Concentration Effects in Polymer Flocculation and Stabilization BY DOROTHY S. DUCKWORTH, ALEXANDER LIPS AND EDWIN J. STAPLES Unilever Research, Port Sunlight Laboratory, Port Sunlight, Wirral, Merseyside L62 4XN Received 18th January, 1978 The technique of photon correlation spectroscopy has been exploited in studies of the hydro- dynamic thickness of polyvinyl alcohol (A& = 45 000) adsorbed on monodisperse polystyrene latex particles. Complications can arise from particle interactions, especially aggregation effects. A procedure has been devised to quantify these and allow for their presence in the interpretation of the photon correlation measurements. This has involved the development of a low angle scattering approach which enables the second virial coefficients of particles to be measured, and which can be exploited with concentrated latices. An unexpected dependence of adsorbed layer thickness on polymer solution concentration was observed with a region of negative slope.Theoretical consideration of the requirements for such behaviour suggested that in principle it is possible in the circumstance of a very high adsorption affinity of the polymer for the surface and a solvent condition only very slightly better than the 8- condition. In the context, however, of the isotherm published for the system under study, the behaviour cannot readily be understood. Conventional and quasielastic light scattering techniques are being increasingly exploited in studies of colloidal interactions. Recent investigations based on con- ventional time averaged scattering have provided information on the organisation of monodisperse spherical latex particles in dispersions, both in flocs2s3 and in the irides- cent structure~~*~ which can be observed at very low electrolyte concentrations. The dynamic light scattering method affords a rapid and highly accurate measurement of the diffusion coefficient of partic1es.l It can also be used in studies of particle inter- action~,~.~ but the information is then less direct than that provided by conventional light scattering.6 Joint application of these methods is especially promising in studies of adsorbed layer effects on colloid stability.In particular, it is possible to determine the second virial coefficient of colloid particles from the time-averaged scattering behaviour, and the hydrodynamic thickness from the quasielastic behaviour.This paper describes such measurements. The system chosen was a highly monodisperse latex in the presence of polyvinyl alcohol whose adsorption had been investigated by other workers.’ During a study of the dependence of the hydrodynamic thickness on polymer concentration it became apparent that, whilst the measurement of hydro- dynamic thickness is far more reliably achieved by dynamic scattering than any other hydrodynamic method, a complex procedure involving also conventional scattering methods is essential to validate the measurement; this is described. The choice of relatively large colloid particles, comparable in size with the wave- length of light, offers the advantages of relative monodispersity and the possibility of scattering studies on dilute systems.In these, the requirement for non-interacting particles, which is essential for the measurement of layer thickness, is more easilyD . S . DUCKWORTH, A . LIPS AND E. J . STAPLES 289 met. Multiple scattering in more concentrated dispersions, however, makes difficult the characterisation of interactions of such particles in terms of, e.g., the second virial coefficient. A new low angle scattering approach is described here which largely overcomes this difficulty. THEORETICAL The quantity most easily measured by the quasielastic scattering technique, referred to as photon correlation spectroscopy, is the normalised autocorrelation function Ig'(K, z) I which for non-interacting identical particles of diffusion coefficient Do is given by4 Igl(K, z)[ cc exp(- DoK2z).