摘要:

Magnetic Birefringence as a Tool for Determining Adsorbed Polymer Layer Thiclcnesses BY P. C . SCHOLTEN Philips Research Laboratories, Eindhoven, The Netherlands Received 4th January, 1978 Suspensions of small elongated magnetic particles show birefringence when subjected to a magnetic field. The decay of the birefringence upon removal of the field is used to obtain the rotational dif- fusion coefficient of the particles, which in turn reveals the hydrodynamic thickness of an adsorbed polymer layer. Results are given for gelatin in water and for cellulose nitrate and a few other polymers in organic solvents. With ax. magnetic fields, polymer layer thicknesses can be observed continuously. Suspensions of magnetic particles often become birefringent when placed in a magnetic fie1d.l In older literature this effect is known as the Majorana phenomenon. It is due to the orientation of the particles by the field; if the particles are rod or disc shaped, or optically anisotropic, orientation makes the suspension as a whole aniso- tropic.As in the case of the analogous electro-optical Kerr effect, the dynamic response (transient, as.) depends on the hydrodynamic friction the particles experience when rotating in the liquid, and hence on their size. As early as 19 10 Corbino tried to use the response to a pulsed magnetic field for determining the size of the particles in a suspension. The hydrodynamic friction depends on the outer dimensions of the particle, including an adsorbed polymer layer. If we know the dimensions of the bare particle from electron micrographs, the difference should be the thickness of the polymer layer.The easiest to interpret is the decay of the birefringence upon removal of the magnetic field. Its time constant depends in a simple way on the friction coefficient. The interpretation of the latter in terms of particle dimensions is rather difficult as friction coefficients for laths, beams, cylinders and discs are generally not known. Another possibility is to use an a.c. magnetic field. Here the amplitude of the a.c. birefringence signal is an indicator of the hydrodynamic friction coefficient. The relation is rather complicated, but this method has the advantage that one can measure continuously. We used the a.c. method with charge-stabilized aqueous suspensions, which were mixed with polymer solution in a stopped-flow cell.In this way the adsorption process could be followed from about 0.2 s after mixing. The particles we worked with were rectangular bars or laths, with a permanent magnetic dipole along their longitudinal axis. THEORETICAL BIREFRINGENCE AND ITS RELAXATION Most of the theory involved in magnetic birefringence has already been developed for the Kerr effect and can be found in the classical paper by Benoit3 or in the review by Stoy10v.~P . C . SCHOLTEN 243 When a suspension of acicular particles with a magnetic dipole moment m along their longitudinal axis is oriented by a magnetic field of strength H, the difference in refractive indices for light polarized parallel and perpendicular to the field is 2ncv n o An = n, - n, = - (gl - g2) [ 1 - g(coth P - ;I].Here no is the refractive index of the medium, c is the number of particles per unit volume, z, is the particle volume, and g, and g2 are the optical polarizabilities (per unit volume) of the particles in longitudinal and perpendicular directions, respectively. The term in square brackets, with P = mH/kT, deals with the (partial) orientation of the particles. It approaches unity for P - co. The polarizability term g , - g , is known in explicit form only for If the axial ratio p = Z/d is larger than about 10, (and the particle length 2 is small compared with the wavelength A of the light) it approaches (2) 1 g1 - g2 = & (n2 - n32/b2 3- nil, n being the refractive index of the (isotropic) particle material.Upon removal of the orienting field, the particles begin to diffuse out over all possible directions. This process and the accompanying decay in the birefringence was treated by Benoit and his surprisingly simple result was confirmed by O'Konski and by Ridgeway.6 Regardless of the initial distribution, Ant = Ano exp(-6Dt), (3) where D is the diffusion coefficient for rotation around a short axis (more general: perpendicular to the orientation axis). For ax. fields, the relation between diffusion coefficient and birefringence signal is rather c0mplex,7-~ especially with our particles which have, besides a per- manent magnetic moment, a polarizability and the possibility of switching their magnetization.1° For low field amplitudes and high frequencies, however, the a.c.component of the birefringence should be proportional to (D/o)2. This was checked by varying the frequency at constant field amplitude. Over the range we worked in, the a.c. signal was proportional to co-l? Changes in the diffusion coefficient can thus be deduced from changes in the ax. birefringence signal. ROTARY DIFFUSION COEFFICIENT For the rotary diffusion around a short axis of prolate ellipsoids of revolution in a medium with viscosity q, Gansll derived 3kT = a y r m with P4 2P2- 1 q+ (P2- "">1. N P ) = 3 p4 - - 1 [- 1 + 2p(p2 - 1)" - (p2 - 1)* (4) Broersma l2 carried out some approximate calculations and also a few model experi- ments on the friction of cylinders rotating around a short axis. His results are summarized in the expression S(p) = In 2p - 1.57 + 7(1/ln 2p - 0.28),, (6)244 MAGNETIC BIREFRINGENCE which takes the place of R(p) in eqn (4).Eqn (6) was intended for p > 4. To make an extrapolation into the lower range of p-values, we plotted eqn (6) and Broersma’s experimental points as S(p)/R(p) against log p , see fig. 1. In this plot the experimental points lie close to a straight line, corresponding to S(p) = RCp)(0.429 + 0.049 lnp). (7) 1 I 1 I I 1 1 1 1 1 I 1 I I I I I I 1 10 100 P FIG. 1 .-Dependence upon axial ratio of friction factor S for cylinders. + , Broersma’s experiments; A, sphere with the same volume as the cylinder with I = d; 0, circumscribed sphere. This line also gives a very reasonable value of S for p = 1, i.e., 0.143. This is between the values for a circumscribed sphere (0.1 18) and for a sphere with the same volume as the cylinder with I = d (0.222).Therefore, we consider eqn (7) to be a reasonable approximation in the range 1 < p < 10. Our particles, however, are not cylinders, but rectangular bars (or laths). The width we measure in electron micrographs is an average projection. We assumed that this projection is close to an effective cylinder diameter, and applied eqn (7) to calculate the diffusion coefficient of the bare particles. A layer of polymer around a particle not only affects length and thickness, but also the shape. The sharp edges which contribute much to the friction are rounded off. For particles with a thick adsorption layer we therefore calculated D for an ellipsoid with the same volume and axial ratio as the covered particle, see fig.2. (The FIG. 2.-Polymer-covered particle - and its ellipsoidal substitute - - - -. polymer layer was assumed to have a constant thickness, even at the edges). With thin polymer layers, a gradual transition from the cylinder to the ellipsoid model was made. The resulting dependence of the relaxation time z = 1/60 upon the thickness of the adsorbed layer 6 is plotted in fig. 3. POLYDISPERSITY As can be seen from the electron micrographs in fig. 4, our particles are hetero- disperse. Lengths as well as thicknesses were found to be log-normally distributed.100 nm 100 nm suspension E suspension F FIG. 4.-Electron micrographs of particles. [To face page 245P . C. SCHOLTEN 245 n x t-" 1 2 6 1 d FIG. 3.-Dependence of relaxation time upon polymer layer thickness, Thus, for example, the fraction of the material in particles with length I is where L is the geometric mean length and cr the geometric standard deviation.The observed birefringence is the sum of the contributions of all particle size fractions. For a point on the decay curve, starting from complete orientation at t = 0, the bire- fringence is co An, = Ano/o P(v) exp(-6Dt) d In v. (9) If we assume all particles to have the same axial ratio p , D is proportional to k3, i.e., to v-? In many samples, the particles have a more or less equal thickness and vary in length. In a very crude first approximation S is proportional to p , hence in this 1 0.8 0.6 0.2 0 1 t 17 2 FIG. S,-Theoretical birefringence decay curves: (a) D cc r2, Q = 2.5.(b) D cc u-*, Q = 1.5 (c) D cc u-l, ~7 = 1.5. (a) Q = 1 (monodisperse).246 MAGNETIC BIREFRINGENCE case D cc k2 or D cx r2. Using these dependencies of D on v, and neglecting in the second case the dependence of the polarizability on shape, we calculated numerically a number of decay curves for various distribution widths. A few examples are shown in fig. 5. It turned out that for a given geometric mean volume, all curves pass through practically the same point at AnJAn, = 0.45, t/z = 0.8, regardless of the value of cr or the power of v assumed in D. (For other than the geometric average this is not true.) Obviously this point on the decay curve is the most suitable one for a single point measurement; it yields the value of z corresponding to the geometric mean size.Two factors in eqn (1) cause the contributions of particles to the birefringence to be less than proportional to their volume as assumed above. One is the optical factor g, - g2, which depends on the axial ratio p . The other is the orientation factor, depending on the dipole moment rn = vJ (J being the magnetization). Both factors were taken into account in the calculation of the effective average particle sizes from the dimensions measured on electron micrographs. EXPERIMENTAL SUSPENSIONS Needleshaped magnetic particles of gamma ferric oxide, chromium dioxide (and Fe) of about 50 x 250 nm are produced in large quantities for use in magnetic recording tape. Particles of this size have such large magnetic dipole moments that it is impossible to make stable suspensions with them.Most samples, however, contain minor quantities of par- ticles that are sufficiently small to be stabilized, i.e., with thicknesses less than about 20 nm. Their dispersibility was used to isolate them. Standard procedure was to put 2 g of magnetic powder, 40 cm3 of solvent containing a dispersant, and 100 cm3 of 3 mm nylon balls in a 200 cm3 glass bottle. The bottles were shaken for 24 h in a vibratory mill to break up sintered aggregates. The balls were then removed, 160 cm3 of dispersion medium was added and the suspension was stirred for a few minutes with a high-speed stirrer (Ultra- turrax). In hours or days, depending on the dispersant used, the large particles aggregated and sedimented, leaving behind a dilute suspension of small particles - lo9 % by wt).Their size range depended upon the dispersing agent used. The experiments were done with a y-Fez03 doped with 3 atom % of cobalt. DISPERSANTS The polymers were technical products, and were used without modification. Solvents were analytical grade. NC: nitrocellulose, 12% N, type E1440, Wolff Wdsrode. EAB: cellulose (acetate 13%, butyrate 3773, EAB 3814, Kodak. PF: poly(vinylformal82%, -acetate 12%, -alcohol 5.579, Pioloform F, Wacker Chemie. PHS: poly(l2-hydroxystearic acid), M, M 1750, by courtesy of D. J. Walbridge, I.C.I. Gelatin: laboratory grade, Baker. Sodium arabinate: gum arabic, purified by repeated precipitation with NaCl and ethan01.l~ The aqueous suspension F was stabilized with a linear polyphosphate (sodium hexameta- phosphate, Merck), which was assumed to adsorb flat.It gave the particles anegative charge. Gelatin and sodium arabinate were not used in the dispersion process, but were added later to suspension F. OPTICS The optical arrangement, shown schematically in fig. 6, was standard. A 55 mW He-Ne laser L ( A = 632.8 nm) provided a narrow light beam that passed through a Glan-Thomson prism P, a cuvette with suspension C, a strained glass plate G, a second Glan-Thomson prismP. C . SCHOLTEN 247 r'F- P FIG. 6.-Optical arrangement. A and finally fell on a photosensitive silicon diode D. Polariser and analyser were crossed and at an angle of 45" with the orienting field. Under these conditions the light intensity falling on the diode is r = 1" sin2(p,/2 4 p,l2) (1 0) where I" is the light intensity for A//P, pe the retardation due to the glass plate and ps that due to the suspension.The latter is ps = 47rs(n, - n,)/d (1 1) where s is the optical path length of the cuvette. The adjustable phase shift of the glass plate increased the sensitivity for low signal levels; it was set at about 0.15 rad. An opera- tional amplifier transformed the high impedance diode current into a low impedance signal of the order of 1 V, which was fed to a voltmeter and a storage oscilloscope. CUVETTES The cuvettes had a width of 1.75 mrn and an optical path length of 10 mm. The one used in decay time measurements was suspended between two thermostatted walls, leaving air gaps of 30 pm; see fig. 7. The stopped-flow cuvette had similar thermostatted walls but no air gaps. A cross-section perpendicular to the magnetic field is given in fig.8, together with a diagram of the flow system. Suspension and polymer solution were stored in vessels S and P, under about 0.5 atm of air pressure. Two electromagnetic valves V controlled the flows of w25 cm3 rnin-l each. The tubing between valves and cuvette, and the labyrinths before the mixing chamber, were thermostatted. * I /' FIG. 7.-Magnet with cell for relaxation experiments. For clarity, the thicknesses of cuvette 1 and thermostatted mantle 2 have been exaggerated by a factor of 2; 3: light beam; 4: magnet core; 5: d.c. field magnets; 6 : coiIs.248 MAGNETIC BIREFRINGENCE r------ I I I I I I L,,,,,- ................. I ------ FIG. 8.-Stopped flow cell.Dotted line: light beam; dashed: outline of thermostatted part; stippled : magnetic field. THE MAGNET The magnetic field was provided by a Weiss-type electromagnet, illustrated in fig. 7. The yoke was a ferrite transformer core with a 10 x 13 mm cross-section and carried a 60 turns Litze wire coil at each side of the 5 mm gap. Switching a magnet off is even more difficult than switching it on. Therefore, we used two ferrite magnets attached to the outside of the yoke. They provided a constant field of 1.3 x lo4 A m-l, which was compensated completely when the coil was energized. Fig. 9 shows the electrical diagram. Upon the 2.2nF M FIG. 9.-Magnet circuit. B closing of mercury relay R, the condenser C , charged to about 600 V by power supply A, was discharged through the magnet coil M.In 2.5 ps the current reached its peak value. At that moment the voltage at P had come down to about zero, diode D began to conduct and power supply B took over to provide the steady current. For the stopped-flow measurements, the magnet was connected to a 21 kHz power source (generator + amplifier) through a 47 nF series capacitor. The field amplitude was lo4 A m-l. The 42 kHz a.c. term in the birefringence signal was amplified, rectified and fed to a recorder (full scale response time 0.25 s). MEASUREMENTS AND INTERPRETATION The suspensions were diluted to give a phase shift of about 0.09 rad in the field of 1.3 x lo4 A m-l provided by the permanent magnets. The oscilloscope was triggered by the magnet current (current on = field off).We measured the time the birefringence signal ( I ) needed to travel 60% of its sweep from initial (H = 1.3 x lo4 A m-l) to final (H = 0) value. This corresponded to An,/Ano z 0.45. The observed time and the initial and final values of I read from the voltmeter were then used to calculate the relaxation time zeXp. With very short relaxation times the initial linear part of the decay curve was extrapolated to the Ano level to find the correct start of the decay. This was 1.9 - 2 ps after the trigger signal. Suspension viscosities were determined in Ubbelodhe viscometers. All measurements were done at 25 rrt 0.1 "C, except for those with gelatin, which were done at 40 & 0.2 "C.P. C . SCHOLTEN 249 Particle sizes were determined from electron micrographs.Lengths and widths of 100- 200 particles were measured. The thicknesses were assumed to be equal to the widths. The weight factor used in determining the geometric average values of I and d was the product of: (1) the particle volume ld2; (2) the polarizability factor g , - g,, calculated with the formula for ellipsoids (with axial ratio Z/d) and (3) the orientation factor 1 - 3 (coth P - l/P)/P, J being measured on a sample of the (coarser) bulk powder (0.4 Wb m-". The average values of Z and d were used to calculate Tcore. After this, we proceeded as though dealing with " average " particles only. With the aid of fig. 3 and some trial calculations, the quotient z ~ ~ ~ / z ~ ~ ~ ~ was translated into a relative thickness 6/d. Multiplication by d,, then gave the polymer thickness 6.RESULTS RELAXATION EXPERIMENTS Table 1 lists the results of a series of decay time measurements. With the aqueous suspension F, we were able to check z,,,, experimentally before the polymer was added. The agreement was reasonable: z,,,,/z,,,, = 1.2, corresponding to a 1.6 nm error in d. (The experimental value of z,,,, was used in calculating the gelatin layer thickness.) A second check was provided by the PHS-stabilized suspension E. With similar PHS (M, % 2000) on Ti02, also in xylene, Doroszkowski et aZ.14 found 6 = 8.0 TABLE 1 .-RELAXATION I?XPERIMENTS. exp. solvent polymer polymer conc. r /(g/lOO cm3) IN s m-2 A isoamyl- acetate B isoamyl- acetate C dioxan D anisol E xylene F water G water NC M 0" 81 x 10-5 NC *Ob 81 x 10-5 PHS 0.63 61 x 10-5 I I 89 x 10-5 PF 0.77 189 x EAB 0.77 148 x 10" gelatin" 0.1 68 x 75 75 90 74 49 93 93 21.4 19.2 17.0 14.3 13.5 14.7 14.7 18.5 237 16.6 129 54.3 725 23.9 211 3.76 9.9 24.8 29.5 21.4d 93 6 /nm 38 27 42 27 7 (1 -6) 19 a stored at 0.2% NC, diluted to % before measurement, stored at w % NC, experiment at 40 "C, pH 6.3,lO" mol dm-3 KCI, =rexP from F, corrected for the change in q and T.nm by a viscometric technique. Barsted et a1.,l5 using a graft copolymer with PHS side chains (M, = 1600) on a latex in aliphatic hydrocarbon, again viscometrically, obtained 6.2 nm. The values obtained for the other polymers are quite large. The reason probably lies in our selection procedure : we searched for polymer-solvent combinations that could stabilize large magnetic particles. The accuracy obtained is affected by several factors.The particle size is less important than one might expect. Especially when the coating is thick, the particle is merely the nucleus of a large polymer coil. In experiment A, for example, changes of 10% (the estimated accuracy) in the average length and thickness change the resulting value of 6 by only 2 and 0.5 nm, respectively. The uncertainty in the friction factor S has consequences only for bare and thinly covered particles. Where 6 is of the order of d, the ellipsoidal model is probably a good approximation. (The friction factor of the core drops out of the calculation of 6.) The estimated accuracies of z,,,, and are 5 and 1%, respectively.250 MAGNETIC BIREFRINGENCE A more serious source of error is aggregation, which would simulate too large Its occurrence, however, is revealed by a non-steady birefringence value thicknesses.at constant magnetic field, and by a trailing decay curve. STOPPED-FLOW EXPERIMENTS Fig. 10 shows some records of a.c. signal amplitude against time; we did not convert the amplitudes to layer thicknesses. The suspension was metaphosphate stabilized y-Fe,O, sol F. Trace (a) was a check, with just water in the second 0 20 40 t l s FIG. 10.-Stopped flow experiments; (a) water; (b) gelatin, final conc. 0.1%, pH 6.3, 40 "C. (c) sodium arabinate, final conc. 0.1%, pH 9,25 "C; ( d ) sodium arabinate, final conc. 0.01 % ,pH 9,25 "C. channel. While the valves were open, the signal was erratic because of the turbulence in the cell. The small dip after the closing was due to a slight temperature difference between cell and incoming liquid (thermal stress in the cell windows changing the d.c.birefringence). Trace (b) was obtained with gelatin ; the final concentrations were as in the relaxation experiment G. The reaction was so fast that even while the liquid was flowing, the t =I: 0 level (as with water in the second channel) was not reached. As the average residence time in the measuring cell was about 40 ms, the relaxation time of the reaction should be of that order of magnitude or less. Only the tail of the reaction curve appears on the recording; a final steady value was reached in about 5 s. Diffusion is probably the limiting process. With sodium arabinate at pH 9 [traces (c) and (d)] the reaction was much slower and appeared to be more complex.A final steady value was reached only after about 20 min. We suspect that here the adsorption reaction is followed by a rearrangement of the adsorbed molecules to make room for more. CONCLUSION Although not generally applicable, with magnetic particles magnetic birefringence proves to be a useful tool for studying adsorbed as well as adsorbing polymers. InP. C . SCHOLTEN 25 1 particular it allows changes in the adsorbed polymer layer, e.g., with time, solvent composition, pH or electrolyte concentration, to be followed easily and accurately. Because of the uncertainty in the friction factor and the variation in particle size the value of thickness itself is less accurate; we estimate 1-3 nm. Minute amounts of very dilute suspensions are needed: only lo-' g of powder and a fraction of that in polymer are present in the light beam. The author acknowledges the help of Mr. J. M. A. Nevelsteen, who did most of the exploratory measurements and sample preparations. He is also indebted to Mr. D. J. Walbridge for the polyhydroxystearic acid. Q. Majorana, Phys. Z., 1902, 4, 145. M. Corbino, Phys. Z., 1910, 11, 756. H. Benoit, Ann. Physique, 1951,6, 561. S . Stoylov, Adv. Colloid Interface Sci., 1971,3,45. C. T. O'Konski, K. Yoshioka and W. Orttung, J. Phys. Chem., 1959,63, 1558. D. Ridgeway, J. Amer. Chem. Soc., 1966,88, 1104. A. Peterlin and H. A. Stuart, Hand icnd Jahrbuch der Chem. Phys. (Akad. Verlagsg., Leipzig, 1943), vol. 8, part 1B. G. B. Thurston and D. I. Bowling, J. Colloid Interface Sci., 1969, 30, 34. * H. H. Kas and R. Briickner, 2. Angew. Phys., 1969,26, 368. lo P. C. Scholten, I.E.E.E. Trans. Mugn., 1975, 11, 1400. l1 R. Gans, Ann. Phys., 1928, 86, 628. l3 H. G. Bungenberg de Jong and P. van der Linde, Biochem. Z., 1933,262, 161. l4 A. Doroszkowski and R. Lambourne, J. Colloid Interface Sci., 1968,26,214. l5 S . J. Barsted, L. J. Nowakowska, I. Wagstaff and D. J. Walbridge, Trans. Faraday SOC., 1971, S. B. Broersma, J. Chem. Phys., 1960, 32, 1626. 67, 3598.

