1096
Langmuir 1989, 5, 1096-1105
Fluorescence Studies of Polymer Adsorption. 2. A Simple Model Describing Adsorbed Polymer Rearrangement Kookheon Char, Curtis W. Frank, and Alice P. Gast* Department of Chemical Engineering, Stanford University, Stanford, California 94305-5025 Received October 5, 1988. I n Final Form: February 9, 1989 A simple model is developed to describe the structure of isolated tracer chains adsorbed from solution onto a planar surface when challenged with displacing polymer. We assume that a tracer polymer adsorbing on a planar surface can be modeled as a Gaussian chain and that the rearrangement of tracer chains on the surface is affected only by a field due to displacing chains. From a modified diffusion equation, we obtain an approximate analytic expression describing the rearrangement. The effects of tracer and displacer molecular weight and displacer concentration on the rearrangement are examined. The rearrangement of tracer chains in this study is described in terms of the change in mean square end-to-end distance, which is related to the fluorescence observable, the excimer to monomer intensity ratio (Ze/Im). The hydrophobic attraction between pyrene ends and the displacement of tracer chains are taken into account, and the predictions are compared with the experimental fluorescence data obtained previously. The model gives qualitative agreement with the fluorescence observations. The quantitative discrepancy at elevated displacer concentrations may be due to nonequilibrium entrapment of some tracer chains by the higher molecular weight displacers. Introduction The physical properties of industrially important materials are enormously improved by the adsorption of various oligomers or polymers at solid/liquid or liquid/ liquid interfaces. Thus, the adsorption of polymer at the interface is involved in many technologically important applications such as micellization, steric stabilization of colloids in organic media, flocculation, adhesion, and lubrication. An understanding of the configuration and concentration of polymer chains at the interface is crucial in these processes. Many theoretical and experimental studies' have concentrated on obtaining a better understanding of these issues. Early theories of polymer adsorption dealt with the development of statistical mechanical models of an ideal chain isolated on the surface.2 Such a treatment is not realistic, however, since excluded volume interactions among adsorbed chains are neglected. Later, the theory for an isolated, adsorbed chain was extended to incorporate intramolecular and multichain interactions. The most comprehensive statistical thermodynamic model for polymer adsorption has been developed by Scheutjens and Fleer.3,4 Using a quasi-crystalline lattice to describe adsorbed chains, they calculated the distribution of trains, loops, and tails as well as the amount adsorbed and the segment density distribution. de Gennes5v6applied scaling theory to the adsorption of linear, flexible, neutral chains on a planar surface from good solvents and showed that adsorbed layers have a self-similar structure. Other approaches such as the renormalization method' and Monte (1) (a) Takahashi, A.;Kawaguchi, M. Adu. Polym. Sci. 1982,46,1.(b) Fleer, G. J.; Lyklema, J. Adsorption from Solution at the SolidlLiquid Interface; Parfitt, G. D., Rochester, C. H., Eds.; Academic: New York, 1983;Chapter 4. (c) Cohen Stuart, M. A.; Cosgrove, T.; Vincent, B. Adu. Colloid Interface Sci. 1986,24,143. (2)(a) Frisch, H.L.; Simha, R.; Eirich, F. R. J . Chem. Phys. 1953,21, 365. (b) Silberberg, A.J. Phys. Chem. 1962,66,1872,1884. (c) DiMarzio, E. A.; McCrackin, F. L. J . Chem. Phys. 1965,43,539.(d) Roe, R. J. J . Chem. Phys. 1965,43,1591. (e) Silberberg, A.J . Chem. Phys. 1967,46, 1105. (0 Chan, D.;Mitchell, D. J.; Ninham, B. W.; White, L. R. J. Chem. Sac., Faraday Trans. 2 1975, 71,235. (3)Scheutjens, J. M.H. M.; Fleer, G. J. J . Phys. Chem. 1979,83,1619. (4)Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1980,84,178. (5)de Gennes, P.-G. Macromolecules 1980,13,1069. (6)de Gennes, P.-G. Adu. Colloid Interface Sci. 1987,27, 189. (7)Wang, Z.G.; Nemirovsky, A. M.; Freed, K. F. J . Chem. Phys. 1987, 86,4266.
0743-7463/89/2405-1096$01.50/0
Carlo calculations* have also been taken. A self-consistent field theory, originally developed by Edwardsg to study the configuration of polymer chains having excluded volume interactions in solution, has been adapted to describe the configuration of polymers adsorbed to surfaces.'O The resulting equation is similar in form to a diffusion equation except for a term containing the self-consistent field created by the excluded volume interaction among segments and the surface. Recently, this model was generalized by Ploehn et al." to describe homopolymer adsorption on a planar surface. They obtained a self-consistent equation with a surface boundary condition derived from the restricted motions of polymer segments near the impenetrable surface. They found an analytic expression for the density profile of the adsorbed polymer as a ground-state solution from the first term in an eigenfunction expansion describing loops and trains. Comparing thicknesses found from integrating the density profile for loops and trains with those measured via ellipsometry or hydrodynamic experiments showed a discrepancy attributable to the presence of extended polymer tails. In their following paper,I2 Ploehn and Russel included a contribution due to tails via a matched asymptotic expansion with different length scales near and far from the surface. Near the surface, the segment length is the relevent scale, whereas the radius of gyration of adsorbate polymer is the appropriate scale far from the surface. Addition of the tail contribution improves the comparison with experiment, a conclusion also reached by Cohen Stuart et al.13 Ploehn and Russell2 also investigated two equations of state (EOS)describing the bulk and surface states of polymer chains. The first is a typical Flory-Huggins EOS based on a lattice description while the other, the van der Waals EOS, requires no lattice description and thus should be more appropriate to a continuum system.14 The latter (8) (a) McCrackin, F. L. J . Chem. Phys. 1967,47,1980. (b) Eisenriegler, E.; Kremer, K.; Binder, K. J. Chem. Phys. 1982, 77, 6296. (9)Edwards, S. F. Proc. Phys. SOC.1965,85, 613. (10)Jones, I. S.; Richmond, P. J. Chem. SOC.,Faraday Trans. 2 1977, 73,1062. (11)Ploehn, H.J.;Russel, W. B.; Hall, C. K. Macromolecules 1988, 21, 1075. (12)Ploehn, H.J.; Russel, W. B. Macromolecules 1989,22, 266. (13)Cohen Stuart, M.A.; Waajen, F. H. W. H.; Cosgrove, T.; Vincent, B.; Crowley, T. L. Macromolecules 1984,17, 1825.
