5 nm. The distance between the mica surfaces,D, could be determined from the displacement of the FECO from their contact position. The motion applied to the fixed end of the cantilever spring, ADO,was calibrated against the motion of the FECO at a distance well beyond that at which the interaction forces were expected to begin. The force between the surfaces was then simply given by the difference between the applied motion and the actual motion, AD, multiplied by the spring constant: F(D) = K(ADo- AD)
io4
(1)
Results were expressed as interaction energies between flat surfaces,E@), by use of the Derjaguin approximation for crossed cylinders:'5 (11) de Gennes, P. G. Adu. Colloid Interface Sci. 1987, 27, 189. (12) Milner, S. T. Europhys. Lett. 1988, 7, 695. (13)Israelachvili, J. N.; Adams, G. E. J. Chem. SOC., Faraday Trans. 1, 1978, 74, 975. (14) Luckham, P. F. Powder Technol. 1989,58, 75. (15) White, L. R. J. Colloid Interface Sci. 1983, 95, 286.
Figure 1. Logarithm of energy,E(D),against surface separation, D, for copolymer adsorbed on mica surfaces compared with predictions from the de Gennes' expression (eq 3), and values , calculated from the osmotic pressure data of Cairns et al.? . first compression;0,first decompression;0 ,second compression; 0,second decompression; A, third compression; A, third decompression; -, prediction from de Gennes' expression; calculated from data of Cairns.
+,
E(D) = F(D)/Prr (2) where r is the cylindrical radius of curvature. The experiments were carried out by bringingthe mica surfaces together in air and measuring the positions of the FECO. The surfaces were then separated to a distance of about 2 mm, and a solution of about 100 ppm of the copolymer in the medium was introduced into the apparatus. The system was allowed to equilibrate for about 16 h to allow adsorption of the polymer onto the mica. Force against distance profiles were then taken. Each compression/decompression cycle took about 40 min to perform, with about 1-h intervals between cycles.
Results and Discussion Mica Force Balance Measurements. Results for the measurements of the interaction between mica surfaces bearing the adsorbed PMMAIPHSA copolymer are given in Figure 1. The interaction energy decays monotonically and approximately exponentially with increasing surface separation. This corresponds with all previous results published for terminally attached polymers.16-18 Results obtained for compression and decompression appear to coincide within experimental error, and there do not seem to be any timeeffects. The detection limit of the apparatus is of the order of 1pJ m-2,and the onset of the interaction can be taken as occurring at the point at which this value is exceeded. Figure 1 shows this to be at a surface separation of about 24 nm. This corresponds to a layer thickness on each surface of 12 nm. The energy of interaction increases with decreasing surface separation by about 3 orders of magnitude over the range of the interaction. The distance of closest approach of the surfaces was 5.5 f 0.5 nm. These data are sufficiently (16) Hadziioannou, G.; Patel, S.;Granick,S.;Tirrell, M. J. Am. Chem. Soc. 1986,108, 2869. (17) Ansarifar, M. A.; Luckham, P. F. Polymer 1988, 29, 329. (18) Taunton, H. J.; Toprakcioglu, C.; Fetters, L. J.; Klein, J. Macromolecules 1990, 23, 571.
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Costello et al.
accurate to compare with theoretical models for the interactions between terminally attached polymers. De Gennes gives an expression12for the interaction per unit surface area between polymers terminally attached to flat surfaces. This expression may be written as
(3)
where L is the adsorbed polymer layer thickness, s is the distance between side chain graft points, and /3 is a numerical prefactor. de Gennes also provides an expression for the calculation of the layer thickness from the side chain molecular weight, but this contains an osmotic pressure term, which is unknown in the present instance. The measured value of 12 nm was therefore used. s was calculated to be 2.3 nm from the known backbone to side chain weight ratio of 1:l and the density of PMMA of 1200 kg m-3. It was assumed that the backbone adsorbed as a monolayer and that a monomeric methyl methacrylate unit was cubic in shape. Interaction energies given by eq 3 using the above values are shown as the solid curve in Figure 1. It can be seen that de Gennes’ expression gives the correct form of the interaction energy against distance profile, although it failes to hold at small separations, where the blob model breaks down. It is interesting to compare these results with earlier data obtained with the same or similar PMMA/PHSA block copolymers used to stabilize PMMA latex particles. Clearly the surfaces of the mica and latex particles will be different, but the interactions will be dominated by the adsorbed polymer. These interactions will be the same if the polymer adsorbs in the same configuration and the solvency conditions are the same. The latter condition is certainly met as similar aliphatic hydrocarbon solvents have been used in all cases. The polymer is designed with a backbone insoluble and side chains soluble in aliphatic media, and it is reasonable to assume that the mode of adsorption is with a monolayer of backbone on the substrate surfaces and the side chains extending into the medium. Evidence that the configuration is the same in all cases is further provided by adsorbed layer thickness measurements. In our experiments the adsorbed layer thickness was about 12 nm, the surface balance work of Dorozskowski and Lambourne gave an average layer thickness of 13 nm, the osmotic pressure data of Cairns et al. gave a thickness of about 7 nm, and the rheological studies indicated a thickness of about 10 nm. Obviously the different sensitivities of the various techniques will result in some differences in the observed layer thicknesses, but these results are sufficiently close to confirm that the polymer configuration is similar in all cases and that meaningful semiquantitative comparisons can be made. Osmotic PressureData. The method for calculating interparticle forces from osmotic pressure measurements is based on that used by Rohrsetzer et al.19 The osmotic pressure of the dispersion, nb,has two main contributions: =dis
= nb -k
(4)
The term IIb is the osmotic pressure due to the dispersion of uncharged hard spheres in an electrically neutral medium, while flint is the contribution that comes from the particle interactions. lib is given by the Carnahan(19) Rohrsetzer, S.; Kovacs, P.; Nagy, M. Colloid Polym. Sci. 1986, 264, 812.