ISSN:0301-7249    

DOI:10.1039/DC9786500242

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Effect of Molecular Architecture of Long Chain Fatty Acids on the Dispersion Properties of Titanium Dioxide in Non-aqueous Liquids BY ANDREW DOROSZKOWSKI AND RONALD LAMBOURNE ICI Paints Division, Wexham Road, Slough, Berks Received 23rd November, 1977 The effect of varying chain length and chain branching on the adsorbed layer thickness of oligo- esters on titania in non-aqueous solvents has been studied and related to the degree of flocculation of the dispersions using viscometry. The oligoesters were a series of monodisperse condensates of 1Zhydroxystearic acid, up to the pentamer. Also, a series of branched esters in which the degree of branching was varied systematically was studied. The latter consisted of the valeric esters of mono-, di- and tri-hydroxystearic acid. It was found that the thickness of the adsorbed layer was not necessarily the criterion for good dispersion stability, but a complex function of surface concentration.This was dependent on main chain length, the size, position and number of branches and the solvency of the medium. The stabilisation of colloidal particles in non-aqueous media has received consider- able attention in recent years. It appears now to be generally accepted that stabilisa- tion in media of low dielectric constant is due to steric considerations involving loss of entropy and/or enthalpy and not to charge repu1sion1p2 except possibly for extremely dilute dispersions. There have been many theoretical publications on steric stabilisa- tion by adsorbed polymers, including statistical approaches, e.g., " loopy " adsorption and involving Flory-type thermodynamic considerations. These all depend on (segment density distribution, distance) calculations. These segment density distri- butions are obtained with difficulty theoretically and are inaccessible to physical measurement, at least for the present. Steric stabilisation, on the other hand, may be more simply studied by the use of simple fatty acids which offer the practical solution of known geometry and are, therefore, amenable to configurational considerations ; but they cannot be considered as polymers in lattice-type calculations.Rehbinder first studied the dispersion properties conferred by the adsorption of fatty acids in non-aqueous media. Ottewill and Tiffany4 also studied the adsorption properties of naturally occurring fatty acids.In this work we have made use of the ester linkage afforded by esterification of hydroxy fatty acids to construct in a controlled manner different species with various degrees of branching at constant chain length (extensibility), and attempted to relate structure to dispersion stability. Additionally we have kept the degree of branching constant and altered the extensibility (chain length). The latter has enabled the further appraisal of viscometric methods for determining the thickness of adsorbed layers on small particles.A. DOROSZKOWSKI AND R . LAMBOURNE 253 EXPERIMENTAL MATERIALS Stearic acid, '' Specially Pure ", (ex B.D.H.) m.p. 70 - 72 "C was used as received. 2- Hydroxypalmitic acid (ex Koch-Light) m.p.84-86 "C was used as received. PREPARATION OF HYDROXY ACIDS 1 2-Hydroxystearic acid was purified from commercial grade material (ex Prices, Bromborough) containing about 8.7% stearic and 0.9% palmitic acid. The methyl ester was prepared and recrystallised three times from petroleum ether (B.P. 100 - 120 "C). It was saponified, acidified and washed with distilled water, collected and stored in a vacuum dessicator over silica gel till required. The product (m.p. 82-83 "C) was analysed for OH value and purity was assessed by t.l.c., which showed the elimination of impurities. 9,lO-Dihydroxystearic acid was prepared from oleic acid (ex Hopkin and Williams) by the method described by Swern et al. ; the product had a m.p. 92 - 93 "C. 9,10,12-Trihydroxystearic acid was prepared from ricinoleic acid (reagent grade) by first acetylating the hydroxyl group.The double bond was then hydroxylated as described in the preparation of dihydroxystearic acid. The product was a white waxy solid, m.p. 105- 107 "C. ACID CHLORIDES Valeryl chloride was prepared from valeric acid (Puriss grade ex Koch-Light) using thionyl chloride as described by V0ge1.~ Stearoyl chloride was prepared from stearic acid using phosphorus trichloride as described by Young et alas Acid chlorides of 12-octadecanoyloxyoctadecanoic acid (dimer), trimer etc. were prepared from the corresponding dimer fatty acid using the same method as for stearoyl chloride. An alternative, simpler method using oxalyl chloride was also employed, which involved refluxing with the appropriate fatty acid and distilling off excess oxalyl chloride, leaving the acid chloride.(cf. Thionylchloride which produced black tars.) OLIGOESTERS The oligoesters were all prepared by condensing the appropriate acid chloride with the hydroxy fatty acid by heating the components at 120-130 "C and removing hydrogen chloride under reduced pressure. The oligoesters made with valeryl chloride were prepared by heating the appropriate reagents in the presence of lutidine. The reaction product was washed with dilute hydrochloric acid, water and then dried. Finally it was passed through a silica gel column to remove impurities. Purity was assessed by t.1.c. in the usual manner. Number average (M,) molecular weights were determined using a Mechrolab Vapour-phase Osmometer.Acid contents were determined by titration using alcoholic potassium hydroxide solution. The 16-mer oligoester was obtained by fractional precipitation of a 13% w/w solution of " poly (12 hydroxystearic acid) ", prepared as described by Walbridge9 in butyl cellosolve, using distilled water as precipitant. The turbid solution was warmed to clarity and allowed to reprecipitate slowly in a thermostatted water bath. The fraction collected accounted for about 9% of the polyhydroxystearic acid and had an M, of 4500, corresponding to the 16- mer hydroxystearic acid. SOLVENTS All solvents used were AnalaR grade except for the aliphatic hydrocarbon (white spirit 100) which was a petroleum fraction of low aromatic content having a boiling range 179- 200 "C.254 OLIGOESTER CHAIN EFFECTS ON TiO, DISPERSIONS PIGMENTS All dispersions were made from commercial grade titania which had been surface treated with SO2, A1203 etc., and was similar to that used by Crow1 and Malati;l* the B.E.T.nitrogen adsorption surface area was 13.4 m2 g-l. The surface area computed from electron micrographs at x 20 000 magnification was found to be 11 m2 g-l. METHODS Adsorption experiments were made with titania dried at 100 "C. The titania with the fatty acid solution was placed in glass jars together with I?' glass beads. The jars were continuously rotated on rollers for at least 24 h. The continuous phase was obtained by centrifugation of the dispersion and analysed for fatty acid content by simple titration with potassium hydroxide solution.Preparation of Dispersion for viscosity measurements. Dispersions were prepared by milling 200 g of titanium dioxide with 250 cm3 of dispersion solution in a + gallon stone jar with 500 g of r' steatite balls for 24 h. The suspensions so prepared were strained off and 5 cm3 pipetted samples were ashed in a muflle furnace at 500 "C to obtain accurate disperse phase volumes. The dispersions were diluted with the appropriate solution where required to obtain lower concentrations. VISCOMETRY The viscosities of the dispersions were measured on a Weissenberg rheogoniometer, fitted with a 5 cm diameter, 3" cone and plate; housed in a 25 "C constant temperature room. The thickness of the oligoester fatty acid layer adsorbed on the titanium dioxide was deter- mined by measuring viscosities at a number of shear rates ranging from 380 to 4776 s-I and extrapolating to infinite shear rate in order to eliminate the effects of flocculation.The application of an empirical equation relating dispersion viscosity at infinite shear rate with continuous phase viscosity and disperse phase volume (DPV) enabled the calculation of layer thickness from the increase in hydrodynamic volume due to the adsorbed layer.5 The results of these measurements are presented in table 2. The dispersion stability of the oligoester fatty acids was assessed in the manner of Asbeck and Van Loo,ll and as used by us previo~sly,~ by plotting log (viscosity) against the reciprocal square root of shear rate as in fig. 1. The gradients of these graphs were used as a measure of flocculation and termed the " flocculation factors ", (see table 6).The smallest gradient indicates the least flocculation of the dispersion. The assessment of flocculation, as measured by the divergence from Newtonian behaviour, is disperse phase concentration dependent (fig, 2) and was, therefore, only made at similar disperse phase concentrations. RESULTS Fig. 1 shows that Ti02 particles, dispersed in a solution of the monovalerate of 12-hydroxystearic acid in aliphatic hydrocarbon are less flocculated than in the equivalent trivalerate solution, which in turn produces a better dispersion than in the equivalent divalerate solution. The most flocculated dispersion being that made using stearic acid as dispersant. The effect on dispersion stability and '' barrier thickness " with increasing chain length are shown in fig.2. Fig. 3 shows the effect of solvency on dispersions stabilised with " dimer " hydroxystearic acid. The adsorption isotherms for the various oligoester fatty acids are presented in fig. 5 and 6 . The Catalin version of H. A. Stuart's molecular models was used to construct models of the oligoester fatty acids from which their projected areas were measured in various orientations. In the case of the dimer, trimer, etc., the projected area in the normal orientation is taken to be that of the shorter chained monovalerate, divalerate analogue. The minimum areas quoted in table 1 were obtained by rotatingA . bOROSZKOWSK1 AND R. LAMBOURNE 255 I 1 .I-I 0.01 0.03 0.0 5 0-45 3 F~G. 1 .-Titania dispersed at high DPV (16.5%) and constant layer thickness in aliphatic hydrocarbon. Titania dispersed with: XII, stearic acid; XI, valerate of 2-hydroxypalmitic acid; 111, divalerate of 9,lO-dihydroxystearic acid; IV, trivalerate 9,10,12-trihydroxystearic acid; 11, valerate of 12-hydroxy- stearic acid.FIG. 2.-Log q against 0-3 plots of titania dispersed with varying chain length oligoesters in aliphatic hydrocarbon (note effect of DFV on flocculation in 2 and 5 dispersions). Titania dispersed with: 1, 16-mer hydroxystearic acid; l’, continuous phase of 1; 2, trimer at high DPV; 3, dimer at low DPV; 4, pentamer at low DPV; 5, trimer at low DPV. (Corresponding numbers “ prime ” refer to continuous phases.)256 OLIGOESTER CHAIN EFFECTS ON TiO, DISPERSIONS 0.01 0.03 0.05 L d l s 5 FIG.3.-Log q against 0-3 plots of titania dispsersed with dimer hydroxystearic acid in different solvents but at the same DPV. Titania dispersed with dimer hydroxy stearic acid in: (A), aliphatic hydrocarbon; (I?), n-butyl acetate; (C), xylol; and (a), (b), and (c) in corresponding continuous phases. 6 r 5 C 4 3 2 L--I_____L-, 0.01 0.03 0.05 &, + FIG. 4.-Log t j against D-4. plots of titania dispersed with dimer, acetate of 12-hydroxystearic acid and oleic acid in aliphatic hydrocarbon at similar DPVs. Titania dispersed in aliphatic hydrocarbon using: (A), dimer 12-hydroxystearic acid (16.5% DPV); (B), acetate of 12-hydroxystearic acid (15% DPV); (C), oleic acid (15% DPV).A . DOROSZKOWSKI A N D R . LAMBOURNE 257 TABLE 1 .<OMPARISON OF MOLECULAR AREAS OBTAINED FROM MODELS AND EXPERIMENTALLY DETERMINED MOLECULAR AREAS USING ADSORPTION ISOTHERMS.molecular areas from molecular area from models/A2 adsorption isotherm/A2 minimum inter- compound cross- mediate aliphatic reference section configur- molecule hydro- butyl no. adsorbate area ation" flat carbon xylol acetate I 9-octadecanoic acid (cis form) (oleic acid) octadecanoic acid (monoval- erate of hydroxystearic acid) I11 9: 10-dipentano- yloxyocta- decanoic acid (divalerate of dihydroxy- stearic acid) IV 9: 10: 12-tri- pentanoyloxy- octadecanoic acid (trivalerate of trihydroxy- stearic acid) V 12-octadecanoyl- oxyoctadecanoic acid (" dimer " hydroxystearic acid) VI 12-octadecanoyl- oxyoctadecano- yloxy octa- decanoic acid (" trimer " hydroxystearic acid) I1 12-pentanoyloxy- - - 29 50 90 45 - 36 50 130 68 160 190 40 I 180 120 38 50 - 250 56 64 70 123 40 120 300 70 109 - a Assuming maximum number of carbonyl groups adsorbed with minimum -CH2- adsorption.Oleic acid included for comparison, assuming that the carboxyl and double bond only adsorbed.258 OLIGOESTER CHAIN EFFECTS ON TiOz DISPERSIONS $ 4 CSI 0 9 3 0, a U 0 a CI 0 5 2 1 1 2 3 4 concentration g per 100 cm3 FIG, 5.-Typical adsorption isotherms. 0, trivalerate; x , divalerate; 0 , valerate; all of hydroxy stearic acid. the individual atoms to give the densest packing allowed by the models and assuming attachment to the substrate through the carboxyl group.12*13 The results are sum- marised in table 1 along with the experimentally determined values of area per molecule obtained from the plateau region of the adsorption isotherms.I m X x n 0 1 2 3 4 concentration g per 1o0cm3 FIG. 6.-Typical adsorption isotherms. 0, Dimer 12-hydroxystearic acid in aliphatic hydrocarbon; x , Dimer in xylol; 0, Dimer in n-butyl acetate. DISCUSSION The oligoester fatty acids may be divided into three groups for ease of reference: group 1 : consisting of the acetate, valerate and stearate esters of 1Zhydroxystearic acid; where the size of the branch chain is varied, but not its position of attachment to the main chain. group 2 : consisting of mono-, di- and tri-valerate of 1Zhydroxystearic acid, 9,lO- dihydroxy- and 9,10,12-trihydroxystearic acids, respectively, where there is an increase in the number of branch chains, and the valerate of 2-hydroxy-A .DOROYZKOWSKI A N D R. LAMBOURNE 259 palmitic acid. All branch chains are of equal length but their positions of attachment differ. group 3: dimer, trimer etc. of 12-hydroxystearic acid where the chain length is uniformly increased, as is the branching. TABLE 2.-ADSORBED LAYER THICKNESS MEASUREMENTS ON TITANIA USING DIFFERENT OLIGO- ESTERS COMPARED WITH CHAIN LENGTH MEASUREMENTS ON THE MOLECULAR MODELS. chain com- length adsorbed pound measured apparent layer ref. from DPV actual thickness no. adsorbate model/A qmlqo DPV IA I I1 111 IV V VI VII VIII IX oleic acid monovalerate of 12- h ydr ox ys t ear ic acid divalerate of dihydroxy- stearic acid trivalerate of tri- hydroxystearic acid " dimer " hydroxy- stearic acid " trimer " hydroxy- stearic acid " tetramer " hydroxy- stearic acid " pentamer " hydroxy- stearic acid " 16-mer " hydroxy- stearic acid 1.94 24 2.21 24 2.21 24 2.21 39 2.21 54 1.42 70 85 1.93 256 (64)b 2.7 16.5-15.8 18.3-17.4 18.3-1 7.4 18.3-17.4 11.65-11.07 9.76-9.28 14.98-1 5.75 20.3-21.35 15 16.5 16.5 16.5 9.0 7.2 10.68 15.60 10-20 10 -20 10-20 10-20 40-50 50-60 70-90 50-70 The two values quoted depend on which correction term is used in determining DPV [see ref.(S)]. Calculated value of r.m.s. end-to-end length in aliphatic hydrocarbon. By comparing the experimentally derived areas occupied per molecule, obtained from adsorption isotherms, with the projected areas obtained from the molecular models (see table 1) it is concluded that all the oligoester fatty acids studied, with the possible exception of oleic acid, are adsorbed with the carboxyl group down and the major axis of the molecule perpendicular to the adsorbing surface.This is in keeping with adsorption studies of stearic and other fatty acids by Shenvood and Rybicka and others,I2J3 who concluded that fatty acids were attached to the surface by both ionic and hydrogen bonding. This orientation is also borne out by viscometric studies on the adsorbed layer thickness. If the London-van der Waals forces of attraction, which are responsible for causing the disperse phase to flocculate, are considered, then the energy of attraction between the titania particles is dependent on the effective Hamaker constant (Al2). This is greatest in aliphatic hydrocarbon and least in butyl acetate.However, contrary to expectation, a greater degree of flocculation of the TiOz has been observed in xylol or butyl acetate compared with aliphatic hydrocarbon. This we attribute to the lower surface coverage (or reduced segmental concentration) of the oligoester fatty acids in the better solvents. Since the adsorption (or partitioning) is probably not wholly ionic, surface cover-260 OLIGOESTER CHAIN EFFECTS ON TiOz DISPERSIONS TABLE 3 .-LIST OF HAMAKER CONSTANTS. attractive potential attractive potential (Al2) x 10l3/erg Y = cm r = 0.5 x cm Hamaker const ant (V) in kT ( V ) in kT mat er id ( A 1) (of rutile in) at separation of at separation of rutile 18" - lOA 20A 3 0 A lOA 20A 30A aliphatic H/C 4.4.F 4.6 93 46 32 46 21 16 xylol 5.2t 3.8 78 39 27 39 20 13 n-butyl acetate 35.3p 2.9 58 29 20 29 15 10 * Average quoted by Visser [ref.(14)] V = Ar/l2hO. t Calculated from refractive index using Gregory's approach [ref. (1 S)]. age might be expected to be influenced by the solubility parameter of the solvent. The solubility parameters and the corresponding solvent " fractional polarity " (re- lated to hydrogen bonding potential of the solvent) are quoted in table 4. The differences in the cohesive energy density (CED) are not, however, large and it is doubtful if differences in solvency (as reflected in CED element) are responsible for the variation in surface coverage. However, the fractional polarity may play an important part in determining whether or not the acidic species are more or less readily displaced by solvent, leading to a significant reduction in surface coverage in the case of butyl acetate solutions.TABLE 4.-LIST OF SOLUBILITY PARAMETERS. solubility parameter [ref. (16)] fractional polarity CED element xylol (mixed isomers of xylene) 8.8 0.001 butyl acetate 8.6 0.167 tetradecane 8 .o 0 fatty acids 9* 0.2-0.3 f * Calculated using Rheineck's approach [ref, (17)]. Estimate. EFFECT OF CHAIN BRANCHING AND SEGMENT DENSITY I N THE ADSORBED LAYER ON DISPERSION STABILITY The size of the branch chain appears to be very important with respect to dispersion stability for, although the acetate and valerates of 1Zhydroxystearic acid have the same " site " density (38 A2 molecule-l) on the substrate, by increasing the acetate side chain length by just three -CHz- links a very large increase in stability was obtained, (fig.4 and table 6). Increasing the side chain to 18 carbon atoms on the other hand, decreased the site occupancy, since the measured area per molecule is greater, but changes in the surface layer thickness have also occurred, compensating for the de- crease in surface density. This indicates that surface concentration is very important in influencing dispersion stability. The acetate of 12-hydroxystearic acid was marginally superior to oleic acid as a dispersant, and both were very much better than stearic acid. (Note flocculation factors, table 5.) All three fatty acids are perpendicularly oriented to the particlePLATE 1 .-Viewing left to right : dimer, divalerate, trivalereate, valerate and acetate of hydroxystearic acid, valerate of 2-hydroxystearic acid.PLATE 2.-Above: trimer, below: pentamer. [To face page 260A . DOROSZKOWSKI A N D R . LAMBOURNE 261 TABLE 5.-cOMPARSION OF " LOCALISED " SEGMENTAL VOLUME WITH FLOCCULATION FACTOR IN ALIPHATIC HYDROCARBON. ____ ~ segments 8 A penetra- com- relevant per floccu- tion pound volume no. of unit lation segments per mol. no. adsorbate /A3 segments volume factor unit volume wt./vol. I oleic acid 45 x 8 9 0.025 6.9 0.022* 0.32 I1 valerate of HSA 38 x 8 63-5 0.036 1.2 0.036 0.51 111 divalerate of DHSA 56 x 12 9+5+5 0.028 3.7 0.025 0.44 IV trivalerate of THSA 70 x 12 9+5+ 0.029 2.4 0.029 0.43 X acetateof HSA 38 x 8 6+2 0.026 6.1 0.026 0.46 XI valerate of palmitic acid 38 x 20 14+5 0.025 7.0 0.021 0.47 5 f 5 * Assuming vertical orientation.7.0 1.2 n u) al .Q a 0 0 d c 0 U ZJ --. * U 6.t c c .- c d g 3.7 L YI 2.4 FIG. 7.-Schematic representation of adsorbed layer showing the position of regions of increased segment density relative to the adsorbing surface with various oligoester acids. (a) Valerate of 2- hydroxypalmitic acid, flocculation factor 7.0; (b) valerate of 12-hydroxystearic acid, flocculation factor 1.2; (c) acetate of 1Zhydroxystearic acid, flocculation factor 6.1; (d) divalerate of 9,lO- hydroxystearic acid, flocculation factor 3.7 ; (e) trivalerate of 9,1O,lZhydroxystearic acid, flocculation factor 2.4.262 OLIGOESTER CHAIN EFFECTS ON TiO, DISPERSIONS surface and, since the stearic acid stabilised dispersion is the most flocculated, then interpenetration of the straight CIS chain must be more probable than with branched chains.The effect of chain branching is perhaps best illustrated by reference to fig. 7, (which deals with the case of groups 1 and 2 acids). Branching gives rise to increases in segment density in regions varying in remoteness from the main chain ends. Thus, flocculation is decreased when the region of increased segment density is closest to the outermost part of the adsorbed layer [cf. fig. 7(a) and 7(b)]. The acetate of 12-hydroxystearic [fig. 7(c)] contributes only a small region of increased segment density, in comparison to the valerate, [cf. fig. 7(b)], and the efficiency is only marginally different to oleic acid or the valerate of 2-hydroxy- palmitic acid, fig. 7(a). The di- and tri-valerates of the appropriate hydroxystearic acids [fig.7(d) and 7(e), respectively] exhibit intermediate levels of efficiency of dis- persion stability due to the positions of the branches. Using the same models, the increase in segment density arising from interpenetration can be calculated. Thus, in table 5, a correlation is shown to exist between the " flocculation factor " (an experi- mental measure of the dispersion stability) and the effective segment density allowing for interpenetration of the adsorbed layer up to 8 A. In the treatment localised concentration effects are thus taken into account. If the total (or average) surface concentration of adsorbed molecules is considered, no correlation appears to exist. The importance of local configurational effects has perhaps been overlooked in the more sophisticated statistical treatment of polymer adsorption, which may explain why the statistical treatments have so far not agreed with experimental data.TABLE 6.-LIST OF FLOCCULATION FACTORS (SLOPE OF LOG 77 AGAINST D' PLOT) SHOWING EFFECTS OF DPV, SOLVENT ENVIRONMENT, CHAIN LENGTH AND CHAIN BRANCHING. chain length measured chain from pound (calc. in at high DPV at low DPV com- length viscometry flocculation factor? ref. from aliphatic aliphatic aliphatic no. fatty oligoester acid models) H/C H/C xylol H/C xylol I XI1 X I1 I11 IV XI V VI VII VIII IX oleic acid stearic acid acetate of HSA valerate of HSA divalerate of DHSA trivalerate of THSA valerate of 2-HPA dimer of HSA trimer of HSA tetramer of HSA pentamer of HSA 16-mer of HSA 20 10-20 6.9 24 20 22.2 24 20 6.1 24 20 1.2 24 20 3.7 24 20 2.4 24 20 7.0 39 45 4.5 54 55 2.5 1.8 70 85 80 256(64)* 60 0.6 - - - 4.4 - - - - 6.1 1.7 2.2 7.7 0.4 0.7 2.4 - 0.2 - - - - - - * r.m.s.in aliphatic H/C. 7 slope of log q against 0-3 plot.A . DOROSZKOWSKl AND R . LAMBOURNE 263 EFFECT OF CHAIN LENGTH O N ADSORBED LAYER (GROUP 3 OLIGOESTERS) The agreement between the experimentally determined adsorbed layer thickness and the corresponding theoretical length of the terminally adsorbed oligoester fatty acids is very close, except in the instance of the 16-mer hydroxystearic acid. In this case it is suggested that the 16-mer, because of its size is behaving more like a true polymer, by adsorbing in a typically coiled manner. The adsorbed layer thickness is, therefore, very much smaller than the linear length of the polyester, and might even be the same as its r.m.s.length in free solution, 64 A (see table 2). Thus the viscometric technique to determine the adsorbed layer thickness on small particles as described by the authors5 is validated, despite the approximations made, and gives values of adsorbed layer thickness consistent with molecular dimensions. Although the degree of flocculation of the dispersion decreases regularly with increase per unit length of oligoester in the group 3 series, there is also a concurrent change in chain spacing which effects the surface concentration. Hence it is difficult to isolate the effect of chain length of stabilising molecules on dispersion stability apart from an overall qualitative appreciation that there is an improvement. It is, however, clear from the results that dispersion stability is not simply a function of the adsorbed layer thickness of the stabilising species but a complex function of surface concentration. The latter is dependent on the main chain length, the size, position and number of branches and the solvency of the medium. D. W. J. Osmond, Disc. Faraday Soc., 1966, 46, 314. G. R. Feat and S. Levine, J. Colloid Interface Sci., 1976, 54, 34. P. Rehbinder, 2. Phys. Chem., 1930, A146,63. R. H. Ottewilf and J. M. Tiffany, J. Oil Coloiir Chem. ASSOC., 1967, 50, 877. A. Doroszkowski and R. Lambourne, J. Colloid Interface Sci., 1968, 26, 214. D. Swern, G. N. Billen, T. W. Findley and J. T. Scanlan, J. Amer. Chem. Soc., 1945,67,1787. A. Vogel, Practical Organic Chemistry (Longmans, 1961), p. 367. a C. G. Youngs, FI. Epp, B. M. Craig and H. R. Sallans, J . Amer Oil Chem. Soc., 1957,39,107. D. J. Walbridge, Dispersion Polymerisation in Organic Media, ed. K. E. J. Barrett (Wiley and Sons, N.Y., 1975), p. 108. V. T. Crow1 and M. A. Malati, Disc. Faraday Soc., 1966, 42, 301. l1 W. K. Asbeck and M. Van Loo, fnd. and Eng. Chem., 1954,76,1291. l2 A. F. Sherwood and S. M. Rybicka, J . Oil Colour Chem. Assoc., 1966, 79, 648. l3 J. J. Kipling and E. H. Wright, J. Chem. SOC., 1967, 3535. l4 V. Visser, Ado. Colloid Interface Sci., 1972, 3, 331. l5 J. Gregory, Adv. Colloid Interface Sci.. 1969 2, 296. l6 J. L. Gardon, J. Paint Tech., 1966,38,43. l7 A. E. Rheineck and K. F. Lin, J. Paint Tech., 1968,40, 61 1 .