0 1989 American Chemical Society
Fluorescence Studies of Polymer Adsorption combines a continuous-phase EOS due to the van der Waals attraction and hard-sphere repulsion between segm e n t with ~ ~ ~a surface EOS for hard disks.16 They calculated the variation of the adsorbed amount (pads) with the statistical number of segments (N) using both EOS and compared the results with available experimental data. Although both EOS give limited agreement with experimental data, it is difficult to distinguish between the two. In parallel with these theoretical advances, a variety of sophisticated experimental techniques have been developed. These yield important information on the bound fraction, layer thickness, and density profile as well as the amount adsorbed. Data on the fraction of segments bound to the surface can be obtained by infrared17 and pulsed NMR measurements.ls The layer thickness and the amount of polymer adsorbed can be measured by ellipsometry,lg while the hydrodynamic thickness of polymer layers can be obtained by either photon correlation spectroscopy or capillary flow Finally, small-angle neutron scattering gives the density profile of the adsorbed polymer layer away from the surface.22 Recently, we investigated polymer adsorption with a new application of a fluorescence techniqueaZ3 The advantage of the excimer fluorescence method employed is that it yields highly localized information. Excimers are only formed when aromatic rings are aligned in an appropriate configuration within about 4-5 A. Comparison of the excimer to monomer intensity ratio, I e / I m ,makes it possible to draw reasonably precise conclusions about the spatial distribution of the chromophores and, hence, the portion of the polymer chain to which they are attached. In contrast to thickness measurements, excimer fluorescence is sensitive to the local segment distribution in the layer. Using interaction between terminal pyrene moieties as a probe, we monitored both adsorption and configurational changes of polyethylene glycol (PEG) on small silica particles. We also examined the effect of the molecular weight and concentration of an untagged displacing polymer chain on the rearrangement and/or displacement of the preadsorbed, labeled polymer. In the present paper, a simple model is developed to capture the essential features observed in the fluorescence e ~ p e r i m e n t .We ~ ~treat our tagged polyethylene glycol as a tracer polymer and calculate its trajectory when subjected to a field due to the untagged chains. A simplification of the Pleohn and Russel density profile provides an exponentially decaying field resulting in an analytic expression for the tracer trajectory. This paper is intended to provide a qualitative verification of the mechanism of polymer rearrangement prior to displacement suggested (14)Dickman, R.;Hall, C. K. J . Chem. Phys. 1986,85,4108. (15)Carnahan, N. F.; Starling, K. E. J . Chem. Phys. 1969,51, 635. (16)Baram, A.;Luban, M. J.Phys. C 1979,12,L659. (17)(a) Vander Linden, C.; Van Leemput, R. J. Colloid Interface Sei. 1978, 67,48. (b) Kawaguchi, M.; Maeda, K.; Kato, T.; Takahashi, A. Macromolecules 1984,17,1666. (18)(a) Cosgrove, T.; Vincent, B.; Cohen Stuart, M. A.; Barnett, K. G.; Sissons, D. S. Macromolecules 1981, 14, 1018. (b) Cosgrove, T.; Barnett, K. G. J . Magn. Reson. 1981,43, 15. (19)(a) Takahashi, A,; Kawaguchi, M.; Kato, T. Adhesion and Adsorption of Polymers; Plenum: New York, 1980. (b) Kawaguchi, M.; Hattori, S.; Takahashi, A. Macromolecules 1987,20,178. (20)(a) Varoqui, R.;Dejardin, P. J . Chem. Phys. 1977,66,4395.(b) Killmann, E.;Maier, H.; Kaniut, P.; Gutling, N. Colloids Surf. 1985,15, 261. (21)(a) Gramain, Ph.; Myard, Ph. Macromolecules 1981,14,180.(b) Cohen Stuart, M. A.; Tamai, H. Macromolecules 1988,21, 1863. (c) Cohen Stuart, M. A,; Tamai, H. Langmuir 1988,4, 1184. (22)Barnett, K. G.; Cosgrove, T.; Crowle:.. T. I. F.; Tadros, Th. F.; Vincent, B. The Effect of Polymers on DisFzrsion a’tability;Tadros, Th. F., Ed.; Academic: New York, 1982. (23)Char, K.; Gast, A. P.; Frank. C. W. Langmuir 1988,4,989.
