Polymer-stabilized Free Liquid Films BY J. LYKLEMA AND T. VAN VLIET Laboratory for Physical and Colloid Chemistry of the Agricultural University, De Dreijen 6, Wageningen, The Netherlands Received 12th December, 1977 The equilibrium thicknesses and drainage have been measured of free liquid films, stabilized only by poly(vinylalcoho1) (PVA) or partially esterifled poly(methacry1ic acid)(PMA-pe). The equilibrium thickness of PVA-films considerably exceeds twice the ellipsometric or the hydrodynamic thickness of one adsorbed layer. This is attributed to the dominant steric repulsion of isolated tails, a conclu- sion that is substantiated by theoretical arguments. The change in drainage behaviour of PMA-pe films as a function of pH correlates well with the conformational transition that this polyelectrolyte undergoes in the bulk and in the adsorbed state.Thin liquid films are familiar models for studying colloid stability. Their equili- brium thickness is determined by the same forces governing lyophobic sol stability. In particular, soap films have been used as a tool to study double layer repulsion and van der Waals attracti0n.l” By the same token, polymer-stabilized free liquid films (henceforth abbreviated as polymer films) can be used to study the interaction between adsorbed polymer layers and hence may be regarded as a tool for measuring the force of steric stabilization. This force is not so easy to obtain. Two examples involving dispersed systems are provided by Doroszkowski and Lamboume4 and by Cairns et ul. Publications on polymer films are particularly scanty: Musselwhite et aL6m7 and Graham and Phillipss reported on protein-stabilized films and Sonntagg gave a preliminary report on thickness measurements of aqueous poly(vinylalcoho1) (PVA) films between oil droplets.The scarcity of such contributions reflects the experi- mental difficulties rather than meagre scientific interest of these systems. Below, we describe equilibrium thickness measurements of PVA-films and a few preliminary experiments on films stabilized by the polyelectrolyte PMA-pe [a co- polymer of poly(methacry1ic acid) and its methyl ester]. The PVA-films permit a force-balance analysis. Since these films are rather thick, dispersion forces play a relatively minor role. As double layer repulsion is absent, the equilibrium thickness is determined by steric repulsion and hydrostatic pressure only, allowing the evaluation of the former.Subsequent analysis in terms of a theory of steric stabilization gives information on the distribution of polymer segments over loops and tails, a piece of information that is not readily obtainable otherwise. EXPERIMENTAL METHODS Film drainage and equilibrium thickness measurements have been made on small hori- zontal films, i,n an apparatus which, apart from some modifications, was identical to that used by Agterof and Vrij at Utrecht,lo who in turn based their construction on ideas by Sheludkom2 Films were formed in a glass ring, inside diameter 3.7 mm and width 3.0 mm. The film diameter varied between 1.5 and 3.0 mm depending on the disjoining pressure. Hydrostatic suction could be controlled between 0 and 10 mm water by raising or lowering a containerwith polymer solution, which was connected to the film.The temperature was 25.00 5 0.02 "C. Thicknesses were obtained using the reflection of light. The light source was a Spectro- physics model 155 0.5 mW He-Ne laser, operating at a wavelength of 632.8 nm. The incident light was attenuated by a factor of 100. Photodiodes were Hewlett Packard PIN diodes (5082-4204). The intensity of the reflected light beam was corrected for fluctuations in the laser beam intensity by taking the ratio of the two intensities. Using a chopper and filtering out only that part of the measured signal with the same frequency as that of a second reference signal derived from the chopper, measurements could be performed in daylight.Details of this technique have been given by van Vliet.ll The polymer films were formed by raising the container, placing a droplet of solution in the glass ring, then lowering the container just far enough for the liquid layer in the ring to remain too thick to form a film. At this stage a waiting time of 1 h, except where other- wise stated, was observed. This waiting time is a characteristic variable for polymeric films since macromolecular adsorption is known to be a relatively slow process. Film thicknesses h were determined from the intensity ratio Irb/Irs of the reflected light from the film to that of a silvery film, (that is: a film for which I, is at its first maximum), using the familiar