ISSN:0301-7249    

DOI:10.1039/DC9786500252

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Influence of Adsorbed Proteins on the Stability of Polystyrene Latex Particles B Y AT VAN DER SCHEER, MARCEL A. TANKE AND CEES A. SMOLDERS Twente University of Technology, Department of Chemical Technology, Enschede, The Netherlands Received 22nd November, 1977 Flocculation experiments on polystyrene latex (PSL) with human serum albumin (HSA) and human fibrinogen (HFb) have been performed above and below the iso-electric points (i.e.p.) of the proteins. The stability of the proteins (HFb, HSA) in solution has been determined as a function of salt con- centration (NaCI, BaC12, La(NO&) and pH. Using a stopped flow spectrophotometer the rate constant of flocculation (or coagulation) kll has been measured at different protein and salt concentra- tions (BaC12, NaCl). A model is proposed and tested to explain the enhancement of kll above the value for bare PSL when bridging occurs at pH-values above the i.e.p.of the proteins. The observed enhancement of kll, being 20-30% for HSA and 5040% for HFb, is a result of two effects: reduced hydrodynamic interaction between the flocculating particles and increased effective collision radius of the latex particles when they are partially covered with the protein. Steric stabilization by proteins occurs only in " good solvent " conditions for these proteins. At pH-values below the i.e.p. of the proteins flocculation is observed in the absence of salt. Measurements of electrophoretic mobilities of the latex particles as a function of the protein concentration demonstrated that this flocculation is mainly due to charge neutralization by adsorbed protein molecules.Restabilization by charge inversion of the latex particles occurs at relatively low protein concentration. This paper deals with the influence of adsorbed proteins on the stability against flocculation of hydrophobic colloids, which is here a polystyrene latex such as those used in immunology where protein coated polystyrene latices are used as test material. The influence of polymers on colloid stability has been reviewed by La Mer,2 Lyklema? Vincent4 and N a p ~ e r . ~ Although a lot of work has been done on stabilization of colloidal systems by non-ionic macromolecUles,6-11 cationic 12-16 and anionic poly- ele~trolytes,l~-~~ only little attention has been paid to stabilization by amphoteric macromolecules like proteins? though some work has been done on g e l a t i n ~ ~ ~ s ~ ~ and Singer24 studied the flocculation of latex by y-globulin.In this paper we study the influence of human serum albumin (HSA) and human fibrinogen (HFb) on the stability of a negatively charged polystyrene latex (PSL). Following the definitions first proposed by La Mer; aggregation due to mechanisms in which protein molecules play a role is termed flocculation, aggregation by London- van der Waals forces is termed coagulation. Experiments have been conducted at pH = 8.9, i.e., above the iso-electric point (i.e.p.) of the proteins (i.e.p. HSA at pH = 4.9, i.e.p. HFb at pH = 5.5) and at pH = 3.5, ix., below their i.e.p. At pH = 8.9, protein and PSL are both negatively charged.At pH 3.5 the initial charges of PSL and protein are opposed. The influence of protein on the stability of PSL at pH 8.9 is two-fold: first at incomplete coverage of the PSL by the protein molecules, the protein acts as a destabilizing agent. This instability is not caused by charge neutralization because protein and latex bear the same charge. According to earlier ~ t u d i e s ~ ~ - ~ ~ it may be necessary to add smallA . VAN DER SCHEER, M. A . TANKE AND C. A . SMOLDERS 265 amounts of electrolyte for flocculation, but these amounts are smaller than those needed for coagulation of the bare PSL. This so-called sensitization is caused by bridging of the protein molecules between the latex particles. Secondly, at high surface coverage, the PSL is sterically stabilized by the adsorbed protein layer.Steric stabilization occurs when the adsorbed layer prevents the colloid particles from approaching each other so close that coagulation by Van der Waals forces can take place. The stabilizing mechanism is characterized by two effects : 25 the osmotic pressure effect and the volume restriction effect. One requires the adsorption of the macromolecules to be strong and the stabilizing chains to be in a ‘‘ good ” solvent environment.26 Accordingly we studied the stability of the proteins themselves in solution as well. At pH = 3.5 on the other hand, we are dealing with positively charged macromolecules and negatively charged PSL. In contrast with the above systems at pH 8.9 it may be possible to get flocculation by charge neutralization, resulting from protein adsorption.Gregory l2 demonstrated this effect by measuring the electrophoretic mobility of PSL as a function of the positively charged flocculant concentration ; he observed neutralization and even charge reversal. From these observations several types of destabilization in our system as a function of salt and protein concentration can be expected. (1) Coagulation of unprotected latex particles resulting from double layer sup- pression by indifferent electrolyte as predicted by the DLVO theory. (2) Flocculation by bridging of protein molecules between the latex particles. This is only possible when the electrical double layer is suppressed by electrolyte addition (pH = 8.9) or by charge neutralization (PH = 3.5) so that its thickness is smaller than half the thickness of the adsorbed protein layer.(3) Hetero-coagulation, in the event that neither the protein nor the PSL is stable under the chosen circumstances. Aggregation has been studied by “ stopped flow ” measurements, a technique which allows us to follow the transmittance of the colloidal dispersions in the earliest stages of the aggregation. Lips and Willis27*28 and later Li~htenbelt~~ showed the relation between the change in adsorbance and the rate constant of flocculation in its earliest stages. We used the method of Lichtenbelt in our calculations. This offers the opportunity of calculating real rate constants of flocculation instead of the well- known relative stability factor W.30 Hitherto, only a few authors have reported kinetic flocculation s t u d i e ~ , ~ ~ * ~ ~ generally using the slope of the (adsorbance, time) curve rather than an absolute rate constant.From the use of real rate constants of aggregation we expect to get a more detailed picture of the hydrodynamic interaction between latex particle^^^*^^ and the influence of the dimensions of the protein mole- cules on the rate of floc~ulation.~~ RATE CONSTANT OF FLOCCULATION EXPERIMENTAL DETERMINATION OF k , ~ According to Lichtenbelt et ~11.~’ the change in turbidity of a latex in the initial stage of coagulation or flocculation is given by where Nl = the initial concentration of singlet particles; kll = the rate constant of flocculation (coagulation) for singlets (m3 s-l) and C, and C2 are the optical cross sections of singlets and doublets, respectively.266 STABILITY OF POLYSTYRENE LATICES Using the relations T = exp(-tL) with T transmittance, L the length of the cuvette and 7, = = CINl, eqn (1) can be rewritten as The optical factor (C2/2C, - 1) can be conceived as the relative change in absorbance when a colloidal system consisting of a number of singlets only, is replaced by a system consisting of half of that number of doublets only. This factor can be calculated using Rayleigh Gans-Debye theory and has been tabulated by Lichtenbelt for different values of O! 2na 3, (3) a=- where a = radius of the colloid particle (nm) and ;1 = wavelength (nm) of the light used in the continuous phase, A.nwater In this work colloidal particles with a radius of 117 nm are used, and light with a wavelength of 546 nm.The particle concentration ATl at t = 0 is always 8.6 x 1015 m-3. From these data cc can be calculated; the matching value of the optical factor is 0.21. THEORETICAL EXPRESSIONS FOR FAST A N D HINDERED COAGULATION Von Smoluchowski 34 described coagulation as a bimolecular reaction, obeying the equation (for initial stages of coagulation of a monodisperse colloid) - '2' = 2kllN:, dt (4) kll = 8nDa = 5.4 x lo-'* (m3 s-') (in- water at 298 K); D = diffusion coefficient (m2 s-l); a = particle radius (m). Fuchs3' considered the flux of particles towards a central particle in a field of force. In the absence of electrostatic repulsion (fast coagulation) this leads to where J, = A ux of particles towards a central one (fast coagulation) (s-I) ; V, = energy of attraction between two equal spheres (J K-l); u = - = - - 2a and R = distance between the centres of two particles (m).Since36 at very short distance the viscous resistance between two approaching particles becomes infinite, Brownian-motion can never cause coagulation. Accordingly, S ~ i e l r n a n ~ ~ and H ~ n i g ~ ~ developed a correction analogous to work by Brenne~-,~~ to the diffusion coefficient as a function of the distance between the particles. a a D = D(4B(u) (6) where D = diffusion coefficient at infinite separation (m2 s-l); D(u) = diffusion co- efficient at relative distance u (m2 s-l); and p ( ~ ) = diffusion correction factor at relative distance u. A useful approximation for P(u) 32 6u2 + 13u + 2 B(') = Gu2 + 4uA .VAN DER SCHEER, M . A . TANKE AND C . A . SMOLDERS 267 representing hydrodynamic interaction can be combined with eqn (5), giving where the energy of attraction between two equal spheres can be described as follows38 2 + u2 + 4u + 4 + lnu2 (9) A1(3,1 = Hamaker constant for two bodies of material 1 embedded in medium 3 (J). A dimensionless rate constant4* of flocculation k* is defined k* = Js 16n DN,a' This constant k* is equal to unity for the theoretical Von Smoluchowski rate (p(u) = 1 and VA = 0), so the dimensionless rate constant k* can also be written as * - kll (observed) kll (Von Smoluchowski)' k - Fig. 1 shows the inverse of k* as a function of the Hamaker constant A1(3)1 for particles with a radius of 117 nm. When two particles are connected firmly by a bridge the probability of aggregation becomes 1.This means that neither hydrodynamic effects nor other interactions can prevent them from aggregating and that integration exp (VA/kT) is of the hydrodynamic factor P(u) and the field of force effect - - not carried out from u = 0 to co but from u = x = hJa (where h is bridge length) to a. 1 (u + 212 I I 10"' 10-a jJ FIG. 1.-Inverse of the dimensionless rate constant k* as a function of the Hamaker constant A1(3)1 for particles with a radius of 117 nm.268 STABILITY OF POLYSTYRENE LATICES Following W a l l e ~ ~ ~ it is assumed that tails on the surface of the particles do not influ- ence the diffusion coefficient of the particle. The larger effective collision radius of the particle will enhance the flux by a factor (a + h)la.For the flux in this case we can write & = [8nDN(a + h)]/\I& - exp(VA/kT)du. The rate of aggregation of colloidal particles is thus enhanced by bridging. This enhancement will be optimal when the diffusion coefficient of the particles is not influenced by the presence of the tails and while there are still enough bare places left on the surface for adsorption of tails of approaching particles. The maximal acceleration factor y can be expressed by a + &z exp(vA/kT)du We calculated y for particles with a radius of 117 nrn as a function of the length (h) of the tails for different values of A1(3)1. The results of these calculations are shown graphically in fig. 2. k 5x10' 10' 5 %lo' hlnm FIG. 2.-Maximal acceIeration factor y for particles with a radius of 117 nm as a function of the length (h) of the tails for different 0, kf1(3)1 = J; 0, A1(3)1 = 10"' J; A, A I ( ~ ) ~ = 10"' J.EXPERIMENTAL MATERIALS Polystyrene latext (PS), purchased from Dow (Dow LS-1047-E), is a monodispersed latex with particle diameter of 234 f 2.5 nm. Human serum albumin (HSA), crystalline fromA . VAN DER SCHEER, M. A . TANKE AND C. A. SMOLDERS 269 Pierce Chemicals (no. 30430), was used without further purification. Human fibrinogen (HFb), from Kabi, Stockholm (grade L, 90% clottable) was used after dialysing against twice distilled water at pH = 9, T = 278 K for 8 x lo4 s. All chemicals used were analytical grade. The water used in the experiments was always twice distilled and degassed. APPARATUS MICROELECTROPHORESIS APPARATUS The electrophoretic mobility of bare and protein coated latex particles was measured with a Rank Micro Electrophoresis Apparatus Mk 11, equipped with a cylindrical capillary cell and reversible platinum electrodes.STOPPED FLOW APPARATUS All flocculation experiments were carried out in a Durmm-Gibson Stopped Flow Spectro- photometer, Model D-110, with a 20 mm path length cell. In this apparatus the solutions to be mixed are contained in two syringes. By a pressure (5 x lo5 N m-2) operated actuator, equal volumes are reproducibly mixed within a few milliseconds. The transmittance of the mixture is recorded on a storage oscilliscope. The wavelength of the light used was 546 nm using a tungsten iodide light-source. METHODS CLOUD POINT MEASUREMENTS These experiments have been carried out as a function of pH and salt concentration.Solutions with protein concentrations of 1 kg m-3 and the desired amount of salt were divided into two equal portions. The pH of one of these portions was slowly increased by NaOH addition and the pH of the other portion was slowly decreased by HCl addition. In this way “ instability areas ” in the pH-salt diagram were determined when the solution was cloudy. FLOCCULATION AND COAGULATION MEASUREMENTS Coagulation experiments have been performed with the stopped flow apparatus, using one syringe for the bare latex and the other for the salt solution. Flocculation experiments without salt are carried out by using one syringe for the bare latex and the other for the protein solution.Flocculation experiments in the presence of salt are performed by using one syringe for the PSL + protein mixture and the other for the salt solution. The PSL + protein mixtures are prepared by adding the PSL slowly to the desired protein solution. Concentrations were always chosen such that after mixing in the stopped flow apparatus the latex concentration was 6 x kg m-3 (8.6 x 1015 particles m”). The value for the rate constant of aggregation kll, is calculated, using eqn (2), from the initial change in the transmission (dT/dt)t = after mixing. The initial transmission To in our experiments was always 36%. Using T, and the optical factor (0.21) it can be calculated that a 1% decrease of the transmission corresponded to 12% conversion of singlet particles into doublets (assuming that only singlet-singlet collisions occur).From the measured value of kll the time to reach 1% decrease in the transmission was calculated and found to be equal to the observed time, supporting the validity of our assumptions. At higher singlet conversions, discrepancies between calculated and observed times develop: thus dT/dt is measured only where the decrease in T is <l%. ELECTROPHORETIC MOBILITY MEASUREMENTS The electrophoretic mobilities of the latex particles were measured as a function of the protein concentration in the following special way. The PSL is mixed with protein solutions in the same concentrations as used in the floccu- lation experiments. These flocculation experiments, however, always take about 10 s, so since we are interested in the mobility after 10 s of contact between the PSL and the protein270 STABILITY OF POLYSTYRENE LATICES solution, the mixture was diluted lo4 times after 10 s of contact.Because the proteins are bound very tightly to the the coverage will not change upon dilution. On the other hand, further adsorption of protein at the latex particles can be neglected after such drastic dilution. When the dilution step was done a few minutes after the mixing, it was difficult to measure the electrophoretic mobility for some experiments where flocculation occurs, because too many aggregates were then present. All experiments were performed at 298 K. RESULTS AND DISCUSSION INSTABILITY AREAS OF THE PROTEINS I N (pH, SALT) DIAGRAMS Fig. 3 and 4 show the instability areas (shaded areas) of HSA and HFb in (pH, For HSA, fig.3, salt) diagrams for three different salts, NaCl, BaCl, and La(N0,)3. 14 ( a ) 12 10 7 0 6 4 2 0 lo-' loo 10' [NaCIl / k m o l m-3 14 ( b ) 12 pH 0 10 ' 6 4 2 0 [BaCI,] I kmol m-3 0 t 4 lo -4 lo-' 10 O " .I lo -4 lo-' 10 O [ La.tNO3I3] I kmol rnm3 FIG. 3.-Tnstability areas of HSA in (pH, salt) diagrams: (a) with NaCl; (6) with BaClz; (c) with La(N03)3.A . VAN DER SCHEER, M. A . TANKE A N D C. A . SMOLDERS 27 1 instability areas have been observed at low pH only. Under these circumstances the protein molecules are positively charged and the Cl- or NO? ions act as counterions. For NaCl and BaCl, the solutions become cloudy at C1- concentrations above 0.9 kmol m-3. For La(N03)3 this happens at NO? concentrations above 0.45 kmol m--3.The instability area with La(N03), at pH-values > pH = 6.5 is mainly caused by hydrolysis of the La(N0J3. At pH-values above the dotted line in fig. 3(c), solutions of La(N03)3 without protein are cloudy. The instability just below this dotted line may be due to the interaction of HSA molecules with primary flocs of the salt. For HFb, fig. 4, in the pH region around the i.e.p. (pH = 5.5) the protein is less stable in solution. Under these conditions the molecule bears hardly any net charge and has its most compact Proteins always show a decreased solubility around their i.e.~.~, resulting from a decreased coulombic repulsion which favours aggregation. It 14 12 10 (4 ? : 4 2 0 14 ( b ) 12 pH lo f 8 6 4 2 0 is striking that under physiological conditions (PH z 7.4 and lo-* lo-' 10 O 10' [NaCl] I kmol me3 10 -3 lo-' 10 O 10' [BaC12] I kmol m-3 10 -5 10 dl 10- 10 -' [ La (NO,) 3l I kmol m-3 FIG.4.4nstability areas of HFb in (pH, salt) diagrams: (0) with NaCI; (b) with BaCl,; (c) with La(N03)3.272 STABILITY OF POLYSTYRENE LATICES [NaCI] = 0.15 kmol mV3) the upper boundary of the instability area goes to a lower pH, indicating a higher stability under these conditions. Also at pH-values below 1 the HFb solution becomes cloudy; at higher salt concentrations this instability area extends to higher pH values. In this region the molecule has a resultant positive charge, so the negative ions will act as counterions. The extension of the low instabi- lity region using NaCl and BaCl, occurs at the same C1- concentration, namely 0.2 kmol which is ~5 times lower than observed for HSA.With La(N03),this extension happens at [NO;] = 0.02 kmol m-3, E 5 times lower than for HSA. The difference between the instability region around the iso-electric point and that below pH = 1 is that the clouding of the protein solution around the i.e.p. is reversible and below pH = 1 it is not. The latter indicates a complete denaturation of the protein. A difference between fig. 4(a) and fig.@) is that the high and low instability regions in the first case are connected whereas in the second case they are not. For BaCl,, a protein solution at pH = 8.9 will become cloudy upon a first addition of BaCl, whereas it will clarify again upon a further BaC1, addition.A second difference between fig. 4(a) and fig. 4(b) is that the high pH instability region extends to higher pH values for BaC1, than for NaCl, indicating that above the isoelectric point, the valency of the positive counterions plays a role in the mechanism of destabilization. One might imagine a kind of physical crosslink of Ba2+ between the protein molecules. Perhaps repeptization at high Ba2+ concentration can be seen as a complete saturation of the available crosslink sites by Ba2+. At pH values below the i.e.p. of the proteins, destabilization by NO; ions is twice as effective as that by C1- ions for both proteins. This indicates that the same mechanism plays a role, although for HSA much higher concentrations are needed than for HFb. Comparison of fig. 3 and 4 leads to the conclusion that HSA is a much more stable protein than HFb.COAGULATION OF THE LATEX WITH SALT Coagulation experiments of PSL with salt only have been performed at pH = 3.5 and 8.9. Fig. 5(a) shows the value of the rate constant of coagulation kll as a function of the BaCI, concentration. It is clear that kll increases with increasing salt concentra- tion. Coagulation results from the decrease in double-layer repulsion between the negatively charged PSL particles due to the Ba2+ ions. For a BaCl, concentration of 0.05 kmol mW3, maximum values of kll = 2.45 x m3 s-l at pH = 8.9 and kll = 2.3 x 10-l8 m3 s-l at pH = 3.5 are observed. The decrease in k,, at higher BaCl, concentration is mainly due to a higher viscosity of the continuous phase, resulting in a lower value for the diffusion coefficient D of the latex particles (D = kT/Gnya).Up to BaCl, concentrations of 0.05 kmol m-3 the viscosity of the salt solutions is almost constant (1 % deviation from ywater). At higher BaCl, concentra- tions the viscosity increases dramatically until at 1 kmol mA3 an increase of 28.5% is reached.43 The difference between kll at pH = 8.9 and at pH = 3.5 is not under- stood. The rate constant of Von Smoluchowski at 298 K is 5.38 x Taking kll (observed) = 2.38 x 10-l8 m3 s-l, the dimensionless rate constant from eqn (10) appears to be m3 s-'. k" = 0.44. Fig. 5(b) shows the dependence of kll on the NaCl concentration at pH = 8.9 and pH = 3.5. m3 s-l at pH = 8.9 and kll = 2.1 x m3 s-l at pH = 3.5 is reached at NaCl concentrations of 1 kmol m-3, where the viscosity of the continuous phase is 1.094 times that of water.43 This For NaCl the maximum value of kll = 2.2 xA .VAN DER §CHEER, M. A. TANKE AND C. A. SMOLDERS 273 results in a kll (Von Smoluchowski) = 4.94 x 10-l8 m3 s-l. Taking kll = 2.15 x 10-l8 m3 s-l the dimensionless rate constant [eqn. (lo)] is k" = 0.44. Using fig. 1, which shows the relation between l/k* and the Hamaker constant A1(3)1, the Hamaker constant can be calculated A1(3)1 z=z 1.0 (-+0.1) x J. ( a ) 2.5 - 2.0 - 'u) 1.5 - c mE Tg 1.0 +- -.- 0.5 t / / I I 1 5 x10-3 I O - ~ 5 x10-2 lo-' 5 x lo-' I BaCl$ / kmol o r I I I I 5x10-* lo-' 5 x lo-' 1 5x10' CNaCl I / kmol rn-3 FIG. 5.-Rate constant of coagulation kll for bare PSL as function of the salt concentration: (a) with BaClz at 0, pH = 8.9 and 0, pH = 3.5; (b) with NaCl at 0, pH = 8.9 and 0, pH = 3.5.Visser's 44 tabulated Hamaker constants of different materials in water provide values obtained from Lifshitz theory (A1(3)1 = 3.5 x and values obtained from colloid chemistry < A1(3)1 < J) for PS in water. Comparison shows that the value obtained from our experiments is somewhat low but not unrealistic. The salt concentrations at which fast coagulation occurs are higher than those reported for classical test tube experiments, but this is expected since in our experiments coagula- tion times are of the order of seconds and orthokinetic coagulation is absent.ll We conclude that our apparatus fulfills the conditions for the type of measurements we are doing.274 STABILITY OF POLYSTYRENE LATLCES FLOCCULATION EXPERIMENTS WITH HSA AT pH = 8.9 When PSL and HSA solutions were mixed in the absence of electrolyte, no flocculation could be detected at HSA concentrations between 0.00 and 0.25 kg m-3 after mixing.Fig. 6(a) and (b) show the dependence of kll on the BaCl, and NaCl 3.51 I A 1 r L h v lo-' 1 C 6aC121 / kmol m-3 P ' m 5xlO-l 1 C NaCll / kmol rn-3 FIG. 6.-Dependence of kii on the salt concentration (pH = 8.9) for curves with constant HSA concentration: (a) with BaClz at HSA concentrations of A, zero; 0, 0.17; A, 0.33; m, 1.67; 0, 3.33; 0, 6.66; 0, 13.33; V, 26.67; x, 50.0; v, 250 x kg m-3; (b) with NaCl at HSA con- centrations of A, zero; 0, 0.5; A, 0.8; ., 1.9; 0, 2.3; 0, 4.0; 0, 8.0 X kg M - ~ concentration for curves with constant HSA concentration.It is clear that at HSA concentrations < 5 x loA3 kg m-3 smaller amounts of salt are needed to start floccula- tion than for PSL without protein. This sensitization is not caused by a decreased electrostatic interaction due to protein adsorption, because protein and latex are both negatively charged, but results from bridging : molecules which are already adsorbed on one latex particle adsorb on the surface of another latex particle. This mechanism can apply when the double layer interaction between the particles has been suppressedA . VAN DER SCHEER, M. A . TANKE AND C. A . SMOLDERS 275 by electrolyte addition such that particles can approach each other closely. It is also necessary that the latex particles are only partly covered with protein molecules.Fig. 7(a) and (b) show kll as a function of the HSA concentration for curves of con- stant BaCl, and NaCl concentration: at higher HSA concentrations kll decreases as a result of steric stabilization of PSL by adsorbed HSA layers. When the latex particles are fully covered by protein, bridging no longer occurs. As particles approach, the adsorbed protein layers must interpenetrate, resulting in steric stabilisation. At HSA concentrations >O. 1 kg m’3 electrolyte addition hardly causes any flocculation. This concentration to reach a fully shielding monolayer is in good agreement with adsorption isotherms of HSA on PSL,39*45 showing that maximum adsorption occurs at this concentration. kg m-3 a maximum of kll exists; these maximum values of kii exceed the maximum value of kll for the bare latex.Gregory13*14 found an enhanced rate of flocculation using It is shown in fig. 7(a) and (b) that at HSA concentrations of about 1.7 x 3.0 2.5 2.0 1.5 1 .o 0 : i @ 0.5 ++---J--f- , % <,! [HSAI /If3 kg m3 B 0 4 8 12 2-4 32 36 50 83.3 250 O* 2 1 6 8 - &--A- 20 lHSAl/ 10” kg m3 FIG. 7.-The dependence of kll on the HSA concentration (pH = 8.9) for curves with constant salt concentrations: (a) with BaClz concentrations of ., 0.5; @, 0.15; 0, 0.05; 0, 0.015; A, 0.005 kmol m 3 ; (b) with NaCl concentrations of 0, 1.5; m, 1.0; 0, V, 0.5; @, A, 0.15; 0, 0.05 kmol m-3.276 STABILITY OF POLYSTYRENE LATICES negatively charged PSL and cationic polyelectrolytes. He explained this in terms of an uneven distribution of negative and positive charges on the PSL surface. This could lead to an extra attractive contribution to the interaction between the particles, due to '' oriented approach".In our case this explanation is not possible, because latex particles and protein molecules are both negatively charged. Another argument is that enhancement to kil values above those for bare PSL only occurs at high salt concentrations, in other words electrostatic interactions cannot play a role. We propose that the increase in kil results from the diminished hydrodynamic interaction through bridging of the protein molecules between the latex particles. X LBaC1,I / kmol rn -3A . VAN DER SCHEER, M. A. TANKE AND C. A. SMOLDERS 277 CNaClI / kmol rne3 FIG. 8.-The dependence of krl on the salt concentration (pH = 8.9) for lines with constant HFb concentration: (a) with BaCl, at HFb concentrations of A, zero; 0, 0.25; A, 2.0; m, 2.5; @, 3.0; 0, 5.0 x 10" kg m-3; (b) with BaCl, at HFb concentrations of 0, zero; 0, 5.0; 0, 25.0; V, 62.5; x, 250 x kg m"; (c) with NaCl at HFb concentrations of A, zero; a, 5.0; 0, 1.3; X, 1.6; A, 1.9; 0, 2.5; w, 8.0 X kgrn-3.From fig. 7(a) and (b) the maximum enhancement of kll at [BaCl,] = 0.05 kmol m-3 and [NaCl] = 1.0 kmol m-3 appears to be 30% and 20%, respectively. Fig. 2 shows the maximal acceleration y [eqn (13)] as a function of the length of the tails on a particle for different values of the Hamaker constant. Using a Hamaker constant of J it can be seen that the observed acceleration factor y, 1.20-1.30, can be caused by tails with a length of 7-10 x m.This is in excellent agreement with the dimensions of the albumin molecule, assumed to be a prolate ellipsoid with major and minor axes of 14 and 4 x 1 1 3 . ~ ~ FLOCCULATION EXPERlMENTS WITH HFb AT pH = 8.9 When PSL and HFb solutions were mixed in the absence of electrolyte, no floccula- tion was observed at HFb concentrations between 0.00 and 0.25 kg m-3 after mixing. Fig. 8(a), (b) and (c) show the dependence of kll on [BaCl,] and [NaCl] for several constant protein concentrations. Analogous to the results with HSA, HFb also causes sensitization at low protein and salt concentrations. In fig. 8(b) it is shown that the sensitization at low concentrations of BaC1, also occurs at HFb concentrations up to 0.25 kg m-3.This phenomenon is related to the instability area of HFb (4.0.). Fig. 9(a), (b) and (c) show the relation between klr and the HFb concentration for con- stant [BaCl,] and [NaCl]. Analogous to HSA, HFb causes an increase in kll at low protein concentration. The maximum value of kll is reached at an HFb concentration of 2.5 x kg m-3. From our own work on the adsorption isotherms of HFb on PSL we know that, in contrast to HSA, all HFb molecules in solution are adsorbed on the latex particles at low initial HFb concentrations (high affinity isotherms). The latex surface available for adsorption in OUT experiments is 1.48 x lo3 m2 m-3. This means that the surface concentration of HFb on the PSL at maximum flocculation rate is 1.7 x low6 kg m-2.From these adsorption experiment^^^ it is also shown that at surface concentrations above 4 - 5 x kg m-2 a certain amount of HFb278 STABILITY OF POLYSTYRENE LATICES remains in solution, although the maximuin surface concentration reached at higher concentrations is 9.8 x From these data we conclude that maximal rates of flocculation occur at surface coverages of 17 - 38%. This is a lower coverage than the 50% predicted by La Mer et aZ.,4 but in agreement with the 35% observed by Singer et aZ.24 for y-globulin on PSL. The observed acceleration factor y [eqn (13)] is 1.60 for BaCl, and 1.50 for NaCl. From fig. 4 it can be seen that, using a Hamaker constant of J, this acceleration can be the result of bridges with a length of 17-20 x m. These values are between the values of the minor and major axes of the HFb molecules, 9 and 45 x 10-9 m,47-49 kg m-2.(5 1 4.01 3.5 A 0 e 0 0 u / - L - - f , I I I t I I 0 2 4 6 12 14 18 20 25 31.3 CHFbl /lff3kg m3A . VAN DER SCHEER, M. A . TANKE A N D C. A . SMOLDERS 279 c v) P) E C HFbI / l o 3 kg m-3 FIG. 9 . T h e dependence of kll on the HFb concentration (pH = 8.9) for curves with constant salt concentration: (a) with BaClz concentrations of 0,0.5; 0,0.15; 0,0.05 kmol mJ; (b) with BaCl, concentrations of 9,0.015; 0,0.005; 0,0015 kmol m”; (c) with NaCl concentrations of A, 1.5; 0, 1.0; 0, 0.5; m, 0.15 X, 0.05; 9, 0.015 kmol m-3. Fig. 9(c) shows that at HFb concentrations above 8 x lW3 kg m-3 the PSL is protected against aggregation on NaCl addition by steric stabilization.Fig. 9(a) and (b) however, show that at higher HFb concentrations the PSL is not always protected against aggregation on BaCl, addition. At higher concentrations of HFb, a drastic increase in kll is even observed for some concentrations of BaCl,. This phenomenon can be understood on inspection of the instability area of HFb in the OpH, [BaC12]) diagram [fig. 4(b)], which shows that at pH 8.9 the HFb solution is cloudy at BaCl, concentrations between 0.003 and 0.1 kmol n ~ - ~ . At these BaCl, concentrations the continuous phase has “ bad solvent ” properties with respect to the HFb mole- cules. At these conditions no steric stabilization can be expected.20 The extremely high values of kll at high concentrations of HFb are the result of a kind of co-sedimentation of the free HFb in the continuous phase with the covered PSL particles.In fact it is not correct to speak of a kll in this region. The aggrega- tion that occurs under these circumstances is not a bimolecular process, but might be described as a kind of bridging. The bridges should not be regarded as composed of one adsorbed protein molecule, but rather as an infinite network formed by physical crosslinks between the protein molecules by divalent Baz+ ions, as has already been proposed for alginates.18 At HFb concentrations between 6 x 10” and 3 x lo-, kg m-3, kll in fig. 9(a) and (b) is independent of the HFb concentration, indicating that in this concentration range the free HFb molecules in the continuous phase do not play a role in the flocculation: flocculation may still be described as a bi- molecular process.From the values of kll in these regions, [fig. 9(a) and (b)] for different BaCl concentrations together with the instability area, fig. 4(b), one can see the influence of the solvent properties on the steric stabilization. Good solvent implies steric stabilization; “ bad ” solvent means no steric stabilization.280 ( 4 2.5 7 2.0 v) g 1.5 s 4" .cI c 1.0 0.5 STABILITY OF POLYSTYRENE LATICES - - - - - FLOCCULATION EXPERIMENTS WITHOUT SALT pH 3.5 At pH = 3.5 both proteins (HFb and HSA) bear a net positive charge, implying a measure of charge neutralization when the positive protein molecules adsorb at the negative latex particles. Results of flocculation measurements of PSL with HSA and HFb are shown in fig.lO(a) and (6). kll increases with increasing protein concentra- tion. At protein concentrations h0.7 x lom3 kg m-3 restabilization of the PSL protein mixtures was observed after an intial onset of flocculation. The electrophoretic mobility of the PSL particles as a function of HSA and HFb concentration [fig. 15(a), (b)] reveals charge reversal at protein concentrations around 0.7 x kg M-~, i.e., at extremely low surface coverage (-5%). This indicates 0 I I , , ,A I 0 0.2 0.4 0.6 0.8 [HSA] / kg m3 2.5 2.0 c I 0.5 0 0.2 0.4 0.6 0.8 [HFbl 1 I d 3 kg rn-3 FIG. 10.-The rate constant of flocculation ( k I l ) as a function of the protein concentration (pH = 3.5) in the absence of salt. (a) Dependence on the HSA concentration; (b) dependence on the HFb concentration.A .VAN DER SCHEER, M. A . TANKE AND C. A . SMOLDERS 28 1 that the observed restabilization results from electrostatic repulsion at these and higher protein concentrations. When restabilization of the mixture is observed, the value of kll is taken to be zero, although immediately after mixing flocculation occurs. The time during which this flocculation occurs may reflect the time necessary for adsorption and reconformation of the protein molecules on the latex particles. Further experiments on this subject are in progress and will be reported elsewhere. Gregory 13*14 found that the optimum flocculation concentration coincides with the flocculant concentration at which the charge of the colloid particles is just neutralized. Our measurements endorse his conclusions, provided we ignore the initial flocculation rate which is found immediately before restabilization at concentrations >7 x lo4 kg m-3 of protein.FLOCCULATION WITH HSA AND SALT AT pH = 3.5 When PSL is slowly added to solutions containing HSA concentrations 2 1.67 x kg m-3 the turbidity of the mixture appeared to be equal to that of a PSL of the same concentration without HSA. The PSL + HSA mixtures at these protein concentrations are stable because of the positive charge of the adsorbed HSA mole- cules. Flocculation experiments of these mixtures with BaCl, and NaCl are shown 1.0 0.5 5 x10-3 (b) 2.5 2 .o vI 1.5 t *€ 99 1.0 \ c -G- 0.5 0 lo-* 5x10-2 lo-’ 5 x lo-’ CBaCl2I / kmol rn-3 5 xu)-* 104 5 x10” 1 CNaCI 3 / kmol rn-3 FIG. 11 .-The dependence of kll on the salt concentration (pH = 3.5) for curves with constant HSA concentration: (a) with BaCl, at HSA concentrations of A, zero; 0, 1.67; 0, 6.67; X, 13.3; 7,250 x kg m-j; (b) with NaCl at HSA concentrations of A, zero; 0,Z.O; 0, 3.0; x, 5.0; @, 10; 1,12.5; A, 80; V, 250 x lo9 kg mS.282 STABILITY OF POLYSTYRENE LATICES in fig.11 and 12. The charge-reversed PSL can still be flocculated by salt addition, confirming that restabilization observed without salt results from electrostatic repulsion and not from steric stabilization. From fig. 11 (a) one might conclude that no sensitization is observed because the HSA + PSL mixture needs higher BaCl, concentrations than does the bare PSL. This conclusion, however, may be wrong because the bare PSL is negatively charged and the PSL particles in the mixture are positively charged.Therefore, Ba2+ ions act as counterions for the bare PSL I 8 12 24 28 32 83.3 250 lHSAl / 1f3kg rn-3 rn A A 0.5/ LL/. ~ , 0 2 4 6 8 10 12 25 100 250 C HSAI /lt3 kg rn-3 FIG. 12.-The dependence of krr on the HSA concentration (pH = 3.5) for curves with constant salt concentration : (a) with BaCL concentrations of Q 0 . 5 ; A , 0.25 ; 0, 0.15 ; V, 0.05 ; x , 0.025 kmol m"; (b) with NaCl concentrations of 0, 1.5; a, 1.0; A, 0.5; 0, 0.15; X, 0.05 kmol m". and the C1- ions for the charge reversed PSL particles. When NaCl is used as electro- lyte, the counterions Na+ and Cl- are both monovalent. From fig. l l ( b ) it can be seen that slight sensitization occurs at a HSA concentration of 2 x Fig. 12(a) shows that at BaCl, concentrations >0.15 kmol m-3 very high HSA concentrations are needed to obtain steric stabilization.With NaCl [fig. 12(b)] it appears that at salt concentrations > 1 .O kmol m-3 no steric stabilization occurs, but at very high HSA concentrations an increase in kll appears. The instability area of HSA with NaCl [fig. (3a)l shows that at pH = 3.5 and NaCl concentrations >1.0 kmol m-3 the continuous phase has bad solvent properties for HSA, which explains the flocculation behaviour. It is remarkable that no " hydrodynamic " acceleration occurs at low protein concentrations. This may be caused by the electrostatic attraction forces between the adsorbed positive protein molecules and the negative kg mM3.A . VAN DER SCHEER, M . A .TANKE A N D C . A . SMOLDERS 283 latex surface. This attraction may result in a flat orientation of the molecules onto the surface and consequently in very short tails. FLOCCULATION WITH HFb AND SALT AT pH = 3.5 Stable HFb + PSL mixtures could be obtained at HFb concentrations >2 x kg m-3. The flocculation behaviour of these mixtures (fig. 13 and 14) is analogous to that of HSA + PSL mixtures. Again no “ hydrodynamic ” acceleration has been observed at low protein concentrations. The denaturated state of the protein 3.5 t 9.68 4 C BaCI,l / kmol ~TI-~ 5 x10-* lo-’ 5 x lo-’ I lNaCl I/ kmol m-3 FIG. 13.-The dependence of kll on the salt concentration (pH = 3.5) for curves with constant HFb concentration: (a) with BaClz at HFb concentrations of A, zero; Q2.5; 0, 5.0; @, 10; My 20; x, 40 x kg mL3; (6) with NaCI at HFb concentrations of A, zero; 0, 2.0; 0, 5.0; x, 10.0; kg ~ n - ~ .a, 25; at 100 x284 STABILITY OF POLYSTYRENE LATICES ( b ) 9' 8 , ( 0 ) 4.0 3.5 101 2.5 2.0 c. e 9.68 0 0 a A 0 2 4 6 8 1 0 2 0 40 C HFbl / ld3 kg m-3 A ci'i 63 59 57 'Lo -- O 0 2 4 6 8 1 0 25.5 l00 CHFbl kg m-3 FIG. 14.-The dependence of kll on the HFb concentration (pH = 3.5) for curves with constant salt concentration: (a) with BaCI, concentrations of 0, 0.5; A, 0.15; V, 0.05; 0, 0.015; 0, 0.005 kmol m4; (b) with NaCl concentrations of X , 1.5; 9, 1.0; A, 0.5; 0, 0.15; 0, 0.05 kmol m". molecule at low pH makes it more flexible,50 which facilitates a flat orientation at the latex surface. Using NaCl [fig. 14(b)] it is shown that at higher NaCl(>O.2 kg m-3) and HFb concentrations (0.1 kg mW3) the value of kll is extremely high.Under these bad solvent conditions for HFb (fig. 4(a)] the rate of " co-sedimentation " is largely influenced by the concentration of HFb in the continuous phase. Comparison ofA . VAN DER SCHEER, M. A . TANKE AND C. A . SMOLDERS 285 fig. ll(a) and 12(a) with fig. ll(b) and 12(b) and comparison of fig. 13(a) and 14(a) with fig. 13(b) and 14(b) shows that the flocculation behaviour of charge inversed PSL is governed by the C1- concentration.. 2 1 ( a 1 - 1 - 2 -3 t i 1-2.0 * 3.0 4.0 -1 - 2 - 3 t FIG. 15.-The electrophoretic mobility Vof the latex particles as a function of the protein concentra- tion at pH = 3.5. (a) with HSA; (b) with HFb. CONCLUSIONS The influence of the adsorption of the proteins HFb and HSA on the stability of a negatively charged polystyrene latex can be summarized as follows: (1) The adsorbed molecules protect the latex particles against aggregation by electrolyte addition if they occupy the surface of the latex particles completely and if the continuous phase has " good solvent " properties for the protein.(2) No steric stabilization is observed when the continuous phase has " bad solvent " properties for the protein. With " bad solvent " properties for the protein286 STABILITY OF POLYSTYRENE LATtCES and high protein concentrations the initial aggregation of protein latex mixtures cannot be described by a bimolecular process. (3) Positively charged protein molecules can induce flocculation of the negatively charged latex by charge neutralization. At relatively low protein concentrations the charge of the negative latex particles is reversed by adsorption of positive protein molecules, resulting in restabilization of the latex by electrostatic repulsion.(4) The latex cannot be flocculated by negatively charged protein molecules in the absence of salt. At low surface coverage of the latex particles by negatively charged proteins flocculation can be caused by very small additions of electrolyte (sensitization by a bridging mechanism). (5) Bridging of latex particles by protein molecules increases the rate of flocculation compared with the rate observed for protein-free latex. This enhancement of flocculation rate can be explained by a reduced hydrodynamic interaction between the particles and an increased effective collision radius of the particles, depending on the size of the protein molecules.(6) At " good solvent " conditions, steric stabilization by HFb occurs at much lower protein concentrations than it does using HSA, this indicates a higher affinity of the HFb for the PS-surface. J. M. Singer and C. M. Plotz, Awzer. J. Med., 1956,21, 888. V. K. La Mer and T. W. Healy, Rev. Pure Appl. Chem., 1963,13,112. J . Lyklema, Adv. Colloid Interface Sci., 1968, 2, 65. B. Vincent, Adv. Colloid Interface Sci., 1974,4, 193. D. H. Napper, J. Colloid Interface Sci., 1977,58, 390. ti S. G. Ash and E. J. Clayfield, J. Colloid Interface Sci., 1976, 55, 645. J. Rubio and J. A. Kitchener, J. Colloid Interface Sci., 1976, 57, 132.P. Bagchi, J. Colloid Interface Sci., 1974, 47, 86. G. J. Fleer, L. K. Koopal and J. Lyklema, J. Kolloid Z., 1972,250, 689. lo G. J. Fleer and J. Lyklema, J. Colloid Interface Sci., 1974, 46, 1. l1 G. J. Fleer and J. Lyklema, J. Colloid Interface Sci., 1976, 55, 228. l2 J. Gregory, Trans. Faraday SOC., 1969,65,2260. l3 J. Gregory, J. Colloid Interface Sci., 1973, 42, 448. l4 J. Gregory, J. Colloid Interface Sci., 1976, 55, 35. G. M. Lindquist and R. A. Stratton, J. Colloid Interface Sci., 1976, 55, 45. M. Ishikawa, J. Colloid Interface Sci., 1976, 56, 596. l7 A. S. Teot, Ann. N. Y. Acad. Sci., 1969, 155, 593. l8 T. Lindstrom and C. Soremark, J. Colloid Interface Sci., 1976,55,69. l9 A. Sommerauer, D. L. Sussman and W. Stumm, Kolloid Z., 1968,225, 147. 2o N. Sarkar and A. S . Teot, J. Colloid Interface Sci., 1973, 43, 370. 21 J. C. Le Bell, V. T. Hurskainen and P. J. Stenius, J. Colloid Interface Sci., 1976,55, 60. 22 T. Meternaghan and R. H. Ottewill, J. Photographic Sci., 1974, 22, 279. 23 S. Kratovil and E. MatijeviC, J. Colloid Interface Sci., 1976, 57, 104. 24 J. M. Singer, F. C. A. Vekemans, J. W. Th. Lichtenbelt, F. Th. Hesselink and P. H. Wiersema, 25 F. Th. Hesselink, A. Vrij and J. Th. G. Overbeek, J. Phys. Chenz., 1971,75, 2094. 26 F. K. R. Li-In-On and B. Vincent, ACS Symposium Series 9, p. 165, ed. R. L. Mittal (Washing- 27 A. Lips, C. Smart and E. Willis, Trans. Faraday SOC., 1971, 67, 2979. *' A. Lips and E. Willis, J. C. Favadaj? I, 1973, 69, 1226. 29 J. W. Th. Lichtenbelt, C. Pathamamanoharan and P. H. Wiersema, J. Colloid Interface Sci., 30 H. Reerink and J. Th. G. Overbeek, Disc. Faraday SOC., 1954,18, 374. 31 L. A. Spielman, J. Colloid Interface Sci., 1970, 33, 562. 32 E. P. Honig, G. J. Roebersen and P. H. Wiersema, J. Colloid Interface Sci., 1974, 36, 97. 33 W. E. Walles, J. Colloid Interface Sci., 1968,27, 797. 34 M. Von Smoluchowski, Phys. Z., 1916, 17, 593. 35 N. Fuchs, 2. Phyx., 1934, 89,736. 36 B. V. Derjaguin, Disc. F h ~ d ~ y SOC., 1966, 42, 317. J. Colloid Interface Sci., 1973, 45, 608. ton D.C., 1975). 1974, 49, 28.A . VAN DER SCIIEER, M . A . T A N K 1 : A N D C . A . SMOLDERS 287 37 H. Brenner, Chem. Eng. Sci., 1961, 16, 242. 38 H. C. Hamaker, Physica, 1937,4, 1058. 39 W. Norde, Proteins at Interfaces, Thesis (Agricultural University Wageningen, The Netherlands, 1976). 40 G. J.-Roebersen, Theoretical Considerations on the Coagulation Kinetics of Hydrophobic Colloids, 41 M . Champagne, J. Polymer Sci., 1957,23, 863. 42 E. J. Cohn, L. E. Strong, W. L. Hughes, D. J. Mulford, J. N. Ashworth, M. Melin and H. L. Taylor, J. Amer. C’lzenz. SOC., 1946, 68, 459. 43 International Critical Tables. 44 J. Visser, Adv. Colloid Interface Sci., 1972, 3, 331. 45 Unpublished results from our laboratory. 46 Th. Peters Jr., The Plasma Proteins I, ed. F. W. Putman (Academic Press, New York, 1975). 47 L. Bachmann, W. W. Schmitt-Fumian, R. Hammel and K. Lederer, Macrornol. Chem., 1975, 48 K. Lederer and R. Hammel, Macroniol. Chetn., 1975, 176, 2619. 49 K. Lederer, Macroitiol. Chetn., 1975, 176, 2641. Thesis (University Utrecht, The Netherlands, 1974). 176, 2603. Fibrinogen, ed. K. Laki (Marcel Dekker, New York, 1968).