Langmuir, Vol. 5, No. 4, 1989 1097
high surface concentration low surface concentration Figure 1. Schematic of the configurational change of adsorbed polymers with increasing surface concentration.
by our experiments. Perhaps more importantly, we also wish to illustrate the utility of combining fluorescence experiments on carefully tagged polymers with field equation calculations of polymer chain trajectories. We believe that this combination affords a unique molecular level study of polymers at interfaces and is amenable to many different applications. We use the two different EOS described by Ploehn and Russell2 and compare the resulting predictions. We then examine the rearrangement and/or displacement of isolated chains in a field created only by untagged displacing polymer exploring the effects of the tracer and displacer molecular weights and the displacer concentration. Finally, the results are compared with fluorescence experimental data,23where the experiment consisted of the adsorption of isolated tagged chains and the subsequent addition of untagged displacing polymer.
Theoretical Formulation We adopt a continuum model to study the rearrangement of a single tagged polymer chain on the surface in the presence of additional untagged chains. There are several advantages of such a treatment. First, unlike a lattice a p p r o a ~ h ,it~ does ? ~ not require the selection of a specific lattice geometry and thus is more appropriate for a real system. The sensitivity to the lattice choice is particularly strong for chains near an interface,12the focus of our interest in chain configuration. Second, the average end-to-end distance, which will be compared with our experimental observable, I e / I m ,can be more readily determined from a continuum approach. Third, when the adsorbed amount is small, a polymer chain is more likely to have many contact points with the surface rather than to protrude into solution, as depicted in Figure 1. Thus, we need to extend the existing adsorption theory, which generally considers only the direction normal to the surface, to a more general three-dimensional one; the continuum model is more easily extended to three dimensions than the lattice model. This necessity was recently suggested by Ouada et al.,24who used electron paramagnetic resonance to study the effect of the density on the organization of PEO chains grafted to silica particles. Finally, from the practical point of view, when we are able to derive an approximate analytic expression from a continuum model with a few reasonable assumptions, we can considerably reduce the computation time, especially when we must consider three dimensions or long polymer chains. The approach we take in this study is to obtain an approximate analytic expression that describes our experimental system reasonably well. For that purpose, we do a “trajectory analysis” using a modified diffusion equation to determine the probability density distribution of our pyrene end-tagged PEG. The dimensionless governing equation is9
(24)Ouada, H.B.;Hommel, H.; Legrand, A. P.; Balard, H.; Papirer, E. J . Colloid Interface Sci. 1988,122,441.
Char et al.
1098 Langmuir, Vol. 5 , No. 4 , 1989
where s is the dimensionless distance along the polymer chain from one polymer end normalized by the segment length 1, G(i;,i;’;s,s’) is the probability of finding a segment s at a position F given another segment s l a t a position P‘, and U(P)is a field created by both probing polymer and displacing polymer chains at a position 7 along with attraction to the surface and = l / k T . There are generally two ways to describe polymer adsorption with excluded volume. One is, as Jones and Richmond’O described, to include the surface attraction term such as a square potential in front of G in eq 1along with a self-consistent repulsive term. Another approach, which Ploehn et have taken, is to split the potential U(i;)into two regions: one is a potential at the “surface phase” including the surface attraction term and the other, derived from the two-dimensional equation of state, is a potential in a “continuous phase”. These approaches are equivalent. In this paper, we take the latter approach, putting the surface attraction term in a potential for the surface phase. To capture the essential features of our rearrangement experiments, we assume that (1)the field U(i;)is created only by the displacing polymer, (2) the probe chain behaves ideally, and (3) polymer chains adsorb on a planar surface. The first assumption is quite reasonable since our experimental conditions were chosen such that there was approximately one probe chain adsorbed on each particle;23 these tracer chains change their configuration due to the adsorption of incoming untagged polymer chains. The remaining two assumptions do not exactly correspond to our experimental system.23 For example, polyethylene glycol is dissolved in a relatively good solvent, water, so that the intramolecular excluded volume effect should be considered in addition to the intermolecular excluded volume repulsion described by the field. Since the silica particles used in the experiment are slightly larger than the radius of gyration of the polymer chain, the assumption of a planar surface used in the Derjaguin approximationz5 is not strictly valid. Nevertheless, we adopt the last two assumptions in order to obtain a tractable approximate description of our system. With these assumptions, we are able to derive an analytic expression showing the effect of adsorbing displacing polymer on the configuration of the probe polymer residing on the surface and to compare it with our experimental results. When the volume fraction of displacing polymer, &(r), is small, the field generated by the existence of displacers, 1 - ebu(p),can be approximated by a Taylor expansion as -u+d(r), where u is the dimensionless excluded volume parameter defined as {(l- 2x). { is the fraction of the segment volume occupied by polymer, and x is the Flory-Huggins interaction parameter. Thus, in order to describe the field U(i;),we require an expression for the concentration profile of adsorbed, homopolymeric displacer chains in both the continuous and surface phases. Recently, Ploehn et al.” derived a self-consistent field equation to describe homopolymer adsorption onto a planar surface from dilute solution. They found an analytic form for the density profile of the adsorbed polymer as a ground-state solution describing loops and trains. The resulting analytic expression for the volume fraction profile in terms of loops and trains of the adsorbed chains is1’
’05
v
. n
e €7
.. 10
0
05
1 .o
1.5
2.0
zlRg
Figure 2. Comparison of the Flory-Huggins EOS (FH) and the van der Waals EOS (VW) for the loop profile of displacing chains adsorbed: -, with VW; - - -, with FH. Parameters used are N x = 0.45, xa = 0.3, and [ = 0.71. = 500, = 1x
where io is the eigenvalue for the ground-state solution determined by iteration, ci is an integration constant, y = (24x0),’/2and u and w are the dimensionless excluded volume coefficients. The above expression for &(Z) can be approximated as an exponential decay (3)
an approximation valid outside a region very close to the surface, in the vicinity of O.lR, for degree of polymerization (N) of 500 in a good solvent (x = 0.451, as shown in Figure 2 . The values of segment-surface interaction energy (x,) and segment volume fraction in free solution (a) used in the figure are typical of our experimental system. Details of the evaluation of the parameters will be discussed later. This exponential decay for loops and trains has also been predicted in other theories.26 The validity of neglecting tails in present study comes from the fact that excimer fluorescence or mean square end-to-end distance is more sensitive to the local segment density than to the details of segment profile. When the molecular weight of the displacing polymer is much higher than that of the preadsorbed tracer chain, as in our experiments, the tracer chain conformation is most influenced by the trains and loops of the displacing chain. The displacing chain loops are of comparable size to the tails of the tracer chain. Therefore, it is reasonable to neglect the contribution to the profile due to tails of the displacing chain. This is in contrast to calculations of thickness in which the tails play an important role. The final governing equation in Cartesian coordinates to be used in the present study is
where A = u(4X0/ci)with initial conditions G(x,y,z;s=O) = 6 ( ~ ) 6 ( y ) 6 ( ~ - ~ ?