(1) Here z is the correlation delay time, K(-471/A sin 8/2) is the magnitude of the scattering vector K, 3, being the wavelength of light in the dispersion medium and B the scattering angle. Recent theoretical 'p8 and experimental studies4s5 have described the effects of particle interactions on diffusional behaviour. gl(K, z) is then no longer exponential, and its initial decay with time is characterised by an effective, K-dependent diffusion coefficient Here S(K) is the well known static structure factor (= ratio of the time averaged scattering from the interacting system to that from the corresponding non-interacting system), Here g(r) is the radial distribution function (= probability of finding a pair of particles with their centres separated by a distance r), p is the particle number density and a the particle radius.H[g(r), K,p] represents the hydrodynamic interactions. The theories available for this term6 cannot readily be exploited in the context of particle aggregation which is of concern in this study. To overcome this difficulty, and to establish a simple link between quasielastic and time averaged, conventional light scattering, a simpler treatment is developed here. Weak aggregation of particles is viewed as a dimer- monomer equilibrium according to which the fractional number concentrations of dumb-bells and singlets are respectively 2 * 9 p2/p = p\ [g(r) - 1127-c r2 dr = [S(O) - 1]/2 pl/p = 1 - [S(O) - 11. It is assumed that particles in dumb-bells are touching.The time dependent scattering can now be described on the basis of the equation derived for polydisperse, non-interacting particle^.^*^^ The result is exp[-D(K)K2r) = - 1 I]" exp(-DoK2z) + BS,(K) exp(-$D,,K2r)]. (6) sm P P Weref2(K) is the ratio of the individual scattering from a dimer to that from the single290 POLYMER EFFECTS WITH COLLOIDS particle, and the reasonable assumption is made that the orientation averaged diffusion coefficient of an isolated dumb-bell is times that of the primary particles." According to Rayleigli-Gans-Debye scattering theory l2*I3 Using eqn (7), (4) and (5), a general expression for S(K) is sin 2Ka 2Ka ' S(K) = 1 + [S(O) - 11 - (7) obtained as follows is> Substituting in eqn (5), it is also straightforward to obtain the following expression for the effective diffusion constant D(K) which characterises the initial decay of the measured correlation function Igl(K,z) 1, viz : sin 2 Ka [S(Q) - 4 '1)1.D ( K ) N D 1 - 1+- .[ ( 2ir(a It is seen that one route to assessing weak aggregation effects and allowing for their presence in the interpretation of the dynamic diffusion parameter D(K) lies in the measurement of the static structure factors at low scattering angles. It is also noted that S(0) has thermodynamic significance, uiz : = 1 + 47c - l]r2 dr = S(0) where n is the osmotic pressure. For weak interactions, [g(r) - l]r2 dr can bz identified as the second virial coefficient. EXPERIMENTAL MATERIALS All chemicals were analytical grade; doubly distilled water was used throughout.The sample of polyvinyl alcohol was a commercially available sample Alcotex 88/10 of ATw = 45 000 and of percentage hydrolysis of the parent acetate of 88%. A monodisperse latex of diameter 330 nm was used. This was prepared by emulsion polymerization with sodium laurate as emulsifier and potassium persulphate as initiator. The latex concentrations were detemiined gravimetrically. QUASIELASTIC SCATTERING A Malvern photon correlator with 48 delay channels was used together with a Spectra Physics 5 mW He/Ne laser (A, = 633 nm). It was ascertained that contributions to the cor- relation function from the scattering from the polymer solutions were small in all cases except the highest concentration, when a small correction was applied.Multiple scattering can have a pronounced influence on the time-dependent scattering and it is essential to use very dilute dispersions (3 x lo8 CM"). All measurements were performed at a scattering angle of 90". The dilute latex dispersions were repeatedly filtered through prewashed 0.45 pin Millipore filters, finally directly into the scattering cell. This ensured that the effective hydrodynamic diameter of the particles as measured by the correla- tion technique was within 1 nm of the electron microscope diameter, 330 nm. Following the measurement on the bare particles, polymer solutions, prefiltered through a 0.22 pmD . s. DUCKWORTH, A . u p s AND E . J . STAPLES 29 1 Millipore filter, were added to the scattering cell. The first measurement was performed after 20 min of equilibration and the thickness was inferred from the difference in the effective Stokes radii.No time effects could be observed over a period of 24 h. The cell was thermo- statted at 25.8 rt 0.1 "C. The procedure given by Oliver l4 for optimizing the correlation