ISSN:0301-7249    

DOI:10.1039/DC9786500264

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

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.

ISSN:0301-7249    

DOI:10.1039/DC9786500288

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Equilibrium Aspects of Heteroflocculation in Mixed Sterically-stabilised Dispersions BY BRIAN VINCENT AND COLIN A. YOUNG Department of Physical Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS AND THARWAT F. TADROS I.C.I. Plant Protection Division, Jealott's Hill Research Station, Bracknell, Berkshire RG12 6EY Received 20th December, 1977 The equilibrium adsorption-desorption behaviour of small, positive polystyrene latex particles onto much larger, negative polystyrene latex particles, in which both sets of particles carry adsorbed poly(viny1 alcohol) (PVA) molecules, has been studied as a function of the molar mass of the PVA, and the ionic strength. Two types of isotherm have been observed: at low ionic strengths, one obtains high-affinity, irreversible isotherms ; at high ionic strengths, S-shaped, reversible isotherms result. There appears to be a critical electrolyte concentration (or at least a very narrow range of electrolyte concentrations) at which the transition, from one isotherm type to the other, occurs.This critical electrolyte concentration decreases with increasing molar mass of the PVA. The results are rationalised in terms of two sets of forces acting in the system: the primary, adsorbing forces normal to the interface, and the lateral interactions between adsorbed particles (which are repulsive at low ionic strengths, but attractive at high ionic strengths). Scanning electron microscopy results broadly confirm the conclusions reached from the adsorption studies. Since many natural, as well as industrial, dispersions in practice contain particles or droplets of more than one type it is important to understand, and hence be able to control, any aggregation processes which may occur.A closely-related phenomenon is the adhesion of particles to flat surfaces. In both areas the interactions between oppositely-charged species is of particular importance. Applications of these con- cepts occur in a large variety of fields such as the " structuring '' of pesticide/herbicide and pharmaceutical formulations, soil conditioning, water purification, filtration, and in the aggregation and adhesion of biological cells. Although numerous papers have been published on the heterocoagulation of oppositely-charged particles and on the deposition of particles onto flat surfaces of opposite sign,2 most of the work in these areas has been concerned with the kinetic aspects.Moreover, no workers that we are aware of, have considered the effects of adsorbed macromolecules on the inter- actions. In this paper we investigate the equilibrium adsorption of small, positive polystyrene particles onto much larger, negative polystyrene particles, where each set of particles carries an adsorbed polymer layer. In this way one can achieve a large surface area for adsorption without departing too far from sphere-plate geometry. Poly(viny1 alcohol) (PVA) was chosen as the adsorbed polymer since its adsorption characteristics onto polystyrene latex particles have been extensively studied by US.^-^B . VINCENT, C . A . YOUNG AND T. F . TADROS 297 The results are presented in the form of adsorption-desorption isotherms, and the variations with polymer molar mass and ionic strength have been studied.EXPERIMENTAL MATERIALS All water used was doubly-distilled from an all-Pyrex apparatus. Sodium chloride (B.D.H. AnalaR grade) was used as supplied. The PVA fractions used were obtained by a precipitation technique5 involving the addition of increasing quantities of acetone to a 5% aqueous solution of the parent PVA [Alcotex '' 88-05 ", from Revertex, i.e., 88% hydrolysed poly(viny1 acetate)]. The molar mass of each fraction was determined by viscosity measure- ments using a Cannon-Fenske suspended level dilution viscometer. The Mark-Houwink equation, relating the intrinsic viscosity [y] to the molar mass M, used was that determined by van den Boomgaard et aZ.,5 i.e., [y] = 3.06 x 10-4M0*70 (25°C).The molar masses obtained in this way were as follows: 37 500, 24 000, 14 000, 10 500 and 7000. The two negative polystyrene latices (A, B) used in this work were prepared by the method of dispersion polymerisation of styrene (B.D.H., redistilled under vacuum) at 70 "C, using potassium persulphate (B.D.H.) as initiator. The positive polystyrene latex (C) was prepared following the method of Pelton6 using azobisisobutyramidinium chloride as initiator (kindly supplied by Dr. P. Stenius, Department of Physical Chemistry, Abo Aka- demi, Finland). Electron microscopy gave the following mean particle diameters : Latex A 3.2 pm; latex B 0.182 p m ; latex C 0.195 pm. Latices A and B were steam-stripped at 100 "C to remove excess monomer, and all three latices were extensively dialysed against distilled water.Latex C was stored and handled in glassware that had been treated with dichlorodi- methylsilane solution in trichloroethane; the objective here was to help reduce possible con- tamination of the latex by polysilicate ions leached from the surface of the glassware.6 M I C R 0 EL E C T R O P HO R E S IS in order to investigate the effect of the presence of the PVA adsorbed layer on the zeta potentials of the latex particles, the electrophoretic mobilities of the latex A particles were measured at 25 "C and pH 6 using a Rank Bros. (Cambridge, England) microelectrophoresis apparatus. The PVA concentration (250 p.p.m.) was chosen to correspond to the plateau region of the corresponding adsorption i ~ o t h e r r n , ~ ~ ~ and various concentrations of NaCl in the range to 10-1 mol dmP3 were employed.Zeta potentials were derived from the mobility data using the tables of Wiersema, Loeb and Overbeek7 and Ottewill and ShawV8 It has so far proved very difficult to obtain reliable data on positive particles using glass electrophoresis cells, because of the problem of leaching of polysilicate anions from the surface, as discussed above. PART I C LE ADS OR P T I ON IS 0 TI-I ER M S The equilibrium adsorption of the small particles (latex B or C) onto the large particles (latex A) was determined as follows. Both latices were allowed to equilibrate separately for 24 h at a PVA concentration (250 p.p.m.) equivalent to the plateau in the adsorption isotherm5 (see above).The ionic strength of each latex was then adjusted to the required level and 1 cm3 of latex A (lo9 particles ~ m - ~ ) added to 9 cm3 of latex B or C (at various particle concentrations in the range 5 x lo9 to 2.5 x loll particles cmm3) in a 10 cm3 Pyrex centrifuge tube (which had been previously treated with dichlorodimethylsilane, as referred to above). The tubes were allowed to stand for 24 h and then placed in an M.S.E. bench centrifuge at 100 g for 60 min, followed by 1000 g for a further 30 min. This procedure was shown to correspond to the optimum conditions for separating the large particles from the free, small particles. No increase in adsorption was observed at larger equilibration times, up to 1 week.The equilibrium concentration of the small particles in the supernatant was298 HETEROFLOCCULATION determined by measuring its optical density at a wavelength of 500 nm in a Pye-Unicam SP1800 spectrophotometer. In some cases the reversibility of the adsorption was investigated. After the centrifugal separation procedure described above, most of the supernatant phase was carefully removed with a pipette and its volume recorded. An equivalent volume of aqueous solution, at the corresponding electrolyte and PVA concentrations, was then added. The sedimented particles were redispersed by end-over-end rotation of the centrifuge tubes for about 1 h and then the centrifugal separation procedure repeated. The new concentration of the small particles in the supernatant phase was measured and the amount of adsorption recalculated.SCANNING ELECTRON MICROSCOPY This was carried out on a Jeol JSM-35 scanning electron microscope. Samples were prepared under similar conditions to those for the corresponding adsorption isotherms, except that the centrifugation was carried out in Hopkins vaccine centrifuge tubes which have a capillary attachment into which the sediment settles. The plug of sedimented particles was recovered, freeze-dried and sputter-coated with a layer of gold. RESULTS Fig. 1 shows the effect of electrolyte concentration c on the equilibrium adsorption isotherms of the small positive particles onto the large negative particles, for the case 0,4 0.3 CD 0.2 0.1 0 0.5 1.0 f i X 1 o 3 n x 1 0 ” ~ / particles ~ r n - ~ FIG.1 .-Adsorption isotherms of the small positive particles onto the large negative particles (PVA M = 10 500) as a function of NaCl concentration: 0, 10”; A, 0 , 3 x lo”; D, 0, 10-l; #, 1 mol dm-3 (full lines). The dotted line represents the adsorption of small negative particles onto the large negative particles at 1 mol dm-3, 6 is the fractional coverage defined in the text ; ~1 and n are the equilibrium volume fraction and number concentration, respectively, of the small particles after adsorption. where the molar mass M of the adsorbed PVA is 10 500. The amount adsorbed is expressed in terms of the fractional coverage, 8, as given by 6 = r/rh.c.p., where r i s the number of small particles adsorbed per large particle, and rh.c.p. is the theoretical number of small particles that can be accommodated in a close-packed hexagonal array on the surface of a big particle.On this basis random close packing of the particles would correspond to 6’ = 0.90.9 It can be seen that two distinct types of isotherm occur, at low and high electrolyte concentrations, respectively. At lowB . VINCENT, C . A . YOUNG AND T. F . TADROS 299 electrolyte concentrations the isotherms are of the high affinity type, i.e., there are no small particles left in the continuous phase at equilibrium, that is, when the initial concentration is small. A plateau level of adsorption is reached beyond a certain initial particle concentration. The height of this plateau increases with increasing electrolyte concentration up to approximately 3 x mol dm-3, but never ap- proaches 8 = 1.At higher electrolyte concentrations low affinity isotherms result. These resemble the S-shaped isotherms on the Giles classification for molecular adsorption from solution.lo The range of electrolyte concentrations over which the switch in isotherm shape takes place appears to be very narrow. For example, for M = 37 500, an electrolyte concentration of 5 x lo4 mol dm-3 gives rise to a high affinity isotherm, whereas 6 x lo-" mol dm-3 gives a low affinity isotherm. Hence it is possible to define a critical electrolyte concentration cs at which this transition in isotherm shape occurs. The dependence of c* on M is shown in fig. 2. 1 high 2 4 H FIG. 2.-Log c* plotted against M, where c* is the critical NaCl concentration at which the isotherm changes from high to low affinity.Also in fig. 1 a comparison is made of the adsorption of small positive particles (latex C ) and small negative particles (latex B), of approximately the same size, onto the large negative particles (latex A), at 1 mol dm-3 electrolyte concentration. In both cases the adsorption is of extremely low affinity, but the adsorption of the positive particles still slightly exceeds that of the negative particles. Fig. 3, 4 and 5 show the variation of adsorption with the molar mass of the ad- sorbed PVA, at fixed electrolyte concentrations. At mol drr3 (fig. 3) all the isotherms, over the whole range of M values studied, are of the high-affinity type, whilst at 10-1 mol dm-3 (fig. 5 ) they are all of the low-affinity type. At low3 rnol dmV3 (fig.4) the transition in isotherm shape is again apparent. Fig. 3 and 4 also show the isotherms obtained in the absence of adsorbed polymer, at low5 and mol dm-3 electrolyte, respectively. (No meaningful results could be obtained in the absence of adsorbed polymer at 10-1 mol dm-3 electrolyte because of extensive coagulation of both the large and small particles.) It would seem that 6 is significantly greater in the absence of adsorbed polymer than in its presence, irrespective of M.300 HETEROFLOCCULATION aJ 0.2 0.1 I I I 0 0.5 1.0 $ X 1 O 3 FIG. 3.-Adsorption isotherms at different molar masses of adsorbed polymer: NaCI: A, M = 7000; Ob, M = 10 500; 0, M = 14 000; +, M = 24 000; x , M = 37 500. no polymer. mol drn-3 A, A 0.4 n n U L U n n - - a 0 0.5 1.0 x 1 ~ 3 FIG.4.-Adsorption isotherms at different molar masses of adsorbed polymer: mol dm-3 NaCl: A,M=7000; .,M=10500; 0,M=14000; f , M = 2 4 0 0 0 ; x,M=37500; A, no polymer. The results described above are in broad, qualitative agreement with the scanning electron micrographs shown in fig. 6. Fig. 6(a) is for the case: A4 = 37 500, lO-5 mol dm-3 NaCI and a particle concentration corresponding to the plateau region of the isotherm. There is a fairly even covering of small particles around the big particles, at a coverage which, visually, appears to be in the range 0.34.5. Fig. 6(b) refers to the system: PVA 37 500, 10-1 mol dm-3 NaCl and an equilibrium volume fraction of the small particles around 5 x 10-4. The coverage is very much sparser and the small particles are adsorbed in clusters rather than individual particles.Moreover, the clusters seem to form more readily in the neighbourhood of the contact points between the large particles. Fig. 7 illustrates the typical desorption characteristics of the various systems studied. The results here are for the case M = 24 000. At low5 mol dm-3 no desorption wasFIG. 6.-Scanning electron micrographs of small positive particles adsorbed on large negative particles, with PVA (M 37 500) adsorbed: (0) mol dm-3 NaCl, corresponding to a high affinity iso- therm: (h) lo-' mol dm-3 NaCI, corresponding to a low affinity isotherm. Magnification: 9700 times in both cases.B . VINCENT, C . A . YOUNG A N D T . F . TADROS 301 0 0.5 1 .o + x lo3 FIG.5.-Adsorption isotherms at different molar masses of adsorbed polymer: 10-1 mol dm-3 NaCl: A, M = 7000; 0, M = 10 500; 0, M = 14 000; +, M = 24 000. observed, implying irreversibility. In carrying out the desorption experiments all the free particles could be removed from the " supernatant " phase, without removing any of the absorbed particles. Hence the single desorption point appears on the Q, = 0 axis at the same 8 value as the several adsorption points in the plateau region of the isotherm. At loa3 and 10-1 mol dm-3, however, the isotherms are completely revers- ible, the desorption points lying on the same curve as the corresponding adsorption a3 c c , u n A " W c 0.2 - 0.1 r - J 1 .o d X 1 o 3 0 0.5 a FIG. 7.-Reversibility of adsorption : open symbols adsorption points ; full symbols desorption points.0,0,10-5; &A, El,., 10-1 mol dm-3 (PVA 24000). points. Thus the (Iog c*, m) curve plotted in fig. 2 may also be regarded as the boundary curve between reversible and irreversible adsorption. Fig. 8 shows the electrophoresis results for latex A plotted in the form of the derived zeta potential as a function of log(electro1yte concentration). It can be seen that there is a large decrease in zeta potential, at all ionic strengths, on adding PVA to the bare particles, but it is significant that the zeta potential does not go to zero, even at the highest M value (37 500) and highest electrolyte concentration (10-l mol dm-3) studied. Unfortunately, the level of accuracy of the measurements (& 10%) does not allow one to distinguish clearly any trend of the zeta potential with M, at fixed ionic strengths.302 HETEROFLOCCULATION > E -r, \s \ - I _ -.:i.- ** 90 I I I I I - 4 - 3 -2 -1 log c FIG. 8.--Calculated zeta potentials, (, as a function of log (NaCl concentration, c). A, bare latex; A, PVA 7000; 0, 10 500; 0,14 500; +, 24 000; x , 3 7 500. DISCUSSION In considering the adsorption of small, positive particles onto much larger, negative particles, two sets of interactions have to be taken into account: the inter- actions normal to the interface, i.e., the primary adsorbing forces, and also, the inter- actions parallel to the interface, i.e., the lateral interactions between adsorbed particles. This situation is depicted schematically in fig. 9, for the case of low electrolyte con- centrations ( mol dm-3).Here the extent of the diffuse double layer is comparable to the size of the smaller particles (i.e., K a - 1, at mol dm-3), whereas at high . . L -- FIG. 9.-Schematic representation of the adsorption of sniall positive particles on large negative partictes for the case where the NaCl concentration is mol dnr3; i.e., where l/x (the effective thickness of the electrical double layer) is approximately equal to the particle diameter.B . VINCENT, C . A . YOUNG AND T . F. TADROS 303 electrolyte concentrations, the extent of the diffuse double layer can be neglected with respect to the particle radius ( K a - 100, at 10-1 mol dxr3). In fig. 10 we present the results ~f some calculations to demonstrate the effect of changing ionic strength on the two sets of interactions referred to above.These diagrams are intended to be purely illustrative, since the absolute magnitudes of the interaction energies depends very much on the theoretical equations one chooses to use. Several theories have been proposed, both for the electrostatic interactions - 160 1 1 1 1 1 I I t 1 1 I t 0 2 4 6 8 1 3 0 2 4 6 8 10 ( a ) hJnm ( b ) hlilim FIG. lO.-(a) normal, and (b) lateral interaction free energy curves (G) as a function of particle separation (h), at different NaCl concentrations (mol dm-3), using the equations of Hogg et al.” and Wiese and Hea1yl3 for the electrical double layer interactions, and that of Vold” for the van der Waals interactions, for the case where the molar mass of the adsorbed PVA is 7000.The following data were used: radius of large particles 1600 nm; radius of small particles 100 nm; thickness of adsorbed layer (6) 4 Hamaker constants: particle 7.8 x J; adsorbed layer 5 x J; medium 3.7 x lo-’* J; zeta potentials were taken from fig. 8. The electrical double layer interaction curves are taken as the mean of the calculated results for the constant potential” and the constant charge’j conditions. For simplicity, the steric interaction is taken as a vertical straight line at h = 26. and the van der Waals interactions,15*16 both for flat plates and spheres of varying size and surface potential, and also for the van der Waals interactions for particles carrying adsorbed layers.17-19 There are several problems which arise in trying to apply these theories to the present case, however.For example, in the case of the electrostatic interactions, at short ranges, the results one obtains depend on whether one assumes constant charge or constant potential condition^.^^ Furthermore, in the case of the van der Waals interactions, the dominant interaction, again at close ranges, is that between the two adsorbed layer sheaths : one then has the problem of assigning a meaningful Hamaker constant to the sheath, which is probably of varying segment density anyway. Also at high coverages, clearly multibody interaction theories are required (as in the case with interactions in concentrated dispersions). Nevertheless, the trends with ionic strength that are demonstrated in fig. 10 are informative. The data presented are for fixed molar mass of the adsorbed polymer, i.e., M = 7000.At low electrolyte concentrations strong, lateral repulsions between neighbouring adsorbed particles result and will be “ felt ” at relatively large separations [fig. lo@)]. On gradually increasing the electrolyte concentration, both the strength and the304 HETEROFLOCCULATION range of these lateral repulsions decrease, such that the adsorbed particles can pack closer together. This would explain the initial increase in the plateau height with increasing electrolyte concentration as observed in fig. 1. Also at low electrolyte concentrations the electrostatic interactions dominate the van der Waals interactions. There is a strong primary electrostatic adsorbing force, corresponding to very large values of Gmin [fig.lO(a)], as well as the relatively long-range electrostatic lateral repulsion force, referred to above. This would account for the fact that, at low electrolyte concentrations, one observes high affinity, irreversible adsorption, as well as a plateau level of adsorption significantly less than that corresponding to close packing [see also fig. 6(a)}. On increasing the electrolyte concentration, the eleciro- static adsorbing force and the lateral repulsion force decrease simultaneously, leading to a much shallower minimum in the normal interaction [fig. lO(a)], and to a change from net repulsion to net attraction in the lateral interactions. One suspects that it is this latter effect which is responsible for the change in high affinity to low affinity behaviour in the isotherms, with increasing ionic strength.At low electrolyte con- centrations the net interaction curve is purely repulsive. At some critical electrolyte concentration (>lo-’ mol dm-3 in the case of PVA 7000) a minimum appears in the lateral interaction energy curve, into which particles may weakly aggregate. At even higher electrolyte concentrations ( w 10-1 niol dm-3) the lateral interaction energy maximum has disappeared leaving a substantial energy minimum. This would account for the low affinity, S-shaped isotherms found at the higher electrolyte con- centrations studied and the clustering of the small particles on the surface [fig. 6(b)]. From the results presented in fig. 3 (1W5 mol dm-3) there would seem to be a strong dependence of the plateau level of the adsorption isotherm on the molar mass of the adsorbed polymer, although all the isotherms at this electrolyte concentration are of the high affinity type.The plateau level is higher for the greater M-values. The thickness of the adsorbed layer, 6, increases with M [ref. (3)-(5)] and, intuitively, one would, therefore, expect a decrease in the zeta potential with M , at fixed ionic strength. (Unfortunately, data for the small positive particles is not available as yet and the trends with A4 for latex A, in this region, are not clear, fig. 8.) Assuming this to be the case, however, the lateral electrostatic repulsive forces should decrease with increasing M and thus the particles should be able to pack closer. One could attempt to incorporate the effects of the lateral repulsion force on the packing at the plateau level by plotting the isotherms in terms of a modified 0, based on an “ effective ’’ radius for the small particles (k, which incorporates the electrical double layer), rather than the bare radius of the particles, a.For example, one could take for the effective radius (a + nfrc), where n is an adjustable numerical factor, which is itself dependent on the strength of the lateral electrical double layer repulsion (n 2 1 for high repulsions; n -+ 0 for very low repulsions). mol dm-3 and M = 37 500 (fig. 3) taking n = 1.0 actually gives a 8 value of 1.0, rather than 0.20. Higher values of n are required to “ fit ” the 0 values to 1.0 for the lower molar mass adsorbed PVA results at mol dnr3, reflecting the increase in strength of the electrical double layer repulsion, with decreasing M, as discussed previously.This idea breaks down, however, in the case where no polymer is present at lo-’ rnol dm-3 (fig. 3). An n value of only 0.6 is necessary to fit the plateau value tQ 8 = 1, despite the very much higher lateral electrical double layer repulsion between adsorbed particles. This implies that considerable interpenetration of the electrical double layers is occurring in this case. The necessary work required to achieve this must come from the very large electrostatic attraction between the large negative and small positive particles under these conditions. On the evidence of the electrophoresis For the results atB.VINCENT, C . A. YOUNG AND T. F. TADROS 305 results (fig. 8) one may expect this attraction force to be much greater when there is no polymer present, since the zeta potentials are so much higher, than when PVA (at any M ) is present. At lo-' mol dm-3 electrolyte (fig. 5) the trend in the adsorption values with M is reversed compared with the behaviour at mol dm-3 (fig. 3), i.e., the lower M, the greater 8. This is probably due to the stronger lateral attractions for the lower values of M in this case. At 1 mol dm-3 electrolyte one might have expected, intuitively, that the electrical double layer interactions would be effectively eliminated, and that the van der Waals interactions were the ones controlling the adsorption behaviour. If this were the case one would expect no difference in adsorption of small positive and small negative particles (of the same size) onto the bigger particles.Although this condition is almost achieved (fig. l), there would appear to be still some preference for the positive particles, suggesting that electrical double layer effects, although greatly reduced, are not altogether eliminated. In this paper we have shown how the equilibrium adsorption of small particles into large particles (or flat surfaces) of opposite charge, can be subtly controlled by the pre-adsorption of polymers of varying molar mass, and by adjustment of the ionic strength. Many of the concepts of " molecular " adsorption can be carried over to the case of " particle " adsorption; the same thermodynamic principles hold in both cases.The system studied also has many features in common with the adsorption of polyelectrolytes onto surfaces of opposite charge. In this respect, one advantage of the systems studied here is that the physical dimensions of adsorbing, charged par- ticles, unlike those of a polyelectrolyte, are independent of such variables as ionic strength. A proposed extension in fact of the work described here is to investigate the use of small charged particles as " bridging flocculants " in dispersions of larger particles of opposite sign. It is a pleasure to thank Mr. Cliff Hart of I.C.I. (Plant Protection) Division for taking the scanning electron microscopy pictures, and also the management of that Division for the provision of a research studentship to C.A.Y. and for permission to publish this work. Useful discussions with F. A. Waite and D. W. J. Osmond at I.C.I. (Paints Division) are also acknowledged. See e.g. review by S . Usui, Progr. Surface Membrane Sci., 1972, 5,223. M. Hull and J. A. Kitchener, Trans. Faraday SOC., 1969, 65, 3093. M. J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1974, 49, 57. M. J. Garvey, Th. F. Tadros and B. Vincent, J. CoZZoid Interface Sci., 1976, 55,440. Th. van den Boomgaard, T. A. King, Th. F. Tadros, H. Tang and B. Vincent, J. Colloid Interface Sci., 1978, in press. R. Pelton, Ph.D. Thesis (Bristol, 1977). P. H. Wiersema, A. L. Loeb and J. Th. G. Overbeek, J. Colloid Interface Sci., 1966, 22, 78. R. H. Ottewill and J. N. Shaw, J. Electroanalyt. Chem., 1972, 37, 133. A. Gamba, Nature, 1975,256, 521. lo C. H. Giles, T. H. MacEwan, S. N. Nakhwa and D. Smith, J. Chem. SOC., 1960,3973. 11 0. F. Devereux and P. L. de Bruyn, Interaction of Plane Parallel Double Lnyers (MIT Press, l2 R. Hogg, T. W. Healy and D. W. Fuerstenau, Trans. Faraduy SOC., 1966, 62, 1638. l 3 G. R. Wiese and T. W. Healy, Trans. Furaday SOC., 1970, 66, 490. l4 G. D. Bell and G . C. Peterson, J. Colloid Interface Sci., 1972, 42, 542. D. Langbein, J. Phys. Chern. Solids, 1971,32, 133, 1654, l6 D. J. Mitchell and B. W. Ninham, J . Chern. Phys., 1972, 56, 11 17. M. J. Vold, J. Colloid Interface Sci., 1961, 16, 1. l 8 B. Vincent, J. Colloid Interface Sci., 1973, 42, 270. l9 J. E. Kiefer, V. A. Parsegian and G. H. Weiss, J. Colloid Interface Sci., 1972, 51, 543. Cambridge, Mass., 1963).