(5)
and boundary conditions ( 2 5 ) Israelachvili, J. N. Intermolecular and Surface Forces; Academic: London, 1985; Chapter 10.
(26) (a) Hoeve, C. A. J.; DiMarzio, E. A.; Peyser, P. J . Chem. Phys. 1965, 42, 2558. (b) Hoeve, C. A. J. J . Chem. Phys. 1965, 43, 3007.
Langmuir, Vol. 5, No. 4 , 1989 1099
Fluorescence Studies of Polymer Adsorption dG -= ax
- edG o
atx=y=O
ay
G=O
G(x,y,O;s)- -(x,y,O;s) as aG
atz=m
1+ 4
(6b)
aG $x,y,O;s)
f ( s ) = clew
(64
(11)
1 d2g ( m + Ae-Y”)g = 0 6 dz2 with c1 an integration constant. The equation for g can be converted by a change of variables
at z = 0 (64
where d in U,d(O)denotes displacer and KAd = e-8[usLu,d(0)l; 4s= KAd#,(0)
KAdand U,d(O)are the variables calculated from the adsorption of displacers. The subscripts s, c, and b stand for surface, continuous, and bulk phase, respectively. The surface phase is composed of only those segments touching the surface. Continuous refers to the region of adsorbed polymer chains excluding the segments actually in contact with the surface. In the bulk phase, no segment of the polymer chain is associated with the surface. The 0 in cp,(O) denotes the segments in the continuous phase in close contact with the surface phase. The surface boundary condition given in eq 6c was originally derived by Ploehn et al.” considering a impenetrable “sticky” surface and an anisotropic contribution due to the discontinuity at the surface. The fields, U, or U,, can be derived from the two different equations of state. From the Flory-Huggins equation of state”
and the van der Waals equation of state12
to a modified Bessel equation d2g dg t- - ( t 2 + q2)g = 0 dt2 dt The solution to eq 12 is the modified Bessel function of the first kind of order q: t2-
+
g ( z ) = c2Zg(ce-yzJ2)
(13)
where c2 is another integration constant. By eigenfunction expansion, the solution for G,(z,s) becomes “,
G,(Z,S) =
k=O
Aklgk(Ceyz/2)f?mks
(14)
The eigenvalue mk is determined from the surface boundary condition, and the coefficients of eigensolutions A k are obtained from the inhomogeneous initial condition by using the Sturm-Liouville theorem. There exists only one eigenvalue from the transcendental equation derived from the surface boundary condition (eq 6c, 11, and 13). After application of orthogonality of the eigenfunctions and the inhomogeneous initial condition (G,(z,O) = 6(z-z’)), the resulting solution for G,(z,s) is I 9 (ce-~*’J2)lq(ce-yZJ2) G,(z,s) = ems (15) Zq2(ce-yz”/2) dz ” where m is an eigenvalue and q is a function of the eigenvalue. In the x and y directions parallel to the surface, the governing equations are
z=o
where a = (7 + 2x)/ 16, Bo = 3.467 00, B1 = 5.379 44, B2 = 3.67599(1 - 2a) - 1.91244, B3 = 0.28413, and B4 = 0.016178. As mentioned above, the potentials for the surface phase include surface attraction terms (-x8)as well as self-consistent repulsive terms. The solution to eq 4 with initial and boundary conditions given above can be obtained by separation of variables since the initial conditions are separable2’ G (X,Y,z;s) = G,(x,s)G,(Y,s)G,(z,s) (9)
The solution to eq 16 with the initial and boundary conditions is a Gaussian distribution:
(”)’”-$)
Gh(h,s) = 27rs
exp(
h = x or y
(17)
Since the x and y directions are equivalent, we can combine them into one variable: r2 = x2 + y2
In the z direction perpendicular to the surface, the governing equation will then be
This equation can be solved analytically since the equation and the boundary conditions are linear and homogeneous. Applying the separation of variables again yields G,(z) = g ( z ) f ( s ) where , (27) Carslaw, H. S.;Jaeger, J. C. Conduction of Heat in Solids; Oxford University Press: Oxford, 1959; Chapter 1.