measurement was closely followed. The data were subjected to a cumulant analysis;I5 in particular the initial decay of the correlation function was taken to represent the difhsion coefficient of the particles. Especially at high polymer solution concentrations, a correction is necessary for the viscosity change in bulk solution; this was measured with an Ubbelohde viscometer. LOW ANGLE METHOD The experimental set up comprises a Spectra physics 5 mW HeNe laser, a variable path- length spectrophotometer cell (of range 10 pm to lo4 pm), a circular annulus (of width 0.05 mc and radius 0.5 cm) and a photomultiplier all mounted in sequence on an optical bench.The annulus is mounted parallel to the cell and its centre coincides with the centre of the laser beam. The annulus and the large distance, -15 cm, from the spectrophotometer cell define a low scattering angle of ~ 2 ' and a narrow solid angle of collection of the scattered light from the dispersion in the cell. This light is collected behind the annulus by the photo- multiplier. The main beam through the cell is blocked off at the centre of the annulus. If the pathlength in the cell is small compared with the distance between annulus and cell, the solid angle of collection is approximately constant for any incremental volume inside the cell.Moreover, because the scattering angle is low, the particle scattering intensity per unit solid angle is largely independent of scattering angle (Rayleigh regime). These observations lead one to expect a linear behaviour of scattered intensity with cell pathlength: fig. 1 con- firms this. The approach can be exploited to obtain the structure factors of dispersions at low scattering angles S(0) from the slopes of the linear intensity against pathlength plots. pathlength Ipm 7, 1000 2000 3000 4000 pathlength l p m FIG. 1.-Dependence of low angle scattering intensity on cell pathlength. 0 = 2", latex diameter 330 nm; pH 5.8, 25 "C; A, = 633 nm. 0, p = 1.5 x 1O1O at a polyvinyl alcohol concentra- tion of 1 x kg m-2, 0, p = 1.5 x 1O'O ~ r n - ~ in absence of polymer.Insert illustrates multiple scattering for a number concentration p = 3 X 10" ~ m - ~ .292 POLYMER EFFECTS WITH COLLOIDS This is not an absolute determination of S(0) : rather the behaviour of the system is compared at fixed instrumental setting with a reference condition for which S(0) is known or can be assumed to be unity (e.g., latex at low electrolyte concentration). As only changes in intensity are important, the problem of stray light from cell windows is circumvented. To illustrate, fig. 1 shows two measurements on the same system which have different absolute values of intensity, due to differences in levels of stray light, but whose slopes are identical. The presence of multiple scattering manifests itself in a nonlinear intensity against path- length behaviour.The ability to define narrow pathlengths greatly reduces this difficulty and renders the approach applicable to concentrations approximately a factor lo3 higher than those which can be employed with conventional scattering photometers. RESULTS AND DISCUSSION Fig. 2 shows photon correlation measurements of the diffusional behaviour of polystyrene latex particles in the presence of polyvinyl alcohol. If the particles can be treated as non-interacting the results represent the hydrodynamic thickness of the adsorbed polymer layer as inferred from the difference between the Stokes radii of coated and bare latex particles. This suggested behaviour is surprising, especially when it is contrasted with the isotherin which is also shown in the figure.25 20 E a \ 15 to 1 _ / - . ,' , I I I I 10 100 0000 lO0OC 106C/kg FIG. 2.-Dependence of adsorbed layer thickness A on polymer solution concentration C. 25.8 "C, pM 5.8, 8 = 90"; latex diameter 330 nm, polyvinyl alcohol ATw = 45 000; 0, no added electrolyte, 9, in presence of sodium chloride at a concentration of mol dm-3, I, sodium chloride lo'-* mol dm-3; ---- represents corresponding adsorption isotherm measurements [ref. (7)1. Major difficulties of interpretation can arise because of possible pre-aggregation of the latex and of changes in its state of aggregation following the addition of polymer. The experimental procedure of repeated filtration ensured the virtual absence of aggregation prior to polymer addition.This was inferred from the close agreement, to within 1 nm, of the size determined by photon correlation spectroscopy and the electron microscope diameter of the particles (330 nm). The difference approach proved to be unreliable in cases of appreciable pre-aggregation and it is important, therefore, to select latices that are virtually free from aggregation.D . S . DUCKWORTH, A . LIPS AND E. J . STAPLES 293 A possible interpretation of the occurrence of the maximum in fig. 2 may be that the particles are flocculated. At the corresponding polymer solution concentration, the isotherm suggests a fractional surface coverage of 4 . 