ISSN:0301-7249    

DOI:10.1039/DC9786500296

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Some New Aspects of and Conclusions on Theory of Stability of Colloids and their Experimental Verification BY €3. V. DERJAGUIN Department of Surface Phenomena, Institute of Physical Chemistry, Academy of Sciences of the U.S.S.R., 31 kenin Prospect rCn-1, B-312, MOSCOW, 117312, U.S.S.R. Received 2nd December, 1977 This paper considers three aspects of colloid stability theory: phase stability, the stability of disperse composition and aggregative stability in relation to the merits of a direct operational deter- mination of the disjoining pressure. Four components of the disjoining pressure are treated: the dispersion, ion/electrostatic, adsorption and structural terms. The simplest and most general way to derive the second and third components of disjoining pressure is to use the Gibbs-Duhem equation generalized by inclusion of terms corresponding to the electric work of charging the particle interface.The theory of the adsorption component of disjoining pressure explains the stability of free films of some binary solutions demonstrated experimentally by Sheludko and Ekerova. With regard to other aspects of colloid stability we note that flow-ultramicroscopic measurements of the concentration of colloid particles are free from the shortcomings of other methods. This makes accessible the kinetics of slow coagulation of sols (e.g., gold sols) and reveals the role of disaggregation here and in the establishment of aggregative quasi-equilibrium. The measurements of molecular attraction between crossed metal wires as a function of gap width are presented.Colloids differ from true solutions in that they possess a redundant degree of freedom, dispersity. As a corollary, colloids are able to change their state in three main ways: (1) Like true solutions, through separation into 2 quasi-phases that differ from each other in the concentrations of particles and possibly in their locations (periodic structures). (2) In contrast to true solutions, colloid systems are able to change their dispersity through the dissolution of less stable (usually finer) particles and the growth of coarser particles. (3) Also, in contrast to true solutions, colloid systems are able to change owing to the aggregation of particles. Hence, three kinds of stability have to be distinguished; namely, phase stability, disperse composition stability and aggregative stability.Within the framework of this scheme, a special place is occupied by disperse systems such as micellar solutions and microemulsions, which are quite stable from the thermodynamic point of view and may possess simultaneously all three types of stability. Colloid science has long concentrated on aggregative stability because it is dis- turbed most easily and at the highest rate. Development of the theory led to funda- mental changes, not only in the theory of the colloid state, but in adjacent problems of physics, physical chemistry and biophysics related to surface phenomena and forces. One of the first results was substantiation of the repulsion of colloid particles caused by the overlapping of ionic atmospheres.In this connection, it is interesting to elucidate why in the treatment of Langmuir the atmospheres of counterions lead to a decrease rather than to an increase in the osmotic pressure of a colloid system, whereby the ionic atmospheres cause a loss of stability resulting in phase separation.B . V . DERJAGUIN 307 This apparent paradox is explained in the following way: when considering the pair- wise interactions, the concentration of ions around the two particles under considera- tion is assumed to be constant. However, in such a collective effect, when the recipro- cal distances between all particles, and hence their concentrations, vary simultaneously in a similar way, the concentration of counterions in the dispersion medium must also change simultaneously.This is what causes the opposite effect of contraction arising from the ionic atmospheres. As is well known, the theory of the aggregative stability of lyophobic systems was developed on the assumption that the interaction forces between particles are a sum of the dispersion and ionic/electrostatic terms. In early papers, those forces were deduced from a consideration of the distribution of the forces applied to the surface of particles as they approach each otherm2 The same approach is the basis of Lifshitz’ macroscopic theory of dispersion inter- action~.~ In some subsequent papers, the free energy of the system was adopted as the basis, the disjoining pressure being taken as its derivative with respect to distance. The first approach is mathematically simpler ; it also has the advantage of requiring only directly measurable quantities with physical meaning.In this case, the essential point was the fundamental concept of the disjoining pressure4 of thin interlays (of liquids,”gases or even vacuum), where this concept is construed to be the difference between the normal component of the pressure tensor in an interlayer (including the Maxwell tensor and the pressure tensor of an electromagnetic fluctuation field) and the isotropic pressure in a bulk phase, the interlayer being the continuation (or the offspring) of that p h a ~ e . ~ * * ~ This definition is of an operational character, directly indicating the method of measuring the disjoining pressure. Only if such a definition is available, is it possible to impart physical meaning to the relationship between the disjoining pressure and free energy.Exhibiting as it does this general character, the disjoining pressure may be applied to a number of general problems, not only of the equilibrium, but also of the hydrodynamics of thin interlayers, independent of the specific nature of the effects and the particular formulae defining the disjoining pressure. The concept is limited by the fact that it cannot be applied in a strictly quantitative manner to systems, in which the radii of curvature of particles are either commensurate with or smaller than the thickness of interlayers, at which the overlapping effects arise, and which cause the appearance of the disjoining pressure. From the conceptual standpoint, disjoining pressure presents advantages over the notion of the interaction force of particles or phase boundaries that are separated by thin interlayers.Indeed, the very concept of the force implies the existence of points to which the force has been applied, such points being located in material bodies. Now one asks what points of application of repulsion forces can be imagined for the equilibrium of a free film between two bubbles filled by infinitely rarefied gases (at a low volatility of the film)? As applied to the theory of stability, one recognises various components of the disjoining pressure, such as dispersion, ionic/electrostatic, adsorption and structural terms. In this case, in order to derive the second and the third components, the most general, strict and simple method will be to use the generalized Gibbs-Duhem equation represented in the form : I where G is the thermodynamic potential including terms --a,yl and -o2y2, where (iL and (iz are the charges on the internal surfaces of two plates that are separated by a308 NEW ASPECTS OF COLLOID STABILITY THEORY plane-parallel interlayer having thickness d ; ly, and ‘y, are the potentials at the surfaces of the plates; Ti are the adsorptions of the components dissolved in the interlayer (taking into account the overlapping of diffuse adsorption layers), pi are their chemical potentials, S the entropy, T the temperature and p the pressure.Assuming dT = 0, dp = 0, dp, = 0, dly, = 0, we are able to write: From this equation and the Poisson-Boltzmann equation, it is easy to derive the classi- cal expression ne as a function of tyl and the intensity of electric field El at an interface of the interlayer: where D is the dielectric permittivity, k is the electron charge, k is the Boltzmann constant, 2, and 2, are the charges of the ions, yn, and yn2 are their respective con- centrations.The first term on the right of eqn (3) expresses the ponderomotive force of electric field; the second term, the excess hydrostatic pressure. For binary solutions of nonelectrolytes, the new result may be obtained from eqn (l), assuming7 dT = 0, dp = 0, dy, = 0, dly2 = 0: On integration, an approximate formula can be obtained : I7, + 2kTC, exp - A [(”)” + (d - d)-3] - kTC,{exp ($-3 + I}. (5) kT 3 Here n, is the dispersion component of the disjoining pressure for the case of a pure solvent (Coo = 0), Coo is the concentration of the dissolved substance in the bulk phase whose part is constituted by the interlayer; 6 is the cutting-off parameter which, in order of magnitude, is equal to the diameter of dissolved molecules.A is the constant in the expression V(X) = A[JG-~ + (d - x ) - ~ ] (6) for the effective dispersion interaction of the molecules dissolved in the solvent, with the phases separated by the interlayer, at the distance x from one of them. In accordance with the calculations of Derjaguin et aL8 where el, E,, c3 are the dielectric permittivities as functions of imaginary frequency i t of concentration C, substrates and solvent, respectively. According to Dzyaloshinskij et aL9 Analysing the formula derived for enables one to come to following conclusions.B .V . DERJAGUIN 309 At large values of d (weak overlap of diffuse adsorption layers), the adsorption component ITa, which is proportional to C,A, may have either a negative or a positive sign. In the second case, given certain dielectric properties for the system, that component may overweigh a negative disjoining pressure, IT,. As the value of d decreases, there can occur transitions in the value II, whether from the negative value to the positive one, or vice versa. The signs may also be reversed. For the simpler case of a binary solution interlayer between two gaseous volumes, for large values of d we obtain the film stability condition (I7 > 0) in the form: Thus, the stability of such a free film requires that the dissolved substance reduces the dielectric permittivity of the solvent to a considerable degree.This conclusion provides an explanation of the stability of free films of butyric acid solutions in water, observed by Sheludko and Elcserova.10 Now, passing over to considering the role of the structural component of the dis- joining pressure n$ in the stability of disperse systems, the absence of a general theory will have to be taken into account: experimental findings must form the basis of the argument. The structural component of the disjoining pressure is indicated by the form of the isotherm of the disjoining pressure of multimolecular adsorption (wetting) layers of water on silicate surfaces (e.g., glass, fused quartz).ll At the greater thicknesses that result from the thinning out of aqueous interlayers @-films) under an air bubble, the disjoining pressure isotherm is well represented by the formulae corresponding to the ionic/electrostatic component.However, after considerable thinning out or break down of an interlayer, or when the multimolecular adsorption of water vapour is observed to develop, thinner a-films (d < 100 A) are obtained. The disjoining pressures of these films cannot at all be represented as the sum of the dispersion and the ion/electrostatic components. At a certain thickness of the film (of the order of 50 to 70 9.) the disjoining pressure of cc-films reverse in sign, becoming negative at greater thicknesses.l2 Now, above 65 to 70 "C, a-films become monolayers: the multimolecular bound- ary layers having a structure which is different from that of the bulk phase then disappear.13 In Peschel's measurements l4 of the disjoining pressure of liquid interlayers between quartz surfaces, the influence of the structural component of the disjoining pressure is noticeable, too.There are also studies available, which serve to emphasise in a number of cases that, in order to explain the coagulation phenomena, the structural component of the disjoining pressure must be used as a basis. For example15 with adsorption of some hydrophilizing tensides, the thresholds for coagulation by indif- ferent electrolytes increase dramatically and practically cease to depend on the charges of the counterions. In this case, it has been additionally shown that the coagulation is not caused by a decrease in the adsorption of tensides under the influence of electrolytes.Most extensively used methods for the examination of coagulation kinetics are quite unsuitable for comparisons with theory; for they either yield readings (such as light scattering) which are only indirectly connected with the concentration of colloid particles (including the aggregates) or (e.g., Coulter counters) they are able to measure concentrations of the order of 1O'O to 1011 only after tremendous dilution (by millions of times). We have suggested a flow ultrarnicroscopy scheme16 which is free3 10 NEW ASPECTS OF COLLOID STABILITY THEORY from such disadvantages and enables one to measure the particle concentrations directly, rapidly and without dilution, iiicluding those for highly-dispersed red sols of gold.Application of this method enabled us to observe the slow coagulation kinetics as a function of the inverse concentration of particles plotted against time: the plot is not linear and has a horizontal portion (or portions).10 This indicates that temporary stationary states are established, corresponding to disaggregation processes counter- balancing aggregation processes. At a particular stage, a new increase in the coagu- lation rate begins, attributable to the formation of coarser aggregates (for example, made up of three and more instead of two particles). In such aggregates, the bonding energy per particle is higher owing to the greater number of neighbours present. By analogy with the phenomenon of nuclea- tion in the formation of a new phase (personal communication from G.A. Martinov), one must accept that the critical nucleus of coagulum formation contains only three to four particles even in the cases where the coagulation rate and, hence, super- saturation are very small. Sometimes, even the rapid coagulation may terminate with the establishment of a quasi-equilibrium, at which the number of aggregates ceases to increase. It is then probable that the depth of the potential well is small owing to the structural component of the disjoining pressure. It is possible that such a component can exist for the red sol of gold because of the adsorption of organic substances, attendant on the Zsygmondy preparation method. Aggregate formation may be facilitated by a reduction in the potential barrier, as compared with ordinary estimates, owing to the discreteness effect. It has been shown by Muller and myself,l* that even at the zero charge of two dense layers of ions that have been adsorbed in a nonlocalized manner on two neighbouring surfaces, the effect of discreteness causes the attraction at close distances.There is an important connection between the dispersion component of the dis- joining pressure and the stability (or rather instability) of colloids. With this in view, it is a pity that the Lifshitz theory for the case of two metals" remains still to be verified. It is the opaqueness of metals which hinders the application of optical methods and prevents measurement of the molecular interaction of two metals in air and in liquids.However, a new improved variant of applying negative feedback to the measurement of molecular attraction of macro-objects allows one to dispense with direct measurement of distances. Recall that in the early studies the negative feed- back performed two functions; it stabilized the gap between the two bodies, and thus compensated for the influence of the molecular attraction force to be measured according to the automatic compensation scheme.20 In the studies of Rabinovich and coworkers,21 the feedback performed yet a third function ; it permitted two objects-two crossed threads that are initially in contact-to be drawn apart to a preset distance. The ultimate separation was not measured but preset. This method was applied to the measurement of attraction forces, whether between quartz threads or platinum or gold.Fig. 1 represents the interaction force F(d) calculated in terms of the interaction energy of planparallel surfaces per unit area, U(d), as a function of distance d. The scale on the axes is logarithmic. The formula connecting F(d) and U(d) is as follows: F(d) = 24R1Rz)* U(d) where R1 and R2 are the radii of the threads. * The chromium-quartz case was studied experimentally, and the theory confirmed at an earlier date.lgB . V . DERJAGUIN 311 0 0 0.5 1 10 20 30 50 100 log ( h x 107 crn 1 I I I I I h l nrn FIG, 1 .-Dependence of the energy per cm2 of the molecular attraction of plane-parallel surfaces, U, on distance, h. (a) @, quartz; (b) 0, platinum; (c) e, gold. Thus we observe, in accord with theory, at distances where the interaction is fully retarded, the interaction energy, U(d), obeys a theoretical relationship : B 3d3’ U(h) = - where the constant B is the same for all metals.The experimentally obtained values of B for gold and platinum are close to each other, and equal to B = 10 x erg cm, which agrees, within the error limits, with the theoretical value of B = 13 x erg cm. energy follows the law At lower values of d, corresponding to nonretarded interaction, the interaction A 1 2nd2 U(d) = -. Within this range of distances, in accord with theory, the constants for platinum and gold differ from each other. In the case of gold, the experimental constant A > 2.3 x erg; whereas for platinum, A = 2.0 x 10-l2 erg. For gold, the theoretical value of A x 3.6 x 10-l2; but for platinum the theoretical value of A is unknown.The same graph plots the results of measuring freshly-drawn quartz threads. In this case, because of the near atomic smoothness of the surfaces, we succeeded in obtaining measurements to still smaller distances. Under these circumstances, the transition between the retarded and the nonretarded interaction is distinct. For quartz, the experimental value of A = 0.5 x 10-l2 erg, is close to the theoretical312 NEW ASPECTS OF COLLOID STABILITY THEORY A = 0.8 x erg cm compares well with the theoretical value B = 0.6 x This technique was also applied by Rabinovich21 to the measurement of the dis- joining pressure as a function of thickness for quartz and glass threads in aqueous solutions.As in Israelachvili's the results of measurements made in dilute KN03 solutions proved to be in good agreement with the DLVO theory; certain deviations may be attributed to the influence of the structural component of the dis- joining pressure, l7,. erg; the experimental value of B = 1.0 x erg cm. I. Langmuir, J. Chern. Phys., 1938, 6, 873. B. V. Derjaguin, Izuesl. An S.S.S. R., Omen, Ser. khirn., 1937, 5, 11 19; Trans. Faraday SOC., 1940, 36, 203, 730. E. M. Lifshitz, Zhur. eksp. teor. Fiz., (J.E.T.P.), 1955, 29, 94. Zhur. (Russ)., 1955, 17, 149. B. V. Derjaguin, Colloid Polymer Sci., 1975, 253, 492; Koll. Zhur. (Russ), 1976, 38,438. B. V. Derjaguin, Koll. Zhur. (Russ.), 1977, 39, 6. ' E. L. Mackor, Rec. Trav. Chim., 1951, 7, 10; S. G.Ash, D. H. Everett and C. Radke, Tram. Faraday SOC., 1973, 69, 125; B. V. Derjaguin and N. V. Churaev, J. Colloid Interface Sci., 1977, 62, 369. B. V. Derjaguin, I. I. Dzyaloshinski, M. M. Koptelova and L. S. Pitaevsky, Disc. Faraday SQC., 1965, 40, 246. I. E. Dzyaloshinsky, E. M. Lifshitz and L. P. Pitaevsky, Uspekhi Fiz. Nauk, 1961,73,381. Univ., 1959/1960, 54, 305 (Sofia, 1961). Interface Sci., 1974, 49, 249. ' B. V. Derjaguin and M. M . Kusakov, Acta Physiochirn. U.R.S.S., 1939, 10, 25, 153; Koll. lo A. D. Sheludko and D. Ekserova, Izvest. khim. Instit. Bolgarsk. AN, 1959,7,105; Godish. Sofii. l1 B. V. Derjaguin and N. V. Churaev, Doklady Akad. Nauk S.S.S.R., 1971,207, 572; J. Colloid l2 B. V . Derjaguin and Z. M. Zorin, Zhur. jiz. Khim., 1955,29, 1010, 1755. l3 G. F. Ershova, Z . M. Zorin and N. V. Churaev, Koll. Zhur. (Russ.), 1975,37, 208. l4 G. Peschel and P. Belouschek, Pvogr. Colloid Polymer Sci., 1976,60, 108. Ju. M. Glazman, Disc. Faraday Soc., 1966, 42, 255. B. V. Derjaguin, J. Colloid Interface. Sci., 1962, 17, 605. l7 B. V. Derjaguin and N. M. Kudryavzeva, The Law of Mass-action (Det. Norske Videnskaps- Akad, Oslo Universitetsforlaget, Oslo, 1964), p. 79; Doklady Akad. Nauk S.S.S.R., 1974, 216, 1319; Koll. Zhur. (Russ.), 1970, 32, 167. '* B. V. Derjaguin and M. M . Muller, Dolclady Akad. Nauk S.S.S.R., 1975,225, 3; Koll. Zhur. (Xuss.), 1976, 38, 6. l 9 B. V. Derjaguin and I. I. Abrikosova, J. Phys. Chem. Solids, 1958, 5, 1. 'O B. V. Derjaguin et al., Disc. Faraday Soc., 1954, 18, 24, 181, 198, 211, 215. 21 B. V. Derjaguin, Ya. I. Rabinovitch and N. V . Churaev, Nature, 1977,265, 520; Nature, Phys. 22 Ya. I. Rabinovich, Koll. Zhur. (Russ.), 1977, 39, 6. 23 J. N. Israelachvili and B. W. Ninham, J. Colloid Interface Sci., 1977, 58, 14. 24 B. V. Derjaguin and N. V . Churaev, J. Colloid Interface Sci., 1978, in press. Sci., 1978, in press.