Due t o intermolecular packing constraints,2s the extent to which an adsorbed probe chain spreads on the surface depends on the surface density of adsorbed chains, or in our case the displacing polymer chain. Since the distribution normal to the surface (Le., in the z-direction) and the lateral distribution are coupled, the lateral spread of the adsorbed tracer polymer can, in principle, be obtained from the one-dimensionalsolution. This approach is more (28) Dill, K . A. Adu. Colloid Interface Sci. 1986, 26, 99.
1100 Langmuir, Vol. 5, No. 4 , 1989
Char et al.
appropriate to a mean field lattice c a l ~ u l a t i o nand ~ ~ can ~ provide a means to compare the continuum results obtained here with a lattice calculation. An indirect and simple way to couple the perpendicular and lateral distribution is to use a scaling theory for the lateral motion. This lateral restriction of the adsorbed chain due to the increase in surface density has been noted by de GennesB for polymers anchored to a surface and by Dill and Flory3O for membranes and micelles. In order to obtain the simplest possible expression addressing this effect, we use the concept of an “equivalent Gaussian link chain”31whose distribution
is described by an effective coil dimension (R2),. We represent this effective coil dimension through de Gennes’ “blob” concept for a semidilute layer.32 Even though the adsorbate solution concentration is very low, the chains in the surface layer are sufficiently dense that it can be approximated as a semidilute solution. Under these conditions, we can invoke blob theory,32where a polymer chain is composed of many blobs behaving as an ideal Gaussian chain
where g is the number of segments in each blob, s is the number of segments for the polymer chain, ( is the “screening length” or blob size,32and a is the segment length. The segments within each blob behave like a chain in good solvent so that g = (l/a)5’3
In the semidilute region32 (/a =
63-3!4
where (see ref 41)
Since the rearrangement and displacement of tracer chain are most affected by the adsorption of displacer segments near the surface, we calculate the size of the first blob near the surface self-consistently and use the volume fraction inside the blob as the lateral field. The volume fraction within the first blob is always below unity in our experimental conditions such that the screening length is larger than the segment size. Combination of eq 20 and these two definitions yields
( R 2 ) ,= s4,-1!4
(21)
which with eq 19 results in G,(r,s) = 34a1/4 e x p ( - y ) 2as
(22)
a concentration-dependent Gaussian distribution in the lateral direction.
Combination of components perpendicular (2) and parallel ( r ) to the surface (eq 15 and 22) leads to the final solution for G(r,z;s) G(r,z;s) = 34,114 3r24,’/4 I (ce-yz’/2)I,(ce-yz/2) ems (23) 2TS eXP(-?);,I Q 2(Ce-?z’’/2) dz” where m is an eigenvalue to be determined from the surface boundary condition. In order to calculate the mean square end-to-end distance, we normalize G(r,z;s)to produce a probability density function. According to Dolan and the normalized probability density function in confined space is defined as G(P,F’;s,O) jG(f“,i;;N-s,O)d r ” P(r,P’;s,O) = (24) C(?”,?’;N,O)d r ”
1
The combination of eq 23 and 24 finally yields the required analytic expression for the normalized probability density distribution of chain ends 345a1J4 I,(ce-yLi2) P(r,z;N,,O) = 2sNt Iq(ce-yZ’/2) dz’ (25) where N , is the degree of polymerization of the probe polymer. The mean square end-to-end distance can then be obtained from integration of the probability distribution
( R 2 )= J m j m ( r 2+ z2)P(r,z;N,0)2ardr dz 0
0
(26)
In order to relate the mean square end-to-end distance obtained here to our experimental observable, I e / I m , we follow the Jacobson-Stockmayer (JS) theory.34 As we showed in our previous paper,35the ground-state dimer formation in aqueous solution is appreciable, and thus the observed excimer fluorescence does not solely reflect cyclization dynamics.36 In fact, the static contribution to the excimer may exceed the dynamic contribution. According to JS theory, the equilibrium cyclization probability in the region corresponding to the close approach of chain ends scales as (R2)-3/2 in three dimensions for Gaussian chains: Ie/Zm (R2)-a (27) where CY is 3 / 2 . Thus, the exponent 3 / 2 for CY is valid for chains whose ends have hydrophobic attractions, which will be discussed in more detail below, as well as for chains with excimers formed by diffusion-controlled process.36 When tracer chains are preadsorbed a t an extremely dilute concentration, they take a flattened conformation, as shown in Figure 1. In this situation, we have a two-dimensional chain. However, the aim of this paper is to show the effect the adsorption of displacing polymer on the rearrangement and displacement of a tracer chain. As soon as untagged displacing chains are added to the system, segments of the preadsorbed short tracer chains are detached from the surface enhancing the excimer fluorescence signal. In this case, the process of excimer formation is three dimensional.
-
(33) Dolan, A. K.; Edwards, S. F. Proc. R. SOC.London A 1975, 343, (29) de Gennes, P.-G. Macromolecules 1980, 13, 1069. (30) Dill, K. A.; Flory, P. J. Proc. Natl. Acad. Sci. 1980, 77, 3115. (31) Freed, K. F. Renormalization Group Theory of Macromolecules; Wiley: New York, 1987; Chapter 2. (32) de Gennes, P.-G Sca!ing Concepts in Polymer Physics; Cornel1 University Press: Ithaca, New York, 1979.