expression Irh I I,, (I + Y ~ ) ~ sin2 A (1- r2)2 + 4r2 sin2 A - _ where Y is the Fresnel coefficient = (nf - no)/(nf + no); nf and no are indexes of refraction of the film material and vacuum respectively, and 2nnfh cos cc 20 A = if cc is the angle of refraction, measured inside the film and lo is the wavelength in vacuum of the light used.Eqn (1) gives the so-called equivalent water thickness, assuming the films to be optically homogeneous water films (nf =n,). However, polymer films have obviously an index of refraction which depends on position in the fiIm, for which a correction must be applied. For an assembly of parallel sheaths of differing thicknesses and differing indices of refraction, Frankel and Mysels have formulated the correction factor.12 Polymer films can be considered as a limiting case with n changing continually.Van Vliet has shown'l that with respect to refraction this situation may to a good approximation be replaced by a block distribution, so that the form of the correction term Ah becomes qualitatively identical to that for classical soap films with no = 1 : However, quantitatively the thickness hl of the equivalent polymer layer exceeds the corres- ponding thickness of a soap film, whereas the index of refraction of this layer, nl, exceeds n, by only a small amount, much less than in the case of a soap film. For nf, the index of refraction of the core, we chose the index of the corresponding bulk solution. The amount of polymer I-',, per surface layer and the thickness of this layer were deter- mined ellipsometrically by Mr.Benjamins and Dr. de Feyter of Unilever Research Vlaard- ingen, Netherlands. The values of n1 and hl were obtained, assuming dn/dc to be a constant for a given polymer. This constant, in turn, was determined in an Abbe refractometer. The low polymer concentration in the heart of the film permitted one to consider the Fresnel coefficient as being independent of h." MATERIALS Two PVA-samples (205 and 2107) were commercial products from Kuraray, Japan; sample PVA-R2 was kindly supplied by Dr. Scholtens of our laboratory. Some characteris- tics are collected in table 1. The M-distribution is rather broad and probably of the Flory- type.13*14 Details of the viscometric molecular weight average determination are given in ref.(1 1); the conformational parameters (r2>*- and o! were obtained, using @ = 2.1 x 1021J . LYKLEMA AND T . VAN VLJET 27 in the Stockmeyer-Fixman eq~ati0n.l~ In order to suppress evaporation the PVA-film measurements were done in 1 mol dm-3 glycerol, which, at least in other cases has been shown to have no measurable effect on h.l0 In 1 mol dmh3 glycerol both (r2>* and a are a few percent lower than in water. TABLE 1 .-CHARACTERISTIC PARAMETERS OF PVA-SAMPLES. r.m.s., end-to- degree of end distance nature of Ac- sample hydrolysis ah. (r")"/nm a distribution 205 88 f 1 42500 20.2 1.06 blocky 21 7 88 f 1 143000 39.2 1.12 blocky R-2 83.4 f 1 149000 35.3 random The PMA-pe sample was manufactured by Rohm AG, Darmstadt, FRG, and available under the trade name Rohagit S, low viscosity grade.Its properties have been described.16 For this polyelectrolyte - lo5; the fraction of ester groups is 0.32, probably random. RESULTS AND DISCUSSION PVA-FILMS Fig. 1 displays equilibrium thicknesses measured under various conditions. These thicknesses are corrected for optical inhomogeneity; Ah in eqn (3) amounted to -2.0 to -3.7 nm, depending on the nature of the PVA. In this figure, each plotted point represents an entirely new experiment, i.e., it applies to a different film, made from a new drop of polymer solution in the ring. Consequently, the uncertainty bars denote the compounded error of inadvertent alterations in the procedure, waiting regime, drainage behaviour, etc., and may be considered as indicative of the absolute accuracy.The effect of waiting time, i.e., the effect of aging of the polymer solution surface prior to film formation, was absent within experimental error for waiting times between 2 min and 2 h, see the inverted (apex down) triangles in the PVA 205, 400 p.p.m. curve. Comparison of the 400 and 4000 p.p.m. curves for PVA 205 shows that a tenfold increase in concentration leads only to a few percent increase in h. The satisfactory accuracy in combination with very good reproducibility, if a given film is measured at several pressures, are strong indications that the stationary states observed are genuinely equilibrium films, that is, films for which the sum of all forces is zero. Below they will be treated in this way. The effects of A4 and the nature of the film material are quite pronounced.An increase