ISSN:0301-7249    

DOI:10.1039/DC9786500306

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. A. Vrij (Utrecht) said: On page 1 of their paper Everett and Stageman men- tion that preliminary experiments carried out by Dr. R. Bown indicated that the former approach (charge stabilization and dipolar repulsion I presume) was unpromising. Could you elaborate on this? Prof. D. H. Everett (Bristol) (communicated) : We did not expect charge stabilisa- tion by ionisation of surface groups to be effective in media of low dielectric constant. We did, however, consider the possibility that dipolar repulsion, for example, between OH-groups of adsorbed alcohols, might confer stability. Preliminary experiments in which gas mixtures of lower aliphatic alcohols and Ar or CH4 were co-condensed rapidly on various fine powders, and subjected to ultrasonics, appeared to give colloidal dispersions.However, similar dispersions were formed without ultrasonic treatment, when the gas mixtures were condensed alone : they were, presumably, dispersions of solid alcohol particles (microcrystals ?) of colloidal size. These appeared to flocculate slowly, the turbidity showing an exponential decrease with a half-life of about 40-60 min. The temperature dependence of the rate constant correlated with the viscosity change of the medium. No further experiments on these systems were carried out when attempts to prepare sterically stabilised dispersions were successful. Dr. B. Vincent (Bristol) said: I would like to emphasise two features of the results presented by Everett and Stageman, which we have also found1 for aqueous systems, i.e., neutral polystyrene latex particles, carrying terminally-anchored poly(ethy1ene oxide) chains, dispersed in aqueous electrolyte solutions.These are: (i) the non- correlation of the flocculation temperature with the &temperature of the correspond- ing polymer in solution; (ii) the apparent particle concentration dependence of the flocculation temperature (fig. 2 of the paper). Napper2 has reported that in most of his work there has always been a strong correlation between the flocculation tempera- ture and the &temperature and this view has been widely accepted as a general feature of sterically-stabilised dispersions. It would now seem that this condition only holds in the limit of high molecular weight stabilisers. With regard to the particle concentra- tion dependence of the flocculation temperature, I wonder if the authors would care to speculate on the reasons for this, and the theoretical significance, if any, of compar- ing values of the flocculation temperature extrapolated to zero particle concentration.I have in mind here the close resemblance of the " phase-separation " behaviour of sterically-stabilised particulate systems and that of polymer solutions. Prof. D. H. Everett and Dr. J. F. Stagernan (Bristol) (partly communicated): In reply to Vincent, the concentration dependence of the flocculation temperatures can be accounted for qualitatively using the following simplified arguments. We assume (i) that a chemical potential of the following form can be defined for dispersed parti- cles : C .Cowell, R. Li-In-On and B. Vincent, J.C.S. Faraday Z, 1978,74, 337. D. H. Napper, J. Colloid Znterface Sci., 1977, 58, 390.3 14 GENERAL DISCUSSION where c is a concentration variable, perhaps most appropriately the volume fraction of particles, and pesp(T) is a standard potential; (ii) that, to a first approximation, the chemical potential of a particle in a sufficiently large floc can be taken as a constant, Ilevf(T>. If the dispersed particles are in equilibrium with those in the floc at T,, and pelf(Tf) - peyp(Tf) = Afpe = RT, In c. dfp* is the standard free energy change accompanying the addition of a particle to the floc. If, as assumed in our paper, flocculation occurs as a result of a sudden deepen- ing of the minimum in the free energy of interaction of particles (i.e., dfpe) as the tem- perature is changed, then the concentration dependence of Tf is, accordng to eqn (2)’ given by If a(Afpe/T) aT < 0; i.e., if Afpe becomes more negative as the temperature rises, the flocculation temperature is an UFT and aT,/a In c < 0.Conversely, at an LFT a(dfp*/T>/aT > 0 and aTf/a In c > 0. Thus the sign of the observed concentration dependence of the flocculation temperature is correctly predicted. Moreover, the more rapid the change of Afye in the neighbourhood of T,, the smaller the concentra- tion dependence of T,. These arguments indicate that at an LFT dfhe is negative; while at an UFT, dfhe is positive and the negative value of A,pe must arise from a positive entropy change dfs*. These considerations give added point to Vincent’s question as to the validity of extrapolating Tf to zero concentration, which we adopted quite empirically.Eqn (3) suggests that if dfhe is constant, a linear relation between Tf and In c will be found over small temperature ranges, and that the range of thermal stability should expand indefinitely as c + 0. This would be consistent with the view of Long, Osmond and Vincent that at sufficiently low particle concentrations no flocculation should occur, while at higher concentrations singlet particles are in equilibrium with aggregates ; moreover Cowell, Li-In-On and Vincent2 have recently found linear Tf against In c relationships experimentally down to volume fractions of -2 x Although we have not explored the properties of exceedingly dilute dispersions, PCS studies in propane down to volume fractions -2 x show that the UFT for such dispersions is virtually identical with the value extrapolated from visual studies at higher concentrations.If further experiments confirm the absence of a logarithmic divergence at very low concentrations, then this must be attributed to a dependence of Afpe on Aoc size : A,pe must become more negative as the floc size decreases in such a way as to counteract the In c term in eqn (2). If the concentration dependence of ,up is given by eqn (l), then p e y f must become more negative as the floc size decreases. This is the reverse of what simple arguments might lead one to expect, so that more subtle factors would have to be examined. Dr. G. Taylor (Cambridge) and Dr.J. V. Dawkins (Loughborough) said: We have prepared and studied dispersions of polystyrene [PSI and poly(methy1 methacrylate) particles in aliphatic hydrocarbons stabilized by a surface layer of poly(dimethy1- siloxane) [PDMS]. The dispersant used in the preparation of such systems was an J. A. Long, D. W. J. Osmond and B. Vincent, J. Colloid Interface Sci., 1973,42, 545. C. Cowell, R. Li-In-On and B. Vincent, J.C.S. Faraday 1, 1978,74,337.GENERAL DISCUSSION 315 AB block copolymer of PS-PDMS having a narrow molecular weight distribution. The molecular weight of the PDMS block was varied from 2400 to 48 000. Thus, dis- persions of essentially monodisperse polymer particles having diameters in the range 400-47 000 A have been prepared with well-defined surface layers of PDMS.l The surface coverage was conveniently estimated from a silicon analysis of the dried particles.Thus, the mean chain spacing of the PDMS chains was calculated, assuming that each chain was terminally anchored on the particle surface at the centre of a regular hexagon. The mean chain separation was of similar magnitude to the radius of gyration calculated for an equivalent free PDMS chain in solution. Hence, an interaction between neighbouring chains on the particle surface would be expected. 50 40 30 \ &o 20 10 0 t 0 10 20 30 40 50 PDMS molecular weight x loe3 FIG. 1 .-Variation of the hydrodynamic thickness of the PDMS layer (6) with molecular weight; 0 from rheology studies; from surface coverage studies. The hydrodynamic thickness (6) of the PDMS surface layer was estimated from rheology studies, using capillary viscometry techniques similar to those described by Barsted et aL2 Fig.1 shows the variation of 6 with the molecular weight of the PDMS. The PDMS chains have a somewhat extended conformation over that of equivalent free PDMS chains in s~lution.~ Surface coverage studies have also led to an estima- tion of the hydrodynamic thickness of the PDMS layer,3 and the results are in agree- ment with those obtained from rheology (fig. 1). We have studied the stability of these dispersions under conditions of decreasing solvency of the dispersion medium, which was chosen to be a mixture of heptane and ethanol. The solvency was reduced by cooling at a rate of 10" h-l, and the tempera- ture at which flocculation was visually observed was recorded as the critical floccula- tion temperature (c.f.t.).The &temperature for PDMS in the same mixed solvent was determined under similar conditions, using homopolymers of PDMS of a narrow molecular weight distribution. The values obtained for c.f.t. were close to the 8- temperature for PDMS, and were independent of the molecular weight of the PDMS. J. V. Dawkins and G. Taylor, Paper presented at a Symposium of the Macromolecular Group of the Chemical Society, Polymer Surfaces (Durham University, March 1977). S. J. Barsted, L. J. Nowakowska, I. Wagstaff and D. J. Walbridge, Trans. Faraday Soc., 1971, 67, 3598. G. Taylor, PkD. Thesis (Loughborough University, 1977).316 GENERAL DISCUSSION Dr. A.E. Smith (Port Sunlight) said: Vincent has drawn attention to the discrep- ancy between flocculation temperatures and 8 temperatures for some systems. At the Unilever Port Sunlight Laboratory, Dr. Thompson has found that for polystyrene latex carrying adsorbed alkyl ethylene oxide surface active agent, the difference of these two temperatures decreases as the latex particle size decreases. In this case the dis- crepancy seems due to the van der Waals attraction between the underlying latex particles, which itself varies with size. Prof. A. Slberberg (Rehouot) said : The cases here investigated fall into the cate- gory of systems involving irreversibly adsorbed polymer layers. The results illustrate very elegantly that it is the characteristics of the soluble part of the irreversibly at- tached copolymers which now determine what Derjaguin terms phase stability.One has replaced the colloid by a strangely constituted but “ soluble ” polymer mole- cule whose solution stability is essentially determined by the usual Flory-Huggins considerations for this kind of polymer. It f o l l o ~ s that stability in this case is inde- pendent of “ steric compression ” and long range van der Waals attraction effects. This is as was to be expected2 and is indeed implicit already in the Hesselink et aL3 model which demonstrates that “ osmotic ” and not steric repulsion is dominant. Prof. D. H. Everett and Dr. J. I?. Stageman (Buistol) (partly communicated): We have also measured the surface coverage of our ABA block stabilisers on acrylonitrile latices by elemental microanalysis of the dried particles.Although this is probably less accurate than direct silicon analysis, we confirm Taylor and Dawkins’ finding that the mean chain spacing on the particle surface, assuming only terminal attachment, corresponds approximately to the root mean square radius of gyration of an equiva- lent PDMS chain in solution. Our measurements of adsorbed layer thickness, how- ever, gave values considerably larger than those quoted by Taylor for equivalent molecular weight PDMS stabilising chains. These differences may be ascribed either to the different techniques by which the thicknesses were measured, or possibly to actual differences in the surface chain configuration conferred by the AB and ABA structures of the respective stabilisers. Taylor and Dawkins’ observation of close correlation between the LFT and the 0-temperature in mixed solvents is interesting.We have not been able, in our systems, to compare the LFT with &temperatures derived from measurements of the UCST of bulk solutions, since solid polymer separated before the UCST was reached and the LFT seems to be closely related to the approach to this solubility limit. We did, however, observe that the UFT’s of dispersions of latex MM31 and the upper O-tem- peratures became more closely correlated the higher the molecular weight of the alkane, and for n-hexane were virtually identical (see our fig. 1). In agreement with the observations reported by Smith, the difference between the UFT of the smaller latex AN63 and the &temperature of the polymer in propane was much less than that for the larger latex MM31. As indicated in our paper, this re- flects the effect of both the smaller van der Waals forces and the thicker stabilising layer in AN63.We thus believe that a close correlation between dispersion stability and limiting bulk polymer solution phase behaviour may only be expected when the core particles are relatively small, the stabilising layer thickness relatively large, and when the configuration of individual adsorbed soluble chains is not too different from that en- ’ B. V. Derjaguin, paper at this Discussion. A. Silberberg, Puog. Colloid Polymer Sci., 1976, 59, 33. F. Th. Hesselink, A. Vrij and J. Th. G. Overbeek, J. P?iys. Chem., 1971,75,2094.GENERAL DISCUSSION 317 countered in free solution.forces become important. For larger particles and thinner layers van der Waals Dr. C. J. Martin (London) said: In fig. 1 of your paper, all the lower flocculation temperatures (LFT) are lower than the &temperatures of poly(dimethy1 siloxane) (BDMS). Such a lowering could only be attributed to the surface interacting with the PDMS segments, either directly or through the poly(styrene) anchor block of the co- polymer. The magnitude of the difference between the 8-temperature and the LFT would thus be a measure of the magnitude of the PDMS/surface interaction. Have you systematically studied such differences beyond the results presented in fig. 1, for example by changing the anchoring copolymer, using a large range of numbers of PDMS segments attached to the anchor, or using another " stabilising " polymer at- tached to the anchor block instead of PDMS ? Such a study may correlate the differ- ences with either the range of the surface forces or the strength of the binding between the surface and the polymer(s), and perhaps give some confirmation of the origins and range of surface forces suggested by existing theories such as the double layer theory, or the theory of van der Waals attractions.Prof, D. H. Everett and Dr. J. F. Stageman (Bristol) (communicated): In fig. 1 of our paper the UFT values all lie below the upper 0-temperatures of PDMS in the alkanes but the LFT values all lie above the lower 0-temperatures; these latter values are not experimentally attainable in the present systems since PDMS freezes out of solution as a solid before the lower 0-region is approached.This has led us to specu- late that the LFT values are a consequence of the surface attached PDMS molecules freezing out of the alkane and collapsing onto the particle surface. This collapse must be dependent on the nature and molecular weight of the stabilising chains, their rela- tive segment-segment attraction and adsorption forces, as you suggest. We have not yet performed any systematic studies to investigate the specific participation of ad- sorption forces in this process although it is interesting to note from our table 2 that the LFT is affected mainly by the nature of the stabiliser and is relatively independent of the size and nature of the core particle.A more complete study of the factors which affect the location of the LFT would be interesting in its own right, but there may be more direct ways of investigating adsorption forces and their effect on surface attached poly- mer molecules than by observations of colloidal instability. Dr. M. L. Hair (Ontario) said: Everett and Stageman report the preparation and properties of sterically stabilized polymer latex dispersions in liquid alkanes, point out that these latex dispersions exhibit both upper and lower flocculation temperatures and show that these correlate closely with the bulk phase properties of the stabilizing polymer in the same liquid. Although well discussed in the recent literature there are few (if any) systems described in which flocculations at both UCFT and LCFT are due solely to changes in polymer-solvent interaction (i.e.as distinct from, say, surface induced crystallization at LCFT). A system which supports the Everett-Stageman hypothesis, was described by Croucher at a recent American Chemical Society meet- ing. A poly(acrylonitri1e) latex, z0.2 pm diameter, was prepared by dispersion poly- merization techniques in n-butyl chloride in the presence of an amphipathic stabilizer previously prepared by grafting poly(acrylonitri1e) onto poly(or-methylstyrene). The resultant particles are stabilized by the poly (a-methylstyrene) and the stabiliz- ing moiety is grafted to the surface as distinct from being physically adsorbed. M. D. Croucher, Abstract #4, Division of Colloid and Surface Chemistry, American Chemical Society, Anaheim, California, March 13th 1978.31 8 GENERAL DISCUSSION Upper and lower critical solution temperatures for PmMS in tBC have been reported by Cowie and MacEwen.l The close agreement between LCFT, UCFT and 8,, 8= is readily seen from the accompanying table.The experimental accessibility of these temperatures suggests that this system might be useful as a model colloid. system 0 ° K LCFT/K UCFT/K poly (wMS) in n-C4H9Cl 263 412 PAN latices in n-C4H9Cl 254 403 Dr. E . Dickinson (Leeds) said : Arising from the interesting correlation2 between upper and lower flocculation temperatures in sterically-stabilised latex dispersions and lower and upper critical solution temperatures in solutions of the stabilising polymer, Stageman has indicated the need for phase equilibrium data on solutions of poly- dianethylsiloxane in the simple liquids.Dispersion media which might be considered in this context are hexamethyl- disiloxane (HMDS) or tetramethylsilane (TMS): HMDS is the shortest oligomer of the dimethylsiloxane series and its PVT behaviour is ~ell-known,~*~ and TMS, despite having no siloxane linkage, has been shown5 to be the natural “ monomer ’’ of the series. Using HMDS or TMS would be attractive from the theoretical viewpoint since results would be comparable directly with rigorous statistical mechanical theories of monomer (or dimer) + polymer systems. There is also the not inconsiderable practical advantage that both solvents are liquid at ambient temperature and pressure. The pressure dependence of the LCST of HMDS -+ polydimethylsiloxane has recently been investigatede6 Dr.E. L. Neustadter (Sunbury) said: I refer to our paper Mechanisms by which Dispersant Additives Stabilise Carbon Dispersions in Non-Aqueous Media.’ We studied the stabilkation of carbon dispersions in n-heptane with two very differ- ent stabilisers, a poly(alkylmethacry1ate) polymer (BP 45) of mol. wt. 500 000 contain- ing about 1% nitrogen as amine groups and a poly(isobuteny1 succinimide) (PV 30 TEPA) with a PIB chain of wt. average mol. wt. 1250. Ethanol was added as non- solvent to the sterically protected carbon dispersions and the dispersants dissolved in heptane and the critical flocculation volumes (CfV) and theta conditions determined. In the case of the BP 45 stabilised dispersions the ratio of the CfV of ethanol to its concentration in the corresponding theta solvent was significantly greater than unity.The surface density of adsorbed polymer was found to be much higher for the strongly terminally adsorbed FV 30 TEPA than for the BP 45 polymer. In the case of a high surface density of adsorbed polymer, there will be apparent agreement between flocculation conditions and theta conditions because of the logarithmic relationship between the precipitation volume of non-solvent and polymer volume fraction. We consider that flocculation of a sterically stabilised system occurs under condi- tions which lead to phase separation of the stabilising polymer in free solution at the same concentration as that of the adsorbed polymer.This means that there will be a Cowie and MacEwen, Polymer, 1974, 16, 244. D. H. Everett and J. F. Stageman, this Discussion. I. A. McLure, A. J. Pretty and P. A. Sadler, J. Chem. Eng. Data, 1977,22, 372, E. Dickinson, I. A. McLure, A. J. Pretty and P. A. Sadler, Chem. Phys., 1975,10, 17. I. A. McLure and J. F. Neville, J. Chern. Thermodynamics, 1977, 9, 957. P. A. Sadler, Ph.D. Thesis (University of Sheffield, 1971). 1975), vol. 1, p. 323. ’ R. J. R. Cairns and E. L. Weustadter, Proc. Int. ConJ Colloid Surface Sci. (Budapest, SeptemberGENERAL DISCUSSION 319 concentration dependence of CfV and that, in general, flocculation conditioiis will not correspond to theta conditions. Dr. B. Vincent (Bristol) said: I would agree with the general point being made by Neustadter that one should not expect a direct correlation between the critical flocculation concentration of a non-solvent for a sterically-stabilised dispersion and the corresponding &solvent conditions for the stabilising chains, except in special cases.Such cases would be exemplified by the types of dispersion which Napper et a2.l have in the main studied, where the stabilising polymer is a high molecular weight, termin- ally-anchored chain. Presumably the polyalkylmethacrylate (BP 45) stabiliser used in Cairn’s and Neustadter’s work is a random copolymer adsorbed from solution. We have shown,2 as indeed have Napper et aZ.,3 that for those cases where the polymer is adsorbed in a loop/train type of conformation, one can have stability in much worse- than4 solvents.One would not expect any necessary correlation between the thermo- dynamic properties of the polymer at the surface and in solution. In the case of the effectively, terminally-anchored low molar mass PIB stabiliser (PV30 TEPA), again I would think that any correlation of flocculation conditions with &conditions is for- tuitous. Everett and Stageman’s paper at this meeting and our own recent work4 have shown that interactions other than the so-called “ mixing ” contribution to the steric interaction have to be considered when one has low molar mass, high segment density polymer chains at the surface, i.e. the “ volume restriction ” term and the London dispersion forces. Dr. S. P. Stoylov (Soja) said: In his paper Scholten states that it was possible for him to control the occurrence of aggregation by a non-steady birefringence value at constant magnetic field and by trailing decay curve.This is true to some extent only for aggregation provoked by the magnetic field applied. First of all birefringence is not very sensitive to aggregation and secondly aggregation could also be important outside the period of application of the magnetic field on the suspensions. I should like to say that the work of Scholten is an excellent example how essentially new results can be obtained without the utilization of very complicated techniques. It is possible that the application of light scattering, which is more sensitive to aggrega- tion and of electro-optic methods might provide new information. Dr. P. C. Scholten (Eindhouen) said: Aggregates present before the experiments can be detected through their multi-domain behaviour.In the native state (or after demagnetization in a high frequency a.c. magnetic field), the magnetic dipoles of the particles in an aggregate generally form a closed loop, and the net dipole moment of the aggregate is small. After a short exposure to a strong magnetic field (exceeding the switching field HJ, the moments of the particles in the aggregate are aligned and the net moment of the aggregate is large. This shows up as an increased orientability in weak (<H,) fields. It is mainly these existing aggregates that show the field- induced aggregation. Light scattering would indeed provide a sensitive check for aggregation. With magnetic particles, electric orientation is less attractive than magnetic orientation ; one doesn’t ride a donkey when a horse is available.They can also be detected in electron micrographs. l D. H. Napper, e.g., J . Colloid Interface Sci., 1977, 58, 390. R. Lambe, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1978,66, 77. J. W. Dobbie, R. Evans, D. F. Gibson, J. B. Smitham and D. H. Napper, J . Colloid Irzterfuce Sci., 1973, 45, 557. C. Cowell, R. Li-In-On and B. Vincent, J.C.S. Farday I, 1978,74, 337.320 GENERAL DISCUSSION Dr. Th. F. Tadros (Jealott’s HiZZ) said: Do you know the molecular weight of the commercial polymers used in your studies? Have you determined the adsorption isotherms of these polymers and if so is the adsorption irreversible and what is the amount of adsorption ? Dr.P. C. Scholten (Eindhoven) said: Our primary interest was in the thickness of the layers that stabilized these particles in spite of their strong magnetic attraction. Molecular weight distributions and adsorption isotherms were not determined. With nitrocellulose, we found irreversible adsorption of about 3 mg mm2. This was also the minimum amount needed for stabilization. Dr. P. C. Scholten (Eindhoven) said: In the practice of stabilizing suspensions and emulsions in apolar media, it is often a mystery why some surfactants work and others don’t. This paper by Doroszkowski and Lambourne is a nice step towards elucida- tion of the relevant parameters. From the data presented, together with the common experience that mixtures of surfactants generally perform better than pure compounds, and that branched or kinked chains are superior to straight ones (e.g., oleic-stearic acid) I have the impression that there is a second requirement.Besides with segments, the outer layer should be packed with entropy. In other words, the randomness in the structure of the chains should make crystallization of single or overlapping layers impossible. Mr. A. Doroszkowski and Mr. R. Lambourne (Slough) said : We agree with Schol- ten’s comment and we should like to take it a little further. We think that not only should the loss of entropy be difficult to attain, on the interpenetration of adsorbed layers (ix., non crystallisation), but that the degree of branching of the adsorbed molecules is such that maximum localised surface concen- tration occurs at maximum inter particulate distance. Dr.H. N. Stein (Eindhouen) said: In fig. 2 of your paper, the logarithm of viscosity is plotted against D-” (D = velocity gradient). (a) Is the viscosity plotted the apparent viscosity (=shear stress/velocity gradient), or some other quantity? (b) Is the plotting of log against D-” based upon a theory which leads to a linear relationship between these quantities for the systems investigated, or is it just an em- pirical approach ? Mr. A. Doroszkowski and Mr. R. Lambourne (Slough) said: (a) Yes, the viscosity plotted is the apparent viscosity. (b) The (log r, D-*) plot is an empirical assessment of flocculation. We have found this approach more suitable than other conventional procedures, e.g., sedimen- tation rate or volume or changes in light scattering properties. However, there are a number of papers relating apparent viscosity with the degree of flocculation of small particles, for example those of Cassonl or Goodeve,2 where the apparent viscosity is considered to be due to a particle volume contribution along with a particle interaction factor.But we have found them insufficient to describe the rheological beliaviour of flocculated dispersions and prefer to use the above approach, provided certain precautions are taken. For instance, the cam- ’ N. Casson, RkeoZogy of Disperse Systenzs, ed. C. C. Mill (Pergamon Press, Oxford, 1959), p. 84. C. F. Goodeve, Trans. Favaday Soc., 1939, 35, 342.GENERAL DISCUSSION 321 parison of the degree of flocculation is only made at comparable disperse phase volumes, and that the continuous phase viscosity is also similar.For if the latter were very different, the energy dissipated at a given shear rate would entail putting in much more work in the case of the higher continuous phase viscosity sample. This would lead to a greater break up of floccules in a given velocity gradient and hence would not be a valid comparison in our assessment of flocculation, which is based on the devia- tion from Newtonian behaviour due to particle flocculation. Dr. J. Visser (Vlaardingen) said: (1) You used two completely different types of proteins: a globular and a fibrous protein having different functions. Could you go into a little bit more detail regarding the consequences for the interpretations of your measurements and say also what one could expect for a random coil protein like P-casein ? (2) Another question I would like to raise is related to the fact that the configura- tion of proteins is strongly dependent on ionic strength, pH, type of ions present and temperature.Did you consider this aspect when changing from pH = 8.9 to pH = 3.5, when diluting your system and when using literature data for interpreting your results ? Dr. A. van der Scheer (Amsterdam) said: (1) The two proteins investigated indeed have different functions in our blood. Albumin for maintaining the osmotic pressure and for many transport functions and fibrinogen for clot formation. It should be mentioned that fibrinogen itself does not formaclot before the so-called a- andb-peptides are split off by thrombin, the remaining molecule is called fibrin and fibrin monomers can polymerise to fibres causing a clot.Most authors place fibrinogen (not fibrin) and albumin both in the class of globular proteins. As can be seen from the instability regions shown in fig. 3 and 4 albumin is much more stable than fibrinogen. In our measurements it is shown that fibrinogen (outside the instability region) gives steric stabilisation at much lower protein concentrations than albumin does (fig. 7 and 9), indicating a stronger adsorption. For other differences between ad- sorbed albumin and fibrinogen layers we want to refer to our published work1 From our calculations and experiments we found a dependence of the reduction of the hydrodynamic interaction by the adsorbed protein molecules on the size of the protein molecules.For a random-coil protein like 8-casein it is very difficult to pre- dict the infiuence on the rate of flocculation (and thus the hydrodynamic interaction. This protein is not structured and, therefore, the size in the adsorbed state may be completely different from that in solution. It is even possible that it unfolds com- pletely upon adsorption at low concentrations, resulting in short tails and loops that hardly produce sensitization and thus hardly give any reduction in hydrodynamic interaction. (2) You are right that these factors influence the configuration of the proteins. The literature data which we used for the size of the protein molecules, however, show that even for the unstable fibrinogen [see ref.(47)-(49)] no major size differences occur at pH values from 5.9-11 at low and high ionic strengths. In our evaluation of the influence of molecular size on hydrodynamic interaction we used VR = 0 indicating high ionic strength. The size of the molecules is only used for experiments at pH = 8.9. So the data may be used in the interpretation. The interpretation of the results which we got at pH = 3.5 indeed do need more information on protein conformation, especially at low ionic strength. A. van der Scheer and C. A. Smolders, J. Colloid Interface Sci., 1978,63,7, and a following paper in the same journal.322 GENERAL DISCUSSION Dr. H. N. Stein (Eindhoven) said: In your paper, the hydrodynamic interaction between two coagulating particles is taken into account by a method introduced by Spielman and Honig et al.[your formula (7)]. In this formula, the distance from the phase boundary enters as the quotient u = R - 2a/a (a = radius of a spherical particle). In the limit of a - co (flat plates), u would become = -2 leading to p(u) = 0 and thus D = 0, irrespective of the mutual distance of the particles. Does the formula imply that the viscosity of the liquid medium becomes very high between two approaching par- ticles, or does it mean that the water cannot easily get away between two approaching particles even if it retains its normal viscosity? In the former case, use of the formula implies a large viscosity at a large distance from the phase boundary, and thus may be used only if we believe in " polywater ", at least near a phase boundary.My question is about the significance of this result. Dr. A. van der Scheer (Amsterdam) said : The formula implies that the water cannot easily get away between approaching particles although it retains its normal viscosity, so we do not believe in " poly water " but in viscous drag. Further you mention the quotient u = R - 2a/2n. The limit of this quotient for a + co is not -2 but 0 because R is not a constant but R = 2a 4- h, where h is the distance between the two phase boundaries and R the distance between the centres of the particles. The diffu- sion coefficient of particles with an infinite radius (a ---t co) is always 0 according to D = kT/6zqa and D(u) = l//?(u) . D also equals 0. It must be quoted here that formula (7) is an approximation of the exact formula for the viscous drag between two approaching equals spheres, as given by Brenner [ref.(37)], which has been tabulated by Honig et al. [ref. (32)]. This formula is valid, independent of particle size and particle distance, and shows the influence of viscous drag on the diffusion coefficient of the particles for motion along the line of centres, contrary to earlier derivations like that of Lorentzl which is only valid for small instantaneous values of a/h. Dr. W . Norde (Wageningen) said: Referring to the paper by van der Scheer, Tanke and Smolders, I would like to make two remarks. First, the authors suggest that at high pH, i.e., pH 8.9, the adsorbed albumin mole- cules have more or less retained their native dimensions, whereas at pH 3.5 albumin would adsorb in a much flatter conformation.From our experiments,2 most clearly from hydrogen ion titrations, we conclude that at pH values away from the iso- electric point (i.e.p.) of dissolved albumin, i.e., pH 4.7-4.8, the structure of the protein molecule changes as it adsorbs on polystyrene. The structural changes at the acid and the alkaline side of the i.e.p. seem to be comparable. This similarity indicates that the extent of structural alteration is primarily dependent on the stability of the structure of the protein molecule in solution, more specifically, on the relative contri- bution from intramolecular hydrophobic bonding to the stabilization of that structure. In the adsorbed state, the requirement of minimum exposure of hydrophobic groups to the aqueous phase does not necessarily involve burying of these groups in the in- terior of the protein molecule, but may also be realized by attaching them to the adsorbent surface.Hence, if under the conditions at which adsorption takes place, the net contribution of the interactions other than hydrophobic interaction would fav- Lorentz, Abh. Theor. Phys., 1907, 1, 23. W. Norde, Proteins at Interfaces, Comm. Agric. Univ. Wageningen 76-6, (1976).GENERAL DISCUSSION 323 our an expanded protein structure, such expansion is likely to occur during adsorp- tion. Obviously, both at the acid and the alkaline side of the i.e.p. the net coulombic interaction favours an expanded protein structure. Second, van der Scheer et al.point to the possible causality between the flat orien- tation of the protein molecule adsorbed at pH 3.5 and the electrostatic attraction be- tween the protein and the latex. From hydrogen ion titrations, we found that on the average the carboxyl groups are closer to the polystyrene surface than the amino groups. This would result in a large positive electrostatic contribution to the Gibbs energy of adsorption if not counteracted by the uptake of cations that are transferred from solution to the adsorbed protein layer. From titration and electrophoresis data, we have deduced that such an ion transfer does occur.1*2 It has also been confirmed by direct experiments (to be published), i.e., by radiotracer techniques using 22Na and by e m . using Mn. Then, accounting for the adsorbed ions, the electrostatic contribu- tion to the overall-Gibbs energy of adsorption is almost independent of pH, provided that the charge density at the polystyrene surface is not too high.It should be noted, however, that these comments refer to maximum saturation of the polystyrene surface by the protein, whereas van der Scheer et al. refer to very low degrees of surface coverage. Dr. H. M. Fijnaut (Utrecht) said: (1) The quantity A in fig. 2 of Lips’ paper is found as the difference between two relatively large quantities, namely the hydrodynamic radius r, of the latex with ad- sorbed polymer and Y, the radius of the pure latex. These radii are found from the measurement of diffusion coefficients. From your experiments you conclude for a maximum in the relation of A against added polymer.Can this maximum be explained by: firstly an increase in A by the addition of polymer, being increasingly adsorbed on the polymer ; secondly, upon further addition of polymer, you have a small number of large particles and a very high number of small particles, giving rise to a small increase in the apparent diffusion coefficient, but a relative large decrease in A ? You need a change of only 2 to 3 % in r, to explain your results . (2) How many photons must you detect in your scattering process to reach the high precision in A permitting the lines to be drawn as is done in fig. 2? Dr. A. Lips and Mr. E. J. Staples (Port Sunlight) (communicated): When first confronted with the unusual behaviour in fig. 2, we had in fact considered the first point raised by Fijnaut.Strictly, the measured correlation function is the sum of two exponentials, one from the slowly moving latex particles and the other from the poly- mer molecules. At fixed latex number concentration, the contribution from the polymer increases with concentration, and at concentrations kg dm-3 it can become significant. Our procedure then was to interpret the correlation function as the sum of two exponentials. An analysis consistent with the observed correlation profile of the polymer solution alone was so achieved. We have in fact done measure- ments at polymer concentrations > 1 x kg dm-3, and these suggest the layer thickness to increase again. We require, however, a much larger number of measure- ments to validate our preliminary findings, and the effect mentioned by Fijnaut is causing us some difficulty.Increasing the latex number concentration is not a solu- tion as excessive multiple scattering then renders the correlation measurement unreli- W. Norde, Pruteins at Interfaces, Comm. Agric. Univ. Wageningen 76-6, (1976). W. Norde and J. LyMema, Roc. Colston Symposium on the Behaviour of Ions in Macromole- 1 x lar and Biological Systems, Bnstol, 1977, (in press).324 GENERAL DISCUSSION able. It is worth also to point out that the necessity to uncouple the sum of two exponentials makes it important to use latices that are virtually free from complications of particle interactions. Regarding the second point made by Fijnaut, there is good reason for expecting a rapid increase in layer thickness in the region of polymer addition, 0.1 to 3 x kg dm-3, in fig. 2: a polymer addition of 3 x kg dm-3 is just sufficient to impart a surface coverage -3 mg m-z which is the expected maximum value.The behaviour in the range, 0.1 to 3 x kg dm-3, suggests that virtually all the added polymer is taken up by the latex particles. In our study so far we have concentrated on the region of negative slope. The results in this region together with the reasonable expectation of the initial increase at lower additions enable us to comment with confidence on the direction of the variation of layer thickness with concentration. The number of photons detected in our scattering process (> 100 per sample time) was indeed high primarily because of the strong scattering power of the latex particles.Photon flux and, relatedly, laser power was not, however, the main determinant of the precision of our measurement. More essential was the use of lasers whose noise content at low frequencies, especially at 50 Hz and multiples, was extremely low. It was also important continuously to monitor the time averaged scattering intensity to ascertain the absence of scattering from adventitious impurities in the cells during periods of data collection. Of course, to maximise statistical accuracy, the usual pro- cedure of taking many repeat samples at high photon flux, and where possible for long experiment times, was strictly adhered to. Dr. Th. F. Tadros (Jealott’s HiZZ) said: Although not mentioned by the authors in their paper, I presume the latex used in their study is the same as used by us.We have already measured the adsorbed layer thickness of the same PVA sample by several techniques including photon correlation spectroscopy. This work which has been published1 was not referred to by the authors. The results we obtained indicated that at concentrations corresponding to the plateau of the adsorption isotherm, the ad- sorbed layer thickness (6) remained constant. The value at the plateau of the iso- therm obtained by three independent methods for the same polymer sample used by the authors agree with each other and are shown below. ultracentrifugation intensity fluctuation slow speed method spectroscopy (IFS) centrifugation 8,hm 32.5 & 5.0 32.7 & 3.0 29.4 We are sure of the IFS measurements as they have been done in two different labora- tories, namely by Dr.P. Pusey (Royal Radar Establishment) and Dr. T. A. King (Manchester University). We are aware of the flocculation problem mentioned by the authors. That is why we have done measurements at concentrations corresponding to the plateau of the isotherm. In this region, there is no evidence of flocculation from the IFS measurements. Moreoever, in this region the latex shows the irides- cence colours which are maintained on centrifugation at 50 g to hexagonal close packed arrays. Thus, the results quoted by the present authors are anomalous and several factors can account for such an anomaly. (1) Non equilibrium: The time quoted by the authors, namely 20 min, is definitely not sufficient for completion of adsorption. Moreoever, the polymer coils rearrange resulting in change of thickness. M.J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Irzterface Sci., 1976,55,440.GENERAL DISCUSSION 325 (2) The polystyrene latex used by the authors has been prepared at least 5 years ago and when left for such a long time, possible hydrolysis of sulphate groups can lead to large changes in PVA adsorption. At least the authors should have checked the adsorption isotherm. (3) There is a large scatter in the data of fig. 2 and the error bars seem to be very large. I do not believe one can draw any line through the points obtained >lom5 kg dm’3. All the results show a much lower 6 than previously obtained by us. (4) The authors did not mention what volume of polymer solution they passed through the millipore filter paper.Experiments in our laboratory have clearly shown significant adsorption of PVA on the filter paper. Again the authors should have analysed their filtrate. One point worth mentioning is the size of the bare latex particles. In a recent papery1 we measured the size of the bare polystyrene latex particles using IFS and compared this with electron microscopy measurements. In that particular case the latex was prepared by dispersion polymerisation. The radius of the latex particles obtained from electron microscope pictures was 118 nm; that obtained from measure- ment of the diffusion coefficient of the particles by IFs was 119 & 1.5 nm. This again shows that the accuracy of 6 obtained by IFS is reasonable even if one uses the radius of the bare particle obtained from EM pictures.Dr. A. Lips and Mr. E. Staples (Port Sunlight) said: Both the polystyrene latex and the PVA sample were the same as that used in the study to which Tadros referred [ref, (l)]. In our view, the claim made by Tadros of having measured the adsorbed layer thickness 6 by three independent methods needs considerable qualification. First, a value of 6 = 29.4 nm was determined by slow speed centrifugation on the assumption that the particles packed in hexagonal close packed arrays. However, ref. (2) clearly indicates that the sedimentation in this particular case was not accompanied by the formation of iridescent structure. The strong sensitivity of the value of 6 inferred by this technique to the type of packing, in the direction of 6 decreasing with increasing randomness of packing, leads one then to expect the true value of 6 to be considerably less than 29.4 A.In principle it could be as low as 17 nm which is of the order of the value we obtain by phton correlation spectroscopy (PCS). In view of its strong sensi- tivity to the mode of packing, slow speed centrifugation can easily be open to mis- interpretation. Even in cases of observed iridescence, a detailed diffraction analysis may be necessary to establish accurate packing fractions. Another technique which Tadros mentions is ultra centrifugation. In this case a smaller latex size was employed than in the slow speed centrifugation measurements and in both his and our light scattering studies.The actual value obtained was 22.6 nm which again is much closer to our values obtained by PCS. Tadros, however, argues that this value needs to be corrected to an “ equivalent thickness ” appropriate to the size of the latex particles used in the light scattering and slow speed centrifuga- tion work. The justification for this large correction, from 22.6 to 32.5 nm, is argued to derive from studies based on PCS. The manner in which these measurements were performed is of some concern to us and even if our reservations prove to be unfounded we cannot agree with Tadros that ultra centrifugation, appearing to require a large correction based on another type of measurement, affords one in this case an independent method of measuring thickness. Our central objection to the work referred to by Tadros is that in none of the Th.van den Boomgaard, T. A. King, Th. F. Tadros, H. Tang and B. Vincent, J. Colloid Interface Sci., in press. M. J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1976,55,440.326 GENERAL DISCUSSION methods described, including PCS, a direct difference measurement was performed. It was assumed that the bare particles were unaggregated and estimates of layer thick- ness were calculated on the basis of the electron microscope diameter of the particles. It is our experience that even freshly prepared latices can suffer from pre-aggregation, the degree of which can be assessed most easily by PCS or by a light scattering method which one of us deve1oped.l The preparation of a truly unaggregated latex is the ex- ception rather than the rule. Now it is obvious that pre-aggregation will distort the estimate of thickness, in the direction of giving much larger values.In view of this, one should be inclined to accept the lowest reported values. In our study we have taken great care to ascertain that the latex, at least at the con- centrations corresponding to the PCS measurement, was virtually free from aggrega- tion. To achieve this, it was essential to subject the latex to careful filtration. We also filtered the polymer solutions prior to adding them to the sols. This step was desirable but not essential as we were able to show that the thickness was unaffected by the filtration of the polymer solutions.We see no possibility of our results, at least those corresponding to high polymer coverage, being anomalous: we have rigorously adhered to a difference method and have shown by low angle light scattering that there is no significant change in particle interaction following the addition of polymer. It is worth considering whether the discrepancy between our conclusions and those of Tadros et al. is the result of differences in the mode of application of polymer to the latex. In our experiments a large excess of polymer was added directly to a very dilute latex dispersion in the scattering cell. In the experiments of Tadros the polymer was added to a relatively large concentration of latex and the system equilibrated for 48 h, the latex was then diluted by a factor of 100 into mol dm-3 electrolyte solution.In our case, equilibration times 220 min were adequate as no significant change in ihickness could be detected on much longer equilibration times (24 h). The justifica- tion for the procedure of Tadros is the observation of negligible desorption of polymer on dilution of the latex; while this may undoubtedly be true on kinetic grounds it has to be recognised that the polymer system is then strictly under non-equilibrium condi- tions. The equilibrium demands that polymer should utimately desorb, and at least an initial response of rearrangement of the polymer on the surface is to be expected. In view of this we would suggest to Tadros that our conditions of measurements are far more representative than his of the equilibria of adsorption.In an attempt to resolve the discrepancy between the results of Tadros and our own, we have measured the adsorbed layer thickness by light scattering using a 0.255 pni polystyrene latex and following both procedures of applying polymer. Direct addi- tion of polymer to a dilute andfihered latex of number concentration -5 x lo8 c ~ n - ~ , to a polymer concentration of -1 x kg dm-3, gave a value 6 = 22 nm. This is close to the corresponding value in our paper (fig. 2) obtained for a larger particle size. The bare particle size of filtered latex was close to the electron microscope diameter. The same value was obtained following the procedure of Tadros provided that the latex was carefully filtered on dilution. The filtration ensured the removal of aggre- gates and rendered more reasonable the assumption of the bare latex size being repre- sented by the electron microscope diameter.When we measured the diffusion coefficients of unfiltered diluted latex in the presence and absence of polymer we ob- tained effective particle sizes which in both cases were -20 nm greater than those measured for the corresponding filtered sols. This clearly shows that aggregated latex particles are not deflocculated by polymer and that it is necessary to employ a direct difference method to obtain a reliable value for the hydrodynamic thickness. A. Lips and E. Willis, J.C.S. Faraday I, 1973,69, 1226.GENERAL DISCUSSION 327 Though the difference method to a large degree overcomes the difficulties caused by pre-aggregation, it is essential for precise measurements to employ latices that are virtually free from aggregation.We note that in the work of Tadros et al. hardly any attention has been paid to the central issue in this type of measurement of hydro- dynamic thickness. In our view, therefore, their conclusions regarding the dependence of layer thickness on particle size should be treated with caution. Prof. R. H. Ottewill (Bristol) said: I should like to comment on the time dependent properties of polystyrene latices found by Lips. It has been our experience with latices prepared using sodium persulphate as the initiator, which therefore have sul- phate groups on the surface, that the latter hydrolyse with time to form hydroxyl groups. Consequently, over a period of years, there can be a substantial loss of charge.Dr. C. A. Young (Bristol) said : Lips reports lower adsorbed layer thicknesses for PVA (Alcotex 88/10} on polystyrene latex particles than reported by Garvey et al.' I I I I I 100 200 300 LOO 500 equilibrium PVA concentration /p.pm. FIG. 1 .