421.
(34) Jacobson, H.; Stockmayer, W. H. J . Chem. Phys. 1950,18,1600. (35) Char, K.; Frank, C. W.; Gast, A. P.; Tang, W. T. Macromolecules 1987, 20, 1833. (36) (a) Wilemski, G.; Fixman, M. J . Chem. Phys. 1973,58, 4009. (bj Wilemski, G.; Fixman, M. J . Chem. Phys. 1974, 60, 866, 878.
Langmuir, Vol. 5, No. 4, 1989 1101
Fluorescence Studies of Polymer Adsorption
m
o.*t
4
D 0.6 e-
{
!-
i
\
0
0 10
20
R
30
40
" "
0
10
' ' " " ' ' " ~ ' ' 20
30
40
Z
1
Figure 3. Effect of equilibrium solution volume fraction on the probability density distributions of isolated tracer chains in two directions. (a) lateral direction (2= 0 ) and (b) ~, direction normal to surface' (R'= 0): -, cpb = 1 'X 10-7;- .-, cpb = 1 x 10-4. Parameters include Nd = 500, Nt = 200, x = 0.45, xs = 0.25, and
0
0
0.2
0.4
0.6
0.8
1.0
f = 0.71.
In the present study, the value of LY is fixed as 3/2, neglecting the two-dimensional conformation of adsorbed tracer chains with no displacer.
Figure 4. Effect of xs on adsorption isotherms: solid lines for FH and dotted lines for VW. Curves 1and 2, xs = 0.25; curves 3 and 4, xs = 0.5. Parameters are Nd = 500, x = 0.45, and f = 0.71.
Results and Discussion General Trends from the Model. In Figure 3, we show the normalized probability density distributions of probe chain ends for two displacing polymer concentrations. The probability density distribution is described along the two directions of a cylindrical coordinate system: a lateral direction ( r ) a t z = 0 (Figure 3a) and a direction normal to the surface ( z ) a t r = 0 (Figure 3b). The Flory-Huggins interaction parameter (x)used in the figure is 0.45, a value for polyethylene glycol in water13 utilized in the fluorescence e ~ p e r i m e n t .Other ~ ~ parameters such as degrees of polymerization of displacer and tracer (Nd and N,, respectively), segment-surface interaction parameter (xJ, and solution volume fraction (a) are typical for the fluorescence experiment23and will be varied later. At a low displacer concentration (6= 1 x lo-' in Figure 3), the probe chain tends to adsorb with many segments in contact with the surface, and the probability distribution is broad in the lateral direction. As the displacer concentration is increased, the extent to which the tracer chain spreads laterally along the surface is restricted due to the adsorption of displacing polymer. Consequently, the lateral distribution becomes narrower as the displacer concentration is increased (cpb = 1 X lo-* in Figure 3), while the probability density of polymer ends extends normal to the surface. This implies that the ends of the probe chain have a tendency to protrude into the solution with an increase in displacer concentration. The trend shown here is related to the increase in average layer thickness with an increase in coverage observed by othersls studying homopolymer adsorption. This prediction corresponds to observations from fluorescence experimentsz3where we investigated the adsorption of tagged chains (pyrene end-labeled polyethylene glycol denoted as Py-PEGPy) on colloidal silica and their subsequent rearrangement and displacement upon exchange with untagged PEG. From the fluorescence experiments along with analysis of the ~ u p e r n a t a n t ,we ~~ proposed that adsorption of the tagged chains onto silica particles substantially reduces the excimer to monomer intensity ratio, Ie/Im,indicating a decrease in pyrenepyrene contacts attributable to the flattened configuration of PEG adsorbed on silica. Addition of untagged PEG causes the excimer to recover, with i t s recovery dependent
on the molecular weight of both the tagged and untagged PEG. More detailed consideration suggests that as the displacer is adsorbed, the preadsorbed probe chain rearranges to accommodate it. This leads to an increase in the mobility of the probes due to their extension into the bulk solution; as a result, the excimer to monomer intensity ratio relative to that in free solution, Le., (Ie/Im)/(Ie/Im),,,increases. We also showed that longer displacing PEG chains are more effective in rearranging and displacing the preadsorbed tagged chains. The longer tagged PEG undergoes substantial rearrangement prior to desorption, resulting in excimer intensities exceeding those of tagged chains in a free solution of the same concentration. The smaller tagged chains also show substantial excimer intensity recovery before desorption; however, I e / I mrarely exceeds that of a free solution. Since I e / I mis related to the change in mean square end-to-end distance, as described in the previous section, this experimental observable is well matched with the theoretical predictions from this model. Figure 4 shows the adsorption isotherms for displacing polymers at two xs values: 0.25 and 0.5. The adsorption isotherms calculated with the Flory-Huggins equation of state (EOS) are compared with those obtained from the van der Waals EOS. According to Dickman and Hall,I4 the latter EOS predicts the osmotic pressure of athermal solutions in continuum space better than the lattice-based Flory-Huggins EOS. As shown in Figure 4a, the FloryHuggins EOS predicts a higher adsorbed amount for the same xs value with the difference between the adsorbed amounts from the two EOS becoming larger as xs is increased. This may be due to the fact that in the van der Waals equation the Carnahan-Starling entropic repulsion term is stronger in the SCF than that in the Flory-Huggins equation. This is also manifest in the segment profiles, as shown in Figure 2, where the loop profile derived from the van der Waals equation extends farther into the bulk solution even though the adsorbed amount is smaller. This extension of the segment profile indicates a more diffuse adsorbed layer structure due to the stronger repulsions in the van der Waals EOS.12 Another thing to note in Figure 4 is that increasing xs causes the adsorption isotherm from the Flory-Huggins equation to begin to change from a low