in M by about a factor of 3 leads to an increase in h by several tens of a percent. Random PVA R2 gives thinner films than the corresponding blocky sample of the same M, PVA 217; moreover, the random sample is relatively more susceptible to pressure changes. This may be related to the lower adsorption of this particular sample (table 2). The remarkably high equilibrium thicknesses deserve special attention. Table 2 collects other characteristic thicknesses of the PVA samples. The value (hz)* = 0.68 hellips. is the r.m.s. layer thickness according to McCrackin and C o l ~ o n , ~ ~ assuming the decrease in the index of refraction with distance from the surface to be exponential. Obviously, h(P, -+ 0) exceeds twice the thicknesses reported in table 2 by at least a factor of 2.Such thick PVA films have been independently found by Sonntagg (al- though in his case dh/dP, is less) and by Onda in our laboratory.28 FREE POLYMER FILMS 100 90 80 Ec -. .c 70 60 5c 1," \ PVA R2 Y "\ \ 1 PVA 217 I f \ 1 1- 20 LO 60 P, I N m-* FIG. 1 .-Equilibrium thicknesses of PVA-films as a function of hydrostatic pressure. Bulk con- centration 4000 p.p.m. except where otherwise stated. V-Experiments with variable waiting time. In explaining the great difference between h(P,+O) on the one hand and lzellips. and <r2)* (see table 1) on the other, it must be realized that the three techniques involved in measuring these three values '' see " different phenomena: h in films is a measure of the steric repulsion force between two adsorbed polymer layers, helllps.is based on an index of refraction contrast between the adsorbed polymer and the solution and (r2)* is related to the extent of drainage through a polymer coil. The very high values of h in films are in our view due to a few long tails present in the adsorbed sheaths. Such tails would be almost invisible in ellipsometry and probably TABLE 2.-ELLIPSOMETRIC DATA OF ADSORBED LAYERS OF PVA. sample c0nc.lp.p.m. he,l*ps/nm ( h2}*/nm rplmg m-2 PVA-205 400 PVA-205 4Ooo PVA-217 4Ooo PVA-R-2 4000 17 11.6 3.1 21 14.3 3 . 2 29 19.8 3.7 18 12.3 2.0J . LYKLEMA A N D T . V A N VLIET 29 80 exert little effect in increasing the hydrodynamic coil radius in solution. However, their presence is strongly felt by a second polymer layer. If this picture is correct, the equilibrium thicknesses of fig.1 virtually reflect the steric repulsion of terminally- anchored, isolated tails. A rigorous quantitative elaboration of this picture is not yet possible because many of the relevant data are not available. For instance, we do not know how long the tails are, how many there are per polymer molecule, nor what their length distribu- tion is. Even so, the following semiquantitative analysis may be helpful. First, irrespective of any specific model, it is always possible to compute the force of steric repulsion F' for these films from the balance F. + Fh + Fw = 0, where Fh is - -4 I A I 1 1 I " 50 60 70 80 90 h inm FIG. 2.-Cteric repulsion in PVA-stabilized films. Bulk concentration 4000 p.p.m.except where otherwise stated. the hydrostatic force and Fw the van der Waals force, in our case calculated with a Hamaker constant of 4.4 x J, correcting for retardation in the same way as Lyklema and Myse1s.l Fig. 2 gives the results. Integration of these curves produces the interaction energy." Such figures can be useful for testing theories of steric interaction. Below, we undertake a semiquantitative interpretation, based on the consideration that tails dominate the repulsion. For equal tails, Hesselink et aZ.18 derived for the increase in free energy due to volume restriction of an assembly of average tails AV,, = 2 vkTW(i,h) (4) where i i s the average number of segments in a tail and v is the number of tails per unit area. The function W(i,h) is tabulated.18 The corresponding osmotic contri- bution, due to the overlap of polymer layers is formulated by the same authors as 3 1 2 ( ~ 2 - 1)kTv2 (r2)M(i,h) (5)30 FREE POLYMER FILMS where a is the linear expansion parameter.Table of M(i,h) values are available. The quantitative problem is that all tails are not equally long; moreover, it is not known how many there are. At any rate, the tail length distribution obviously depends on the dispersity of the polymer in the adsorbed state. In order to obtain this distribution, we have assumed that it equals the bulk distribution, which is probably of the Flory or " most probable " type, i.e., f ( M ) = TABLE 3 .