-Adsorption isotherms by several workers-see table 1. TABLE DETAILS OF LATICES USED number diameter/nm initiator surfactant purification reference I 236 potassium TI 200 azobisisobutyr. persulphate amidinium chloride persulphate IT1 190 potassium TV 3 30 potassium persulphate none dialysis 2, 3 none dialysis 2 none steam stripping 2 (100 "C); then dialysis 2 sulphate dialysis 1 sodium dodecyl M. J. Garvey, Th. F. Tadros and B. Vincent, J. Colloid Interface Sci., 1974,49,74. C. A. Young, unpublished work.Th. van den Boomegaard, T. A. King, Th. F. Tadros, H. Tang and B. Vincent, J. Colloid Infer- face Sci., 1978, in press.328 GENERAL DISCUSSION It is worth pointing out that the amount adsorbed and, therefore, presumably the ad- sorbed layer thickness, depends strongly on the nature of the latex used. In fig. 1 are collected adsorption isotherms by several workers ; details of the corresponding latices are given in table 1. All isotherms were measured using the method described in ref. (1). It can be seen that the latices prepared without surfactant show a higher affinity for PVA than latex IV which had surfactant present. Even exhaustive dialysis pre- sumably does not remove all the surfactant (a proportion of the sodium dodecyl- sulphate seems to become hydrolysed to dodecanol which is virtually insoluble in water).2 The result is a more hydrophobic surface, leading to lower PVA adsorption. Steam stripping also leads to reduced adsorption.It is not clear at the moment why this is so; possibly some form of surface hydrolysis occurs. Changing the nature of the surface groups from sulphate to amidine does not alter the adsorption significantly. Dr. A. Lips and Mr. E. J. Staples (Port Sunlight) said: Ottewill, Tadros and Young all refer to the problem of loss of surface charge by hydrolysis of polymer latex con- taining sulphate groups. It seems reasonable that this would be accompanied by a decrease in the stability of latices and in changes in the adsorption of polymers such as PVA. More recent measurements in our laboratory of the adsorption of PVA on the latex used in our study has given a value for adsorption at the platea which is in good agreement with the value previously reported by Garvey et aZ.l On the subject of aggregation of latices on storage, we should like to comment that it is our experience that even fresh latices can suffer from appreciable aggregation and that the aggregates are generally extremely stable to dilution forces which suggests that primary minimum forces are implicated.Prof. A. Silberberg (Rehovot) said : A non-monotonic dependence of adsorbed polymer layer thickness for some molecular weight fractions has also been observed by us in the adsorption of polystyrene from toluene onto glass but is probably of different origin.3 The effect occurs at a much lower concentration than here observed and is believed by us to demonstrate the transition from a " tail " dominated adsorbed layer to a " loop " dominated adsorbed layer as the molecular weight increases.Mr. F. A. Waite (Slough) said: This contribution is not only relevant to the paper of Lips but also to those of Lyklema, Smitham and Vincent and to the contributions by the numerous other speakers who have taken part in the discussions relating to the behaviour of PVA at an interface. The Discussion has included several papers in which measurements relating to the adsorbed layer thickness of and steric forces exhibited by PVA at interfaces were described. The results have been discussed in relation to each other and to current theories both of polymer adsorption and steric stabilisation.In order to do this sensi- bly the structure of PVA must be considered very carefully. The material generally referred to as PVA or polyvinyl alcohol is not a homopoly- M. J. Garvey, Th. F. Tadros and €3. Vincent, J. Colloid Interface Sci., 1974,49,74. J. W. Goodwin, personal communication. Z. Riel and A. Silberberg, J. Polymer Sci. in press, also quoted in A. Silberberg, Colloques Internationaux du C.N.R.S. No. 233, PoZym2res et Lubrificution, 1975, p. 81.GENERAL DISCUSSION 329 mer. It is, in fact, partially hydrolysed polyvinyl acetate, the hydrolysis being carried out in such a manner, that the product is a " good commercial surface active polymer ". Herein lies the problem. As Lyklema indicates in his paper the material is a block copolymer.The polymer chains contain blocks of acetate groups which associate with hydrophobic surfaces and blocks, rich in hydroxyl, which remain extended to some degree in the aqueous phase. In order to discuss the behaviour of " polyvinyl alco- hol " at an interface the average number of acetate groups in a block and the distribu- tion of these blocks in the polymer chain must be known. Fractionation of the com- mercial polymer with respect to molecular weight does not alleviate the problem. Although the acetate content of each fraction is rather similar it is not known whether the block size and/or block number change with molecular weight. Since this informa- tion is not available the relevance of the experimental work presented at this confer- ence to the theories of polymer adsorption and steric stabilisation is minimal.Further, comparing the properties of the whole polymer in solution with those of the solvated component of the adsorbed layer does not appear to be justified. At least some of the acetate blocks will be at the surface, effectively in a separate phase, i.e. the chemical composition of the solvated adsorbed layer is not the same as that of the whole polymer. Ottewill said that " polyvinyl alcohol ", as a polymer for study, was far from ideal. Since it is of the essence of current theories of polymer adsorption that the adsorbing species is a homo-polymer, the ideal polymer for related experimental work is a true homo-polymer. On the other hand steric stabilisation, in the practical sense, derives in the main from polymers which are indifferent to the surface but which are attachedl anchored at the surface at one or a few points on the chain.A convenient way of achieving this is to use block or graft copolymers, containing at least one component capable of associating with the surface and at least one component which is indifferent to the surface and is solvated by the medium. Ideally, the structure of such a block or graft copolymer should be known with some degree of certainty. This cannot be said of PVA. Indeed, all that can be said of PVA in this context is that it is cheap and commercially available. Mr. D. J. W. Osmond (SZough) said: Waite has said that cost and availability are the only virtues of" PVA "; I suggest that its popularity may also be because, in many cases, it is the only " homo-polymer " which adsorbs strongly enough to provide any useful degree of steric stability, but the only reason for this is that it is not actually a homo-polymer at all, but a poorly defined amphipathic block copolymer! This suggests that the subject of the adsorption of homopolymers in the absence of any strong anchoring points, as discussed by Fleer yesterday, and as distinct from the analysis of Levine, for example, warrants some further thought.A decade ago, when the subject became suddenly popular in the hands of Roe, DiMarzio, McCracken and so on, the systems studied implied (though rarely stated) that the polymer was in an atherma2 solvent and that the molar volume of the polymer segments and the solvent molecules were very similar. This implies, for all except specially contrived models, that the segment and solvent are chemically similar, i.e., we are normally discussing systems such as polystyrene in ethyl benzene or xylene.At the same time, enthalpies of adsorption per segment of many kT were considered. However, all surface sites not yet occupied by polymer segments are filled by solvent molecules, which have to be displaced for polymer adsorption to occur; but we have just agreed that usually the composition of the two is very similar, so that the net enthalpy of segment-adsorption (after subtracting the work of desorption of the solvent330 GENERAL DISCUSS ION molecule) must tend to zero! Values for the enthalpy of adsorption per segment, large compared to kT, are obviously impossible. Of course, in modern analyses, the thermodynamic quality of the solvent for the polymer is explicitly taken into account (usually via the x parameter) and there is also a correction for the work of solvent-desorption.Yet nevertheless, it still seems desir- able to point out that, although not implicit in the algebra, in the real world these three quantities, the polymer/solvent, the polymer/surface and the solvent/surface enthalpies of interaction, are not totally free and independent variables. Having arbitrarily defined any two, there are, for most physically real systems, severe con- straints on the possible values for the third. As a result, segmentlsurface interaction with net enthalpic gains larger than a small fraction of kT are not usually found for strictly athermal polymer solutions ; equally, reasonable strong adsorption is normally found only in the case of solutions in thermodynamically rather poor solvents, nearer the 0 than the athermal regime.This is of course in accord with common experimental observation. Homopoly- mers are rarely very good steric stabilisers for particles having homogeneous surfaces, but are least bad broadly mid-way between the 8 and athermal limits, the fall-off at one end being due to inadequate solubility as opposed to inadequate adsorption at the other. The point has been made twice already at this meeting; Ottewill has described how the adsorption of polyethylene glycol from water on to polymethyl methacrylate sur- faces is too weak to allow meaningful measurement of the repulsion and Robb has mentioned the feeble adsorption of the higher aliphatic hydrocarbons from their lower homologues in the absence of surface crystalline associations. One therefore concludes that, while the adsorption of ideal homo-polymers at ideal surfaces may well be a worthwhile theoretical and experimental study in its own right, it is not very relevant to the study of practical levels of steric stabilisation.Prof. J. Lyklema and Dr. T. van Vliet (Wageningen) said: Although qualitatively we agree that one must be careful in generalizing results, obtained with block co-poly- mers to random homo-polymers and in identifying polymer properties in solution with those in the adsorbed stage, quantitatively the differences are less than Waite antici- pates.First, the great similarity between properties of adsorbed and free macro- molecules has been proven by us l s 2 for a polyelectrolyte undergoing a conformational transition as a function of pH. The transition range was very similar for the adsorbed and the dissolved polyelectrolyte, and as this range is certainly dictated by subtle details in the spatial configuration, this is a sensitive test in support of conformational analogy. Unless the contrary is proven, there is no reason to assume that PVA would behave differently. Considering the blockiness of our PVA-samples, in our PVAs 205 and 217 the average lengths of the blocks are 10 and 8, re~pectively.~ In the adsorbed state the acetate contents in loops and tails are lower because of preferential adsorption in trains.The crucial question is then what value to assign to a for tails. According to Scholtens’ analysis a in tails exceeds V. in bulk by maximally 0.08. As a occurs in the equation for steric repulsion four eqn (5)] as (a2 - 1) and as u is of the order of 1.1 (table l), this would lead to an uncertainty in the mixing term of the order of 1.7-2.4. The influence on the volume restriction term is zero and the influence on the sum is at most a factor 2. However, inspection of fig. 3 shows that this difference would T. van Vliet and J. Lyklema, Int. Conf. Colloid Surface Sci. (Budapest, 1975), vol. 1, p. 197. T. van Vliet and J. Lyklema, J. Colloid Interface Sci., 1978,63, 97. B. J. R. Scholtens, Meded. Landbouwhogeschool Wageningen, 1977,77,7.GENERAL DISCUSSION 33 1 already be accounted for by allowing 5% more segments to be present in tails, so that this uncertainty does by no means detract from our conclusions.Prof. A. Silberberg (Rehovot) said: Arising from a general comment by Osmond, there is no question but that protection by physical adsorption is optimally achieved by a suitable copolymer, but terminal (covalent) attachment of a highly soluble polymer is best. When I published my first two papers on polymer adsorption in 1962, I already emphasized the independent contribution of polymer solubility as embodied in x and polymer surface interaction as embodied in xs. Not only the athermal case was considered. It was stressed that adsorption is a displacement of an adsorbed solvent molecule by a polymer segment [see eqn (4), (11) and (12) of my present paper].The main burden of my 1962 papers, however, was that xs could be small, of order 1, but in excess of its critical value and adsorption would nevertheless be strong, essen- tially complete. The energy levels e,,, E,, and epo occur both in x and xs but the latter also depends upon E=, and cap. There are thus five quantities involved (four differ- ences) which can vary independently. Solvent power is a guide but not the only reason why xs may be large or small. The second important conclusion of that early paper was that the behaviour of concentrated surface phases was very different from the behaviour of the isolated macromolecules on the surface and that studies of the latter case whether by analytical or by computer techniques, give only the poorest insight into the real case.Treatments such as the one presented by Levine and by Fleer and the earlier work on which they are based have fortunately now moved away from the isolated chain case. A proper understanding of the cases treated by these analyses is thus essential and must logically precede the special theoretical problems created when practically more valuable materials such as special copolymers or surface crystallizable materials, are employed. Dr. J. M. H. M. Scheutjens and Dr. G. J. Fleer (Wageningen) said: In reply to Osmond we would like to point out that the fact that polymers in good solvents can have only very small net adsorption enthalpies per segment does not necessarily mean that no adsorption can occur from good solvents.First, the solvent quality (X-para- meter) and segment-surface interaction &,-parameter) contain in addition to an en- thalpy contribution also entropy terms which are not necessarily the same for the exchange of a segment with sovent in bulk and with solvent on the surface. Secondly, the size ratio between segments and solvent molecules is not unambiguously defined. This also has consequences for the entropy change of mixing and that of adsorption (e.g., if a segment is exchanged against several solvent molecules on the surface) and will generally not be the same for the two cases. Admittedly this last effect cannot yet adequately be accounted for in theoretical treatments, but certainly needs further attention.Finally, the theories for polymer adsorption are not only relevant for steric stabilisation but also for the destabilisation of colloidal systems by polymers. As to Osmond’s point that copolymers are better stabilizers than homopolymers, we mention that at present we are extending our theory to (random and block) copolymers. Results will be reported shortly. Dr. A. Lips (Port Sunlight) said: I agree with most of the remarks made by Waite on the suitability of PVA as a model polymer for studies of adsorption or steric stabilisation. I am little concerned, however, by the appearingly exclusive emphasis which is placed in so many studies on the steric aspect of polymer mediated effects. Polymer bridging by comparison is a relatively poorly researched, let alone quantified phenomenon. We know, however, that homopolymers, under good Solvent condi-332 GENERAL DISCUSSION tions far removed from the theta point, can be excellent flocculants, particularly so at intermediate surface coverage.At the highest surface concentrations achievable with a particular polymer, the osmotic term usually wins but is the bridging contribution then truly negligible. Existing theories and experiment do not really enable one to make a reasonable judgement, and we should not lose sight therefore of the possibility that polymer mediated effects with model homopolymers may be a delicate interplay of competing bridging and osmotic contributions even at fairly high surface concentra- tions, in which case it would not be permissible to discuss measurements in relation to theories of the steric contribution in isolation.Dr. J. F. Padday (Harrow) said: Vincent et al. have indicated in their paper that the adsorption isotherm were indeed reversible and that the same point may be reached first by approaching the equilibrium first by increasing the concentration in solution and then, in a further experiment, by decreasing the concentration in solution resulting in desorption. Have the authors attempted the same reversibility experiments by changing the ionic strength? If so, what results were obtained? Dr. B. Vincent (Bristol) said: Padday has raised a very interesting point. We have recently in fact carried out experiments to determine the degree of reversibility of the high affinity isotherms on changing the ionic strength, at fixed total particle number concentration.To this end we selected the system in which both sets of latex particles were covered with an adsorbed layer of PVA 24 000 and in which the electrolyte con- centration had been adjusted to rnol dm'3 NaCI. Three parallel sets of ad- sorption experiments (a, b and c) were set up. After equilibration, series (a) was used as a control set, in the sense that the previous particle adsorption isotherms was re- established. The ionic strength in series (b) was adjusted to rnol dm-3 by the addition of the necessary quantity of solid NaCl; that in series (c) was adjusted to rnol dm-3 by dialysing against a large excess of NaCl solution at that concentra- tion. In both cases, after re-equilibration, it was found that the adsorption isotherm changed to that found previously for the adjusted electroyte concentration.Thus, at rnol dm-3, which had been previously found to correspond to a low affinity iso- therm, small particles had desorbed from the large particles. Also at rnol d ~ l l - ~ , which had been found to correspond to a high affinity isotherm (but having a lower plateau level than mol dm-3), again desorption of small particles occurred, sug- gesting that the lateral repulsion forces between nearest neighbours are stronger than the normal attraction forces by the large particles in these systems. Thus, one con- cludes that, although, in the case of the high affinity isotherms, the adsorption is apparently irreuersibk when the particle concentration is diminished at the same ionic strength, the adsorption is reversible to changes in ionic strength.Dr. I. D. Robb (Port Sunlight) said: If the slope of an adsorption isotherm changes abruptly or adsorption takes place only above a finite concentration of adsorbate, it implies that the adsorption (at the point of abrupt change) is a cooperative process. Such isotherms are shown in fig. 1 of your paper at higher salt concentrations and it suggests that the small positive particles adsorb in clusters on the large negative ones. Measurements of the flocculation of the small positive particles on their own would determine whether these clusters existed in solution prior to adsorption or whether the surface of the negative particles acted as a nucleating site for the clusters.Dr. B. Vincent (Bristol) said: We detected no flocculation of the small positive latex particles alone in the presence of 10-1 mol dmm3 NaCI, when there was an adsorbedGENERAL DISCUSSION 333 PVA layer on the particle. (However, these particles did coagulate at this electrolyte concentration in the absence of PVA. This point is referred to in the paper). The two-dimensional appearance of the clusters [fig. 6(b)] of small particles on the large particles would also suggest a cooperative adsorption process at the surface, rather than pre-aggregation in the continuous phase. Prof. T. W. Healy (Melbourne) said: I refer to the [c, log (NaCl concentration)] isotherm of fig. 8 for the " bare latex ". The reported potentials at loe2 mol dm-3 are of the order of twice that usually reported for materials similar to latex A of the present paper.Again, one might expect a reduction in [-potential from, say, -40 to -50 mV at to -20-35 mV at lo-' rnol drne3. At such high salt concentra- tions, surface conductance effects will be minimal. Could the authors comment on such anomalously large potentials for bare latex A? Again, if the PVA-coated latex reflects the electrostatic properties of PVA or bound PVA itself, the positive latex colloids coated with PVA might be expected to show [-potentials in 10-2-10-1 mol dmm3 of 3 -10 to -15 mV. Was such an effect observed? Alternatively, did the PVA at high concentrations reverse the sign of the c-potential of positive latex sols ? Dr. B. Vincent (Bristol) said: The electrophoresis data for the large (3 pm) nega- tive bare latex particles shown in fig.8 are, I agree, unusual, in the sense that it is not what one might intuitively expect. However, very similar results have been found by another group at Bristoll working with similar large, high surface density latices. There is, on the other hand, a slow ageing effect in that the zeta potential does drop slowly with time; this is thought to be due to the gradual hydrolysis of surface sul- phate groups. (Latices can suffer from old age!) With regard to the implicit suggestion that PVA itself is charged: there is no ex- perimental evidence for this. Fleer and Lyklema? for example, have made a detailed study of this point. As we report in the paper, it was very difficult to obtain reliable, consistent electrophoresis results with the small positive latex particles, but the data we did obtain always indicated that the zeta potentials of these particles remained positive in the presence of PVA.Since the paper was submitted, however, we have been able to obtain electrophoresis data on small negative latex particles (i.e., latex B in the paper) ; these have a very similar particle size and magnitude of surface charge density to the small positive particles (latex C) reported in the paper. The data are given in fig. 1 shown here. As may be seen, the trends with ionic strength could be considered more " normal ". Moreoever, because of the much higher adsorbed layer thickness/particle radius ratio with this latex, there is now a definite trend of zeta potential with molar mass of PVA (in the direction expected), compared to the case of the larger latex (fig.8). Prof. J. Lyklema (Wageningen) said: In cases like the one studied by Vincent et al., where steric repulsion and double layer interaction are simultaneously operative the electric repulsion equation to be used should be based on interaction at constant Outer Helmholtz Plane (OHP) potential $vd. That interaction should be interpreted at constant potential follows from the rela- tively long interaction times, permitting the double layers to adjust themselves com- pletely. R. Buscall and J. W. Goodwin, personal communication. See e.g., G. Fleer, PhD. Thesis (Wageningen, 1971), p. 20.334 90 r GENERAL DISCUSSION -5 -4 -3 -2 log c FIG.1.4alculated zeta potentials, That, for the potential, Wd should be used and not < is because of the fact that the ions in part of the double layer between the OHP and the slipping plane (or slipping region) are still quite mobile. As a first approximation the ionic mobilities are not influenced at all by the low volume fraction of polymer segments in that layer. In that case the charge distribution would satisfy the unperturbed Poisson-Boltzmann law. The starting point of the diffuse part of the double layer part being the OHP, the potential to be used in the equations is vd. Obviously, it is not easy to find a value for this parameter in the presence of ad- sorbed polymer. It is clearly not justified to use for tyd the electrokinetic potential in the absence of adsorbed polymer because the potential drop over the Stern-layer is affected by the adsorption of train segments.Perhaps the best chance is to obtain 'y, from the effective hydrodynamic thickness d and the electrokinetic potential in the presence of polymer. Equations for this are avai1able.l Dr. B. Vincent (Bristol) said: We would certainly agree that, given the relatively long equilibration times in these experiments, the assumption of constant potential is more valid than that of constant charge for the electrical double layer interactions. However, it is presumably the surface potential that remains unchanged when two charged particles come together during an equilibrium encounter. It is possible that both the OHP potential ( ~ 8 ) and the zeta potential change as the ion distribution in the double layer changes during such an encounter.In the current case the situation is L. K. Koopal and J. Lyklema, Faruday Disc. Chern. SOC., 1975,59,230.GENERAL DISCUSSION 335 even more complex, because it is difficult to define the electrical double layer structure at high coverage of the small positive particles around one large negative particle (cf. the comment by Goodwin and our reply). However, we agree that changes in the OHP potential are likely to be less than those in the zeta potential, and formally, it may be better to use the former in any calculations. We would stress again, on the other hand, that these calculations were meant to be only illustrative and semi-quantita- tive in order to show trends with ionic strength.Exact calculations would need to take account of the many-body nature of the interactions. Dr. J. W. Goodwin (Bristol) said: (a) The results of the calculation of the electrostatic interactions between positively charged particles at a negatively charged surface are shown in fig. 10 of the paper. At low values of rca (e.g., 7ca < 10) this calculation is not as simple as indicated in the paper. For example, if we consider the schematic representation in fig. 9, the over- lapping electrical double layer of the positive particles are existing within the double layer of the negatively charged surface. How was this taken into account in the calculation ? (b) Following Silberberg’s informal comment to Lyklema with regard to the experiments of Brooks and Seaman.It is interesting to note that Brooks, Goodwin and Seaman1 found that the coagulation/redispersion boundary occurred at a critical l,-potential over a wide range of ionic strengths for erythrocytes with adsorbed low molecular weight dextran. Dr. B. Vincent (Bristol) said: Goodwin is quite correct when he asserts that the calculated interaction energy curves shown in fig. 10 may be based on an oversimplifi- cation of the true situation. As we stress in the paper, however, these calculations are only intended as a semi-quantitative guide to the trends in the normal and lateral interactions with ionic strength. The main problem arises, as he points out, at low ionic strengths (corresponding to the high affinity isotherms), at coverages where lateral interactions become really significant (i.e., in particular in the plateau regions of these isotherms).One essentially has a many-body problem (fig. 9 illustrates the 3-body situation). It may prove more profitable to discard the formal division into normal and lateral interactions and to try to calculate instead the free energy change in bringing a small positive particle up to the surface of big particles as a function of separa- tion, and as a function of coverage. Dr. D. B. Hough (Strathclyde) said: The origin in the maximum in the curve of zeta potential against log (NaCl concentration) in fig. 8 for the uncoated polystyrene particles has been questioned. The effect, rather than requiring a physical explana- tion, may be explained in terms of the use of the tabulated mobility data of Wiersema et al.Curves of mobility against log rca at various values of zeta potential, drawn from the tables used by Vincent et al., are shown in fig. 1. If Wiersema’s solutions are accepted as representing the practical system then in this region of K a and under conditions of high zeta potential, where electrical double layer relaxation effects are important, small errors in mobility or 7ca will result in a large degree of uncertainty of derived zeta potential. The mobility data of the authors are superimposed on fig. 1 together with the stated -&lo% error bars. It is observed that the curve of zeta potential against log (NaC1 D. E. Brooks, J. W. Goodwin and G . V. F. Seaman, Biorlzeology, 1974,11, 69.336 GENERAL DISCUSSION I / I I I 1 I I I I 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2 logK a 3 Fro.1 .-Electrophoretic mobilities as a function of log rca for different values of zeta potential (mv) using the tabulated data of Wiersema et al. 0, Experimental points of Vincent et ul. reproduced by permission of the authors. concentration) could in fact be drawn to show a plateau in the region of -110 to - 120 mV rather than a maximum as in fig. 8. A further degree of uncertainty would be similarly introduced if KU of the measured particles is not accurately known. Thus, the natural tendency to measure the mobili- ties of the larger, brighter particles in the field of view will result in the true values of rca being larger than those calculated from the mean particle radius. However, the above conclusions do not explain the excessively large zeta potentials obtained for the uncoated sol particles.Dr. B. Vincent (Bristd) (communicated) : Hough is correct in pointing out the rela- tively large errors in zeta potential values derived from mobility data in this region of Ka. With regard to the ‘‘ excessively large ” zeta potentials he refers to, I would reiterate the remarks we made in connection with Healy’s comment that similar results had been found by other workers. Dr. P. Richmond (Port Sunlight) said: A couple of years ago I was working on theories of wetting. Specifically I was interested in understanding the relation between the adsorption isotherms, onset of multilayer wetting and the underlying intermolecu-GENERAL DISCUSSION 337 lar and molecule-substrate interaction potentials.To analyse the problem I used the Percus-Yevick approximation to handle correlations between the particles and the interparticle potential consisted of a hard core plus a short attraction. By appropriate limiting procedures the range of the attraction was taken to be zero, this enabled an analytic solution to be obtained and isotherms of types I and I11 in the B.E.T. classi- fication were obtained according to the relative magnitudes of the potential para- meters.le2 Replacing the above potential by a more realistic potential will yield other isotherms in addition to types I and 111. Specifically using the appropriate potential, it should be possible to understand the results presented by Vincent, Young and Tadros. It should also be noted that correlation of particles of the sort referred to by Robb (above) are automatically (albeit approximately uia the Percus-Yevick method) included in this treatment.Dr. B. Vincent (Bristol) said: We thank Richmond for bringing his theory to our attention and will certainly look into the possibility of fitting OUT data to his equations. We would just add that we did try to fit the particle adsorption isotherms to the Hill- de Boer equation, in a suitably modified form, following a suggestion by Lyklema. The Hill-de Boer equation, which predicts both type I and type I1 isotherms, is based essentially on a two-dimensional gas model, taking into account lateral interactions on the surface, i.e. in linearised form: ' + In (&@} - In 9 = In Kl + K28 1 - where Kr and K2 incorporate the normal and lateral interactions, respectively.Its application at low ionic strengths is, however, questionable because of the irreversible nature of the adsorption. In the high ionic strength region, non-linear plots were ob- tained. Dr. S. Levine and Mr. I. S. Jones (Manchester) said in part: The question of inter- preting the electrophoretic measurements in terms of the zeta potential when the particles are coated with polymer can be answered, at least qualitatively, by the following simplified theory. We imagine the charged surface of a (large) polystyrene particle to be planar, at potential ( and covered with a polymer layer of thickness d. We use the linear Debye-Huckel expression for the potential in the diffuse layer t , ~ = where IC'~ is the characteristic Debye thickness and z is distance measured normal from the polystyrene surface. On applying a uniform electric field E in the x direction paral- lel to the surface, the electro-osmotic velocity u may be identified with the electro- phoretic velocity.In the region 0 < z < d of the polymer film, the x component of Stokes hydrodynamic equation reads where ,u is the viscosity of the fluid, u the fluid velocity in the x direction, p the diffuse layer charge density, N the number density of segments of the polymer andf the fric- P. Richmond, Phys. Chem. Liquids, 1976,5,251. * P. Richmond, J.C.S. Faruduy 11, 1977,73,251.338 GENERAL DISCUSSION tion coefficient of a segment. This equation follows from Debye and Bueche,' Kirkwood and Riseman' and more recently Felderhof and D e ~ t c h .~ Substituting where E is the dielectric constant, and applying the no-slip condition u = 0 at the boun- dary z = 0, we can write the solution of eqn (2) in the form where u2 = NAp and B is a constant of integration. In the region z > d, we omit the factor Nfu in eqn (2) and so obtain as solution noting that u = U at z =; co. The two constants B and U are determined by applying the conditions that u and duldz are continuous at z = d. This yields the electro- osmotic velocity where Us = -(E4/47r,u) is the Smoluchowski formula. It has been assumed that the diffuse layer charge distribution is not affected by the polymer layer. If we choose a Stokes resistance law f = 6npa where a is the effective radius of a segment, then for typical values a = 1 nm N = 5 x lOI9 (about 5% volume fraction of polymer segments) and 0.1 mol dm-3 of a 1 - 1 electrolyte, u % K.For a > K, U E Use-Kd which means that the shear plane is practically at z = d and the zeta potential calculated from the Smoluchowski formula refers to the outer boundary of the polymer layer. For a < K, U E Use-ad and if further ud < 1 then U z Us and use of the Smoluchowski formula yields the potential at the polystyrene surface. Obviously these are the two extreme cases. Dr. J. W. Goodwin and Prof. R. H. Ottewill (Bristol) (communicated) : Following our recent work on the preparation of monodisperse polystyrene latices of various s i ~ e s , ~ * ~ in the absence of added surface active agents, using as initiators both 2-azo- bis-(2-methylpropamidinium) dichloride and 2-azo-bis-(2 -isopropyliminazolium) dichloride, these latices have been used to study the heterocoagulation of cationic polystyrene latices with anionic polystyrene particles.These studies have included particle size effects and electrolyte concentration effects but have not included the addition of surface active or macromolecular species to the systems. It has been our impression from these studies that lateral interactions between the adsorbed particles are not of great importance. For example, in studies by Mr. S. Cheung using 2 pm diameter anionic polystyrene particles and 0.5 ,um diameter catio- nic particles in dilute electrolyte solutions scanning electron microscopy indicated that the cationic particles invariably close-packed on the larger anionic one.This is illus- P. Debye and A. M. Bueche, J. Chem. Phys., 1948,16,573. J. G. Kirkwood and J. Riseman, J. Chem. Phys., 1948,16,565. B. U. Felderhof and J. M. Deutch, J. Chem. Phys., 1975,62.2391. R. Pelton, Ph.D. Thesis (University of Bristol, 1976). J. W. Goodwin, R. H. Ottewill and R. Pelton, Colloid Polymer Scieirce, 1978, in press.FIG. 1 .-Scanning electron micrographs of the heterocoagulation of cationic latex partic (a) anionic latex particles-full coverage, (6) anionic latex particles-partial coverage, (c) on : glass surface-partial coverage. [To face page 338GENERAL DISCUSSION 339 trated in fig. 1, where micrograph (a) shows the close-packing at essentially full cover- age and (b) the close-packing which occurs even at partial coverage of the surface.It was also found even with planar glass surfaces (negatively charged) and dilute cati- onic latex dispersions that when adsorption occurred the latex particles tended to close-pack in small groups as shown in fig. l(c). Dr. P. Richmond (Port Sunlight) said : The measurements of van der Waals forces between metals are very interesting. Recently Chan and I looked at the problem of van der Waals forces between metal surfaces and found that effects of spatial dispersion in such systems causes the inter- action to deviate from that given by the usual Lifshitz theory? We computed the results for aluminium shown in fig. 1. The dotted line is the result obtained by con- ventional Lifshitz theory. At small separations, the Hamaker ‘‘ constant ” is con- stant; at large separations it drops in magnitude due to retardation. The solid line shows the effect of taking into account spatial dispersion via the dielectric permittivity. Clearly the difference becomes quite marked at distances less than -50 A. At small distances (-4/kF, where kF is the Fermi wavenumber for the metal) we expect our results will start to become inaccurate due to overlap of electronic charge distribu- LO Y d d E LA 1 ‘kF 10 100 1000 separation /A FIG. 1.-Hamaker “ constant ” for aluminium in units of kT. tions. Nevertheless, at this distance, which for our example is 12 A, spatial dispersion has resulted in a 20% reduction in the Hamaker constant. Results for platinum and gold should be qualitatively similar and I would be interested to know if the experi- mental method of Deryaguin can be used to study accurately the small distance regime. Prof. B. V. Derjaguin (Moscow) (communicated) : In deriving the ionic electro- static repulsion using the Gibbs-Duhern equation, let us consider a system made LIP of two parallel metal plates each having an area equal to unity, the metal plates being immersed in an electrolyte solution having a concentration of y mol ~ m - ~ ; the electrolyte contains n1 cations having charges zle and n2 anions having charges z2e, where e is the electron charge. Relative to infinitely remote places in the solution, the potentials of plates y1 and w2 are maintained constant, owing to two sources of electromotive forces and to an electrode which has been placed in infinity. However, this does not alter the fact that a part of the potential (or the whole potential) of each plate is set up by the specific adsorption of ions. D. Chan and P. Richmond, J. Phys. C. : Solid State Phys., 1976,9,153.340 GENERAL DISCUSSION The Gibbs-Duhem equation generalized with due regard to the electric work of charging the interfaces may be written in the following form: dG + S dT - V dp + 2 T'i dpi + I7 dh + 01 dvl + 02 dy/2 = 0, (1) i where G is the thermodynamic potential including terms -cl )y, and -c2y2; I', indicates the adsorptions of ions ; pi indicate their chemical potentials ; S the entropy ; T is the temperature ; h is the gap between the plates, and I7 is the disjoining pressure set up by the overlapping of double ionic layers in the interlayer h. Being interested in the overlapping effects, we shall consider a, and c2 as the charges on the internal surfaces of the plates, whose values depend on h. In a general case, the adsorption values in the system under consideration depend on h. Now, we shall not discuss other, non-electrostatic components of disjoining pressure. From eqn (l), it follows that at T = const, p = const, pi = const, y, = const, In order to calculate a@), it will be necessary to apply the Poisson-Boltzmann equa- tion where a = 81~10 enlz,y, b = e]kT, D is the permittivity of the electrolyte solution; y is the concentration in mol crnB3; x is the coordinate which is read off, the internal surface of plate 1, in the direction of the normal to it. Defining by -C the integra- tion constant (see fig. l), the first integral of eqn (3) gives the following expression: Atx=O,wehavey=y/l,al=- - (9) ; hence it follows: 4~ dx x = o Using a well-known identity: and an obvious relationship (see fig. 1):GENERAL DISCUSSION 341 db h we derive from eqn (5'): From this expression and from eqn (2) and (4'), we obtain by integrating and taking into account that at h = 00, 17 == 0, and owing to eqn (4") C = 0, the well known ex- pression : (9) D 17 = C = kTy[n,(ezlbvl - 1) + nZ(e-Z2bwl - l)] - 8n E: . 8Zb The first term expresses the hydrostatic pressure, and the second one expresses the Maxwell electrostatic tension. We see that the value of 17 derived depends only on the potentials applied to the boundaries of an electrolyte interlayer at the given moment, hence cannot depend on what will occur, when its thickness h varies in a real process nor on the material and the electrical conductivity of plates.