1102 Langmuir, Vol. 5, No. 4 , 1989 1.2LI
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Figure 5. Effect of displacer molecular weight on the end-bend distance of isolated tracer chain relative to that of free solution, ( ( R Z ) o / ( R 2 ) ) for 3 / 2two different EOS: -, FH with Nd = 500; - - -, FH with Nd = 400; VW with N , = 500; -, = 400. Parameters include N , = 200, y = 0.45, xS = 0.27, and { = 0.71. -a,
0.2
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affinity isotherm to a high affinity isotherm, while the isotherm from the van der Waals equation retains a high affinity shape for both xs values. The effect of the displacer molecular weight on the tracer end-to-end distance in the adsorbed layer with respect to that in bulk solution is shown in Figure 5. Since, as explained in the previous section, ( ( R 2 ) 0 / ( R 2 ) ) 3is/ 2 proportional to (Ie/Im)/(Ie/Im)o, the trend shown in this figure can be compared with f ,perimental fluorescence data.23 Figure 5 shows a great r change in the configuration of a tracer chain adsorbed on the surface when the higher molecular weight displacer (Nd = 500) is added than that caused by addition of a lower molecular weight displacer (Nd = 400). This tendency agrees with the experimental observation (Figure 3 in ref 23), showing that the initial rise in (Ie/Zm)/ (Ie/I,J0with displacer concentration is much steeper for a higher molecular weight displacer (PEG of molecular weight 22000). The comparison between the two different EOS is also made in Figure 5. Although the general influence of molecular weight on the relative end-to-end distance change remains the same for a given value of xs,the effect obtained with the van der Waals EOS is less dramatic than that with the FloryHuggins EOS. The relative end-to-end distance, ( ( R 2 ) o / ( R 2 ) ) from 3 / z , the van der Waals equation is below unity over the entire concentration range while ( ( R 2 ) o / ( R 2 ) ) 3 / 2obtained from the Flory-Huggins equation can exceed unity. This difference arises from the reduction in adsorbed amount from the van der Waals equation relative to the Flory-Huggins equation, providing a chance for a tracer chain to spread laterally. The effect of tracer molecular weight on the relative end-to-end distance, ((Rz)o/(R2))3/2, is illustrated in Figure 6. A higher molecular weight tracer chain changes its end-to-end distance over a broad range, and its end-to-end distance at high displacer concentrations can be smaller than that in bulk solution, exceeding the line of ((R 2 ) o / ( R 2 ) ) 3 /=2 1. This trend also agrees with our experimental observationz3that longer tagged chains undergo substantial rearrangement prior to displacement. Detailed comparison between theoretical prediction and experimental data will follow. Again, the effect of the tracer molecular weight
Figure 6. Effect of tracer molecular weight on ( ( R 2 ) 0 / ( R 2 ) ) 3 ~ 2 for two EOS: -, FH with N , = 200; - -, FH with Nt = 100; -., VW with Nt = 200; -.-, VW with Nt = 100. Parameters include Nd = 500, x = 0.45, xs = 0.27, and { = 0.71.
-
obtained from the van der Waals equation is smaller than that from the Flory-Huggins equation due to the lower amount adsorbed. Consideration of Hydrophobic Attraction between Pyrene Ends. We showed in a previous study35 that when pyrene-end-labeled polyethylene glycol (Py-PEG-Py) is dissolved in water, there exist ground-state dimers. The existence of ground-state dimers has been clearly shown in both excitation spectra and time-resolved fluorescence spectra.% We concluded that the ground-state dimers form due to an attraction between hydrophobic pyrene ends attached to a hydrophilic polymer chain when the chain is dissolved in water. We also demonstrated that when methanol, a less polar solvent, was added to the aqueous solution containing Py-PEGPy, the preformed dimers are preferentially solvated, reducing the excimer to monomer intensity ratio, I e / I m . Finally, when the Py-PEG-Py is in pure methanol, the excimers are more closely described by a diffusion-controlled process, as shown in time-resolved fluorescence spectra. There we showed that the time evolution of excimer intensity approximately follows the Birks' kinetic scheme for a diffusion-controlled process. Since, in our fluorescence studies of polymer ads0rption,2~ the Py-PEG-Py chains are dispersed in water containing silica particles, the possibility of enhanced I e / I mdue to hydrophobic attraction must be taken into account in order to compare the predictions made here with the experimental results. A simple way to describe the hydrophobic attraction is to use the so-called "capture process", as depicted in Figure 7 . If one hydrophobic end (a pyrene chromophore in our experiment) is within a distance of twice the capture radius from the other, those two ends are hydrophobically attracted to each other causing an immediate excimer formation. Thus, this mathematical model considers the ground state-dimers, normally observed for Py-PEG-Py in water, to be captured ends. We assume that the introduction of hydrophobic probes does not significantly perturb the conformation of a PEG chain, so we can use the a priori probability density function derived in the previous section.37 The modified probability density (37) Char, K.; Frank, C. W.; Gast, A. P. Macromolecules, in press.