-NUMBER OF ADSORBED POLYMER MOLECULES IN THE VARIOUS MOLECULAR WEIGHT FRACTIONS weight number of polymer molecules range of M this range PVA 205 PVA 217 fraction in (x 10-15/m-2 )adsorbed in this range 0-M 0.632 57.3 M-2M 0.233 21.1 2M-3M 0.0855 7.75 3M4M 0.03 15 2.85 4M-5M 0.01 16 1.05 5M-00 0.0067 0.61 19.7 7.26 2.67 0.98 0.36 0.21 AMye-AN with y = 0 and A = A.13914 It is given in table 3.Using these data, the steric repulsion energy can be computed, if the number of tails per adsorbed molecule and the fraction X , of the polymer segments present in tails are chosen as adjustable parameters. Fig. 3 gives some characteristic examples. For lack of more detailed information, we assumed Xt to be constant in each M-fraction, this tends to over- estimate the slopes at lower h. However, given the approximations that had to be 14 12 10 E 7 ',& L r- 9 4 2 0 -2 PVA 205 0.60 I 2 PVA 217 0.3511 40 b I n m FIG.3.-Comparison of measured steric repulsion energies with model computations, based on interaction of isolated, terminally anchored tails. Each theoretical curve is indicated by a two- parameter code, the first representing the fraction of each polymer molecule available in tails, the second is the number of tails per adsorbed molecule. The van der Waals attraction is also given for comparison.J . LYKLEMA AND T . V A N VLIET 31 made, a reasonable fit between theory and experiment is obtained. In agreement with expectation, X,(PVA 217) < X , (PVA 205). If there is only one tail per molecule, lower values of X, are needed because in that case this single tail tends to be relatively long, that is: it would contribute relatively strongly to repulsion.The main point we wish to make is that these calculations confirm our conclusion that tails play a dominant role in the steric interaction in PVA-films. In due course our data will be used to test theories of steric repulsion. In connection with this study, recent calculations made by Mr. Scheutjens in our laboratory may be mentioned. This work is an extension of the lattice statistics of polymer adsorption by Di Marzio and Rubin,lg in that self-excluded volumes and polymer-solvent interactions are taken into account. It was found that although the fraction X , is usually to the lower side of the values required in our analysis, the lengths of the tails appear to be considerable, again supporting our main findings. Finally agreement is also obtained with theoretical work by Roe20 and Motomura et aL2’ POLYELECTROLYTE FILMS For PMA-pe in 0.05 mol dmV3 NaCl the drainage behaviour is less regular; firm data on equilibrium thicknesses have been obtained only in a few cases.The degree of neutralization a’ is a very important variable. At a‘ = 1 .O the films have a mobile character, they drain rapidly ( M 1 h), initially with a dimple, to iz - 120 nm, after which a slower thinning occurs till after 16-24 h an equilibrium is attained. For a’ z= 0.5 the films drained rapidly in the early stages, but below h z 100 nm drainage became very slow. For a’ = 0.1 the films are rigid and irregularities ensue; they are very stable. In this case we succeeded only twice in obtaining an equilibrium film with visually plane-parallel surfaces.The most interesting feature of this transition in drainage behaviour between mobile and rigid films with decreasing a’ is that it correlates well with the conforma- tional transition that PMA-pe undergoes in solution. We have shown that the transition occurs also in adsorbed PMA-pe layers and that it is reflected in the inter- action between adsorbed layers of this p~lyelectrolyte.~~*~~ There is also a correlation with the surface dilational modulus.11 In table 4 equilibrium thicknesses are compared with values obtained from TABLE 4.-THICKNESSES OF PMA-pe STABILIZED FILMS. CONCENTRATION 1000 P.P.m. ELECTROLYTE 0.05 mol d m 3 NaCl. a’ glycerol present h/nm h,llips.lnm 0.1 0.5 0.7 1 .o 45 f 20 12 50 f 10 25 60f 6 32 $1 3 15 (after 1 day) ellipsometric measurements.The trend of these exploratory data is that h exceeds 2hellips less than with PVA, which could mean that polyelectrolytes are less inclined to adsorb with long tails than are uncharged polymers. The authors thank Mr. Maasland and Mr. Wegh for their technical assistance and Drs. Van den Tempe1 and De Feyter of Unilever Research for constructive discussions,32 FREE POLYMER FILMS J. Lyklema and K. J. Mysels, J. Amer. Chem. SOC., 1965,87, 2539. A. Sheludko, Adv. Colloid Interface Sci., 1967, 1, 391. R. Aveyard and B. Vincent, Progr. Surface Sci., 1977, 8, 60. A. Doroszkowski and R. Lambourne, J. Colloid Interface Sci., 1973, 43, 97. 1976,54,45. P. R. Musselwhite and J. A. Kitchener, J. Colloid Interface Sci., 1967, 24, 80.' P. R. Musselwhite and J. Palmer, Proc. Vth Int. 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