5 at which bridging floccula- tion is expected to be relatively favoured. Particle aggregation effects in principle manifest themselves in changes in S(K).However, the range of K that is accessible with commonly available scattering photometers together with the latex size employed in this study imply that 2 Ka n. In this regime the structure factor is largely insensitive to particle aggregation [eqn (S)]. Thus the observed lack of changes in S(K) on addition of polymer cannot be considered as diagnostic of a lack of aggrega- tion; the need is evident for measurements of S(K) at much lower scattering angles. Low angle scattering studies on dilute systems are difficult. The applicability of the low angle approach described here to relatively more concentrated systems, in addition to alleviating some of the experimental problems, enables the particles to be studied under conditions in which the consequences of weak interactions are more apparent.Low angle measurements of S(K) were performed in the absence of added electrolyte and at particle concentrations up to two orders of magnitude >3 x los ~ m - ~ , which was the concentration employed in the correlation measurements of particle diffusion. At the polymer concentration, 1 x kg mV2, which is close to the maximum in fig. 2, the second virial coefficient - [g(r) - 11 2zr2 dr was deter- mined to be -1.3 x 10-lo cm3 (this is subject to reservations which are discussed later). At polymer concentrations 2 3 x kg dmA3, the corresponding values are orders of magnitude smaller and cannot be measured by the technique. The implications are that, in the dilute latex dispersion, interactions are of no consequence at high polymer additions, but near the maximum in fig.2 some aggregation can be observed. According to eqn (9) this implies a 2% correction in the effective diffusion coefficient of coated particles near the maximum and a consequent decrease in layer thickness of -3 nm. Though tending to decrease the height of the maximum, the above correction cannot remove it altogether ; other experimental factors lead one to question whether the unexpected behaviour in fig. 2 is solely attributable to aggregation. First it should be noted that there was a delay of several months between the photon correlation measurements and the low angle studies. Over that period the latex had undergone considerable aggregation. Moreover, it had also become far less stable to electrolyte addition both in the presence and absence of polymer.To illustrate, some of the results in fig. 2 near the maximum are for different electrolyte concentrations and indicate that the diffusion coefficient in the earlier study was independent of salt concentration. Subsequently, however, the latex displayed substantial flocculation in the presence of electrolyte under corresponding conditions. In view of the well established sensitivity of bridging flocculation to the degree of double layer screening, the above observations argue strongly against significant polymer-bridging-induced aggregation of the latex in its original state especially at low electrolyte concentrations. A further argument against aggregation in the earlier study stems from a detailed analysis of the decay of the correlation function Igl(K,z) I.The method of cumulants was followed; 15~10 the first cumulant Kl yields D(K)(initial decay), the second cumulant K2 describes the deviation from exponentiality of g'(K,z). The latter is also an indica- tion of particle interactions.6 It was found that K2 was very small in all cases of un- coated particles, indicating insignificant pre-aggregation ; moreover, no change could be detected on addition of polymer. Judged thus on a number of criteria, the unexpected behaviour in fig. 2 is not as readily attributable to particle