Langmuir, Vol. 5, No. 4 , 1989 1103
Fluorescence Studies of Polymer Adsorption
veloped here. Nevertheless, it is possible to correct for this displacement by using the experimentally determined fraction of tagged chain in bulk solution. As mentioned earlier, our experimental observable, Ie/Im,is proportional to the inverse 3/2 power of the mean square end-to-end distance ((R2)):
Excimer
where the left-hand-side term is the experimental observable used in the fluorescence measurement and the subscript 0 denotes the reference state, Py-PEGPy in free solution. The right-hand-side term can be corrected for the displaced tracer chains:
( g ) g)2 +
Figure 7. Schematic of the hydrophobic attraction and modified probability distribution function of end-to-end distance.
function, shown schematically in Figure 7, determines the fraction of captured pyrene ends in cylindrical coordinates as (4R2-Z?'/' f, = 1 2 R ' d z l 2ar dr P(r,z;N,O) (28) 0
0
where R, is the dimensionless capture radius normalized by the segment length. The modified dimensionless mean square end-to-end distance, which is related to Ie/Im,is defined as
+ z2)P(r,z;N,0)2ar dr (r2+ z2)P(r,z;N,0)] (29)
(R2) = (1- fc)[i m L m 2 7 r dr r dz (r2 .
J2RcdtJ
.
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where P(r,z;N,O) is the normalized probability density distribution of chain ends derived in eq 25. The PyPEG-Py chain in free solution is taken as a reference. When Gaussian statistics for the Py-PEGPy in solution is applied to the capture process as described here, we obtain analytic expressions for the capture fraction in solution (Ico) and the mean square end-to-end distance ( (R2)0):37. fco = 4 4
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where y is the fraction of tagged chains displaced in solution, determined experimentally from the analysis of the supernatant solution. Thus, the change in the mean square end-to-end distance is considered only for that fraction of tagged chains remaining on the surface. Second, the hydrophobic interaction between pyrene ends in aqueous medium should be taken into account. As explained above, when a model of a capture process is adopted, there is one parameter to be determined for our experimental system. The parameter is a dimensionless capture radius (R,). This R, can be determined from an independent solution study5where Ie/Imof Py-PEGPy of three different molecular weights in water was measured. There is remarkably consistent agreement between the experimental data and the theoretical predictions made with eq 30 and 31 for all three molecular weights at R, = 4.3.37 This is equivalent to about 20 A. In other words, the range of hydrophobic attraction is approximately 40 8, for hydrophobic pyrene ends. This value is reasonable when compared to the range of hydrophobic interaction observed for a linear hydrophobic chain determined with a surface force apparatus.38 The displacer concentration used in the experiment is related to the volume fraction of the adsorbed phase and the bulk solution in equilibrium with the adsorbed phase ((Pads and 6) by
(30)
cd(M)
=
r
-(@b Mvsp
where a = 3/2N and the subscript 0 denotes free solution values. Comparison between Theory and Experiment. Before making a direct comparison between the theoretical predictions and the fluorescence experimental results, we must consider a few issues. First, the probability density function of chain ends derived in the previous section is based upon the fact that the tagged chain remains a t the surface, as described in the boundary condition (eq 6b). However, we showed in our supernatant analysis23that the tagged chain is displaced into bulk solution by the addition of untagged polymer chains of greater molecular weight. The partitioning of the tagged polymer chains between surface and bulk phases has not been considered in the theory de-
y
+ cm@adsAs)
(34)
where M is a molecular weight of polymer, uSpis a specific volume, [ is the fraction of the segment volume occupied by polymer (0.71 for PEG), C, is a characteristic ratio of mean square end-to-end distance at 8 condition relative to that of random flight chain and is set to 3, and A, is a surface area of suspended particle per volume. Finally, the segment-surface interaction energy (x,),the only adjustable parameter, must be determined, as mentioned above. The criterion for determining the xs best modeling our experimental system is to compare the theoretical predictions at various xs values with the experimental data for two different molecular weights of tracer polymer chain. Fluorescence experimental data23show that when Py-PEG-Py chains of molecular weight 4250 (Nt 100) are preadsorbed on the silica particles and subsequently displaced with higher molecular weight untagged PEG (Nd 500), Ie/Imremains lower than that in free solution at all displacer concentrations examined. By
-
-
(38)Israelachvili, J.; Pashley, R. Nature 1982, 300,341.
Char et al.
1104 Langmuir, Vol. 5, No. 4 , 1989
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Figure 8. Effect of on ( ( R 2 ) o(R2))3/2 / calculated from FH EOS for tracer chains of two different molecular weights: (a) Nt = 100 and (b) Nt = 200; -, xs = 0.29; ---,xs = 0.33. Parameters include Nd = 500, x = 0.45, { = 0.71, and R, = 4.3.
Figure 9. Comparison of theoretical predictions with fluorescence experimental data: (a) Nt = 100 and (b) Nt = 200; -, with FH EOS and x s = 0.29; -.-, with VW EOS and xa = 0.38; - - - , fluorescence experimental data. Parameters used for the theoretical predictions are Nd = 500, x = 0.45, { = 0.71, and R, = 4.3.
contrast, an overshoot, where I e / I m is higher than that in free solution, is observed when a higher molecular weight tracer chain (Nt 200) is used at the same experimental conditions. Using the observation of overshoot in one but not in another as our criterion described above, we found that xs for our experimental system (PEG adsorption on silica particles in water) is approximately 0.29 when the FloryHuggins EOS is used, as shown in Figure 8. When the van der Waals EOS is used, xs is slightly