ISSN:0301-7249    

DOI:10.1039/DC9786500313

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

INDEX OF NAMES* Agterof, W. G. M., 101. Buscall, R., 114, 133. Cain, F. W., 33. Cebula, D. J., 76, 122. Clark, A. T., 227. Cooper, W. D., 115, 182. Cornell, R. M., 182. Daish, S. R., 65. Darling, D. F., 190. Dawkins, J. V., 314. Derjaguin, B. V., 306, 339. Dickenson, E., 127,318. Doroszkowski, A , 252, 320. Duckworth, D. S., 288. Dumont, F., 177,185. Everett, D. H., 215,230, 313, 316,317. Fijnaut, H. M., 101,130,323. Findenegg, G. H., 226. Fleer, G. J., 221,226, 331. Frens, G., 146, 175, 177-181. Goodwin, J. W., 136, 138, 182, 184, 189, 335, Hachisu, S., 132. Hair, M. L., 317. Hams, N. M., 76, 125, 126. Healy, T. W., 115, 130, 156, 183, 184, 186-188, Homola, A., 156. Hough, D. B., 335. Hunter, R. J., 156, 186, 187. Israelachvili, J. N., 20, 45, 47-49, 189. James, R. O., 156.Jones, I. S., 337. Joseph-Petit, A. M., 178, 179. Klein, J., 54. Lal, M., 227. Lambourne, R., 252, 320. Levine, S., 44, 134, 202,224, 228, 337. Lips, A., 56,288, 323, 325, 328, 331. Lyklema, J., 25,47,50, 52-54, 175,187,228,330, Martin, C. J., 317. Mewis, J., 58, 114. Neustadter, E. L., 318. Nieuwenhuis, E. A., 101, 123. Norde, W., 322. Osmond, D. W. J., 329. 338. 333. 333. Ottewill, R. H., 33,47, 54,55, 122, 124, 126, 135, Overbeek, J. Th. G., 7, 44, 116, 131, 144. Padday, J. F., 332. Payens, T. A. J., 164,192. Ramsay, J. D. F., 65, 115-117, 119, 137, 139. Richmond, P., 336, 339. Robb, I. D., 219, 332. Robinson, K., 202. Ruckenstein, E., 141, 144, 181. Scheutjens, J. M. H. M., 221, 226, 331. Scholten, P. C., 187, 219, 220, 242, 319, 320. Schoukens, G., 58.Silberberg, A., 44, 51, 55,194,218-220,225,229, 316, 328, 331. Smith, A. L., 179, 316. Smitham, J. B., 33, 53-56. Smolders, C. A., 189, 191, 264. Snook, I., 43, 92, 127, 130, 131, 135, 137. Stageman, J. F., 230, 313, 316, 317. Staples, E. J., 56, 288, 323, 325. 328. Stein, H. I?., 117, 118, 180, 320, 322. Stoylov, S. P., 120, 175, 176, 319. Tabony, J., 76. Tadros, Th. F., 50, 56, 117, 118, 141, 184, 296, 320, 324. Tanke, M. A., 264. Taupin, C., 140. Taylor, G., 314. Thomas, R. K., 76. Thomlinson, M. M., 202. van den Tempel, M., 114. van der Scheer, A., 264,321,322, van Helden, A. K., 123. van Megen, W., 43, 92, 127, 130, 131, 135, 137, van Vliet, T., 25, 50, 52, 53, 118, 330. Verwey, E. J. W., 45. Vincent, B., 50, 187, 296, 313, 319, 332-337. Visser, J., 49, 189, 321. Vrij, A., 101, 120, 125, 137, 138, 141, 313. Waite, F. A., 328. Walstra, P., 53, 190. Watillon, A., 177-179, 185. White, J. W., 45, 49,76, 119-121, 124-126. Whittington, S. G., 127, 218, 228. Wright, C. J., 65, 121. Young, C. A,, 296, 327. 137, 138, 182, 327, 328. * The pages numbers in heavy type indicate papers submitted for discussion. 342

ISSN:0301-7249    

DOI:10.1039/DC9786500342

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Subject Dare 1907 Osmotic Pressure 1907 Hydrates in Solution 1910 The Constitution of Water 191 1 High Temperature Work 1912 Magnetic Properties of Alloys 1913 Colloids and their Viscosity 1913 The Corrosion of Iron and Steel 1913 The Passivity of Metals 1914 Optical Rotatory Power 1914 The Hardening of Metals 1915 The Transformation of Pure Iron 1916 Methods and Appliances for the Attainment of High Temperatures in a Laboratory 1916 Refractory Materials 1917 Training and Work of the Chemical Engineer 191 7 Osmotic Pressure 1917 Pyrometers and Pyrometry 1918 The Setting of Cements and Plasters 191 8 Electrical Furnaces 191 8 Co-ordination of Scientific Publication 1918 The Occlusion of Gases by Metals 1919 The Present Position of the Theory of Ionization 1919 The Examination of Materials by X-Rays 1920 The Microscope: Its Design, Construction and Applications 1920 Basic Slags: Their Production and Utilization in Agriculture 1920 Physics and Chemistry of Colloids 1920 Electrodeposition and Electroplating 192 1 Capillarity 1921 The Failure of Metals under Internal and Prolonged Stress 1921 Physico-Chemical Problems Relating to the Soil 1921 Catalysis with special reference to Newer Theories of Chemical Action 1922 Some Properties of Powders with special reference to Grading by 1922 The Generation and Utiliz+tion of Cold 1923 Alloys Resistant to Corrosion 1923 The Physical Chemistry of the Photographic Process 1923 The Electronic Theory of Valency 1923 Electrode Reactions and Equilibria 1923 Atmospheric Corrosion.First Report 1924 Investigation on Oppau Ammonium Sulphate-Nitrate 1924 Fluxes and Slags in Metal Melting and Working 1924 Physical and Physico-Chemical Problems relating to Textile Fibres 1924 The Physical Chemistry of Igneous Rock Formation 1924 Base Exchange in Soils 1925 The Physical Chemistry of Steel-Making Processes 1925 Photochemical Reactions in Liquids and Gases 1926 Explosive Reactions in Gaseous Media 1926 Physical Phenomena at Interfaces, with special reference to Molecular 1927 Atmospheric Corrosion. Second Report 1927 The Theory of Strong Electrolytes 1927 Cohesion and Related Problems 1928 Homogeneous Catalysis 1929 Crystal Structure and Chemical Constitution 1929 Atmospheric Corrosion of Metals. Third Report 1929 Molecular Spectra and Molecular Structure 1930 Colloid Science Applied to Biology Elutriation Orientation Volume Trans.3 3 6 7 8 9 9 9 10 10 11 12 12 13 13 13 14 14 14 14 15 15 16 16 16 16 17 17 17 17 18 18 19 19 19 19 19 20 20 20 20 20 21 21 22 22 23 23 24 24 25 25 26 26344 Date 1931 1932 1932 1933 1933 1934 1934 1935 1935 1936 1936 1937 1937 1938 1938 1939 1939 1940 1941 1941 1942 1943 1944 1945 1945 1946 1946 1947 1947 1947 1947 1948 1948 1949 1949 1949 1950 1950 1950 1950 1951 1951 1952 1952 1952 1953 1953 1954 1954 1955 1955 1956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 GENERAL DISCUSSIONS OF THE PARADAY SOCIETY Subject Photochemical Processes The Adsorption of Gases by Solids The Colloid Aspect of Textile Materials Liquid Crystals and Anisotropic Melts Free Radicals Dipole Moments Colloidal Electrolytes The Structure of Metallic Coatings, Films and Surfaces The Phenomena of Polymerization and Condensation Disperse Systems in Gases: Dust, Smoke and Fog Structure and Molecular Forces in (a) Pure Liquids, and (b) Solutions The Properties and Functions of Membranes, Natural and Artificial Reaction Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry The Electrical Double Layer (owing to the outbreak of war the meeting The Hydrogen Bond The Oil-Water Interface The Mechanism and Chemical Kinetics of Organic Reactions in Liquid The Structure and Reactions of Rubber Modes of Drug Action Molecular Weight and Molecular Weight Distribution in High Polymers.(Joint Meeting with the Plastics Group, Society of Chemical Industry) The Application of Infra-red Spectra to Chemical Problems Oxidation Dielectrics Swelling and Shrinking Electrode Processes The Labile Molecule Surface Chemistry.(Jointly with the Sociktk de Chimie Physique at was abandoned, but the papers were printed in the Tramuctions) Systems Bordeaux.) Published by Butterworths Scientific Publications, Ltd. Colloidal Elktrolytes and Solutions The Interaction of Water and Porous Materials The Physical Chemistry of Process Metallurgy Crystal Growth Lipo-Proteins Chromatographic Analysis Heterogeneous Catalysis Physico-chemical Properties and Behaviour of Nuclear Acids Spectroscopy and Molecular Structure and Optical Methods gating Cell Structure Electrical Double Layer Hydrocarbons The size and shape Factor in Colloidal Systems Radiation Chemistry The Physical Chemistry of Proteins The Reactivity of Free Radicals The Equilibrium Properties of Solutions on Non-Electrolytes The Physical Chemistry of Dyeing and Tanning The Study of Fast Reactions Coagulation and Flocculation Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions of Tnvesti- Configurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Effects in Inorganic Solids The Structure and Properties of Ionic Melts Volume 27 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 35 36 37 37 38 39 40 41 42 42 A 42 B Disc.1 2 Trans. 43 Disc. 3 4 5 6 7 8 Trans. 46 Disc. 9 Trans. 47 Disc. 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32Date 1962 1962 1963 1963 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1978 1978 GENERAL DISCUSSIONS OF THE PARADAY SOCIETY Subject Inelastic Collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance The Structure of Electronically-Excited Species in the Gas-Phase Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Photo-effects in Adsorbed Species Physical Adsorption in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Radiation Effects in Liquids and Solids Ion-Ion and Ion-Solvent Interactions Colloid Stability Oxidation For current availability of Discussion volumes, see back cover.345 Volume 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

ISSN:0301-7249    

DOI:10.1039/DC9786500343

出版商:RSC    

年代:1978

数据来源: RSC