Starling equation of statem which can be written as
where a is the particle radius, 4 is the volume fraction of the spheres, T i s the temperature, and k is Boltzmann’s constant. This shows n h s to be negligible compared with measured values at high-volume fractions, as indeed has been shown by Ottewill et al. using scattering method^.^ For example, at 4 = 0.50 nhs is calculated to be 14 Pa, and at 4 = 0.60 IIb is calculated to be 34 Pa. This compares with measured values of the order of 10-100 kPa in this region. The interaction force, F ( D ) ,between two particles can then be calculated from the equation given by Rohrsetzer et al.:
F(D) = Hi,,A/n (6) where A is the surface area of a particle and n is the coordination number of the packing arrangement. To convert the data to energy between flat plates/ distance curves, the Derjaguin approximationfor spheresI5 is used; i.e.
E(D)= F(D)/aa (7) It should be noted that strictly this approximation should only be used where the particle radius >> compression distance. In the present case the radius of the particles is -75 nm and the adsorbed layer thickness -7 nm. Combining eq 7 with eq 6 gives E(D) = 411i,,a/n (8) For comparison with our force balance measurements, results calculated using eq 8 from the data of Cairns et al.? obtained using a pressure cell, are also included in Figure 1. These researchers used PMMA particles dispersed in dodecane. The stabilizing copolymer was prepared according to the same formulation as that used in the present work, the degree of polymerization of the side chains being given as 5. The surface separation, D, is available from the expression
D = 2a(4,/4)1/3 - 2a
(9)
where 4 is the volume fraction of the core particle and & is the maximum volume fraction for the adopted packing arrangement. A value for 4, of 0.7405, the maximum possible for spherical particles, representing cubic or hexagonal close packing, was assumed in the calculation of surface separations from the volume fractions quoted. The pressure cell implied an almost hard interaction at a surface separation of 14 nm. The force balance revealed much more detail of the softness of the interaction, showing the higher sensitivity of the surface forces apparatus. There was nonetheless a reasonable correlation between the magnitude of the interaction energies obtained from the two techniques. Rheological Data. A general expression for the high shear limit of the storage modulus for a system of monodisperse spherical particles is provided by the statistical mechanical treatment of Zwanzig and Mountain.21 (20) Carnahan, N. F.; Starling, K. E. J. Chem. Phys. 1970,53,600. (21) Zwanzig, R.; Mountain, R. D. J. Chem. Phys. 1965,43,4464.
Interaction Forces of Polymer-Coated Surfaces
where N is the particle number density, g(R) is the radial distribution function, with R being the center-to-center separation between the particles, and V ( R )is the particle interaction potential. The treatment assumes that the particle interactions involve only central pairwise additive potentials. This condition only applies if the particles slip freely over each other without contact friction. Both short-range and long-range order have been observed in dispersions of monodisperse spheres, and it is likely that at least the short-range order is retained where the system is under oscillatory shear with a low strain amplitude. Assuming that within the short-range domains a perfect lattice arrangement of the particles exists, g(R) can be approximated as a 6 function centered at the nearestneighbor spacing R . Such a model was used initially by Buscall et al.22and formed the basis of a more elaborate description by Evans and L i p ~ , ~ who 3 showed that eq 10 reduces to
Langmuir, Vol. 8, No. 2, 1992 467
0
..............."*.. ... ,......-
1
e........
* 0 0 4 . . - .. 0.35 0.40
.
0.45
- 1
0.50
4
or, in terms of forces
Figure 2. Logarithm of storage modulus, G'-,calculated from direct force/distance measurementa against particle volume fraction,4, compared with experimental data of Frith et al.:lom, data of Frith (plateauregion);0 ,data of Frith (nonplateauregion); -.,hard sphere prediction of Wagner and Russel; -, soft sphere prediction (& = 0.74); - - -,soft sphere prediction (4,,, = 0.68).
G', = NkT-*{4F(R) +R 5XR2 with F(R) as the interparticle force, since by convention fractions). This deviation is due to the soft interaction, F(R) = -dV(R)/dR. and dominates where the distance of separation is such As in the osmotic pressure case dealt with above, the that the polymer layers overlap. high shear limit of the storage modulus for a system of The independent soft sphere contribution can be spherical monodisperse particles consists of two contricalculated from eq 12 by an expression for FIR derived butions, a soft sphere contribution arising from particle from the macroscopic force/distance profiles given in Figure 1. The data of Figure 1 are shown as interaction deformation, and a hard sphere contribution arising from hydrodynamic, Brownian, and other thermodynamic energy between flat plates, E(D),against distance, D. stresses. These contributions are additive for small Conversion to force between spheres is again through the appropriate Derjaguin approximation (eq 7)) and since R deformations, as in the present case. The hard sphere contribution has been calculated by Wagner and R ~ s s e 1 ; ~ ~ = D + 2a, eq 12 becomes the result of this calculation is plotted in Figure 2 as a dotted curve. G', = NkT - -{4E(D) + R (13) 5R2 dD Figure 2 also shows th&experimental data of Frith et al.lo obtained using PMMA particles with a diameter of Figure 1 shows that E(D)against D can be fitted by an 84 nm stabilized by an adsorbed layer of the PMMA/ exponential function, and G', may therefore be calculated PHSA comb copolymer. It is noteworthy that in the this from eq 13 for any given packing arrangement. Figure 2 work the same batch of copolymer was used as in the gives the results of such a calculation for I$, = 0.74 (solid present work. Frith et al. present results for latices of curve) and &, = 0.68 (broken curve). difference particle size elsewhere, but it is only in the 84Figure 2 shows that although there is good qualitative nm case that the volume fraction has been taken suffiagreement between the predicted and measured values of ciently high for overlap of the stabilizing polymer layers G'-, the slopes of both sets of data being very similar, the to occur. Five data points (closed symbols) are given for former give an overestimation of 1-2 orders of magnitude. which G' appears to have reached a plateau value; two Clearly there is an error in the approach adopted. In this other points are also plotted (open symbols) where G' has simple analysis we have applied the cell model with the not reached its high shear limiting value. All the points particles centered on a lattice; incorporating a more are within the region of adsorbed layer overlap for any realistic radial distribution function will only increase the packing arrangement. It can be seen that at low volume predicted G', values, so this is not the source of error. It fractions reasonable agreement between experiment and seems to us that one possible explanation may lie in the hard-sphere theory is obtained, but at high volume polydispersity of the PMMA particles. It is well known fractions the correlation becomes poor. (Frith et al. also that a polydisperse system will have a significantly lower showed experimentally that for larger particles the agreeviscosity and storage modulus than a monodisperse system, ment with hard sphere theory continues to higher volume sometimesby as much as an order of magnitude. No data for the polydispersity is given by Frith et al.lo We should (22) Buscall, R.; Goodwin, J. W.; Hawkins, M. W.; Ottewill, R. H. J. say, however, that we have obtained similar results for PS Chem. Soc., Faraday Tram. 1 1982, 78, 2887. (23) Evans,I. D.; Lips, A. J. Chem. SOC.,Faraday Tram. 1990, 86, latex stabilized by PEO/PMMA graft copolymers26where 3413. the polydispersity was sufficiently low for the dispersion (24) Wagner, N. J.; Russel, W. B.Physica A, 1989,155,475. to iridesce. Perhaps there is an alternative explanation (25) Luckham, P. F.;Costello, B. A. de L.; Tadros, Th. F. J. Colloid Interface Sci., submitted for publication. for these observations.
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Summary In conclusion it is clear that data obtained by many researchers over a period of 20 years or so are by and large consistent with each other. The direct force measurements have enabled the bulk properties of concentrated steric stabilized dispersions to be predicted, and although the absolute magnitude may not correspond to experiment, the scaling laws are consistent.
Costello et al.
Acknowledgment. We thank Mr. Trevor Strivens for kindly supplying the copolymer used in this work. We also thank Dr. Ian Evans for bringing eq 11to our attention, and for many valuable comments. We thank the SERC for supporting One Of us (cOstellO) and the "Wement of IC1 PlC for Permission to Publish this work* Registry No. PHSA/PMMA (graft copolymer), 128364-067.