aggregation as might have been supposed. Though I294 POLYMER EFFECTS WITH COLLOIDS further work with a fresh unaggregated latex is in progress, it is instructive to comment on the suggested behaviour at this stage.There is little ambiguity about the measurements at high polymer solution concen- tration. The thickness corresponding to the minimum position is 16 nm. This value is lower than that reported by Garvey et aZ.,9 nevertheless, it reinforces their general observations that the volume per molecule on the surface is substantially the same as that in bulk solution and that the polymer coils are elongated in the direction normal to the interface. The equivalent sphere radius of the volume per polymer molecule in the adsorbed layer is 4.9 nm, which is close to the hydrodynamic radius, 5.2 nm, of the free polymer molecule. Expression (10) is a statement of the equality of chemical potential changes of polymer molecules in bulk solution d,ub with those on the surface dpS: It is assumed that the solution concentration C of polymer is sufficiently low to enable dpb to be represented by the ideal gas expression (1.h.s.).The first three terms on the r.h.s. constitute the Flory-Huggins expression, where yp is the volume fraction of polymer in the assumed homogeneous surface phase. x is the well known parameter which describes the quality of the solvent, rn is the number of lattice sites which the polymer molecule is capable of occupying (=lo3). It is supposed that beyond a solution concentration 6 x kg dm-3 (maximum in fig. 2) all available surface sites are covered. The fractional coverage per adsorbed polymer molecule then varies as l/r, where l? is the amount adsorbed per unit area.Correspondingly, the contribu- tion from segment attachment to the chemical potential is represented by the term BIT, where B is a positive constant. It is straightforward to show from considerations of partial specific volumes that y, N 7.5 r/A, where r is expressed in units of mg m-2 and the thickness A in nm. If the isotherm in fig. 2 (broken line) is used to define yp, the application of eqn (10) to the region of solution concentration, 6 x to 4 x lo-" kg dm-3, requires x to be >0.52 and, therefore, to be close to phase separation on the surface. The amount by which x is required to exceed 0.52 depends primarily on the segment attachment term B/yp. As the experimental value for x is ~0.47,' and as the polymer at high coverage displays good stabilising qualities, which is suggesting x to be <+, the above inference argues against the behaviour suggested in fig.2. kg m-2 instead of at -3.7 x kg dm--3 as required by the isotherm. The segment attachment term B / r then remains constant and does not have to be considered over the range of solution concentration, 6 x to 4 x kg m-2. Eqn (10) is then satisfied with a value of x -0.48. This calculation shows that the observation of a negative slope in fig. 1 could, in principle, be supported thermodynamically for cases of polymer systems close to a &condition. It follows that, to employ such a simple interpretation here, one requires to postulate more favourable adsorption conditions in the diffusion experiments than in the adsorption isotherm studies to which reference was made. Let us suppose that the onset of plateau adsorption occurred at 6 x Photon Correlation and Light-Beating Spectroscopy, ed. H. Z . Cummins and E. R. Pike (Plenum, New York, 1974). * D. Giles and A. Lips, J.C.S. Faraday I, 1978,74, 733. W. A. House, J.C.S. Faraday I, 1978,74, 1045, 1 112. J. C. Brown, P. N. Pusey, J. W. Goodwin and R. H. Ottewill, J. Phys. A, Math. Gerz., 1975,8, 664.D . S . DUCKWORTH, A . LIPS AND E . J . STAPLES 295 D. W. Schaefer, J. Chem. Phys., 1977,66, 3980. M. J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1974, 49, 57. P. N. Pusey, J . Phys. A, Math. Gen. ,1975,8, 1433. T. L. Hill, Introduction to Statistical Mechanics (Addison-Wesley, Massachusetts, 1969), chap. 15. lo P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero and S. H. Koenig, Biochem., 1974,13,952. l1 F. Perrin, J. Phys. Radium, 1934, 5, 497. l2 M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, New l3 A. Lips and E. Willis, J.C.S. Faraday I, 1973,69, 1226. l4 C. J. Oliver, in ref. (l), pp. 151 to 223. ti B. J. Ackerson, J. Chem. Phys., 1976,64,242. York, 1969). D. E. Koppel, J. Chein. Phys., 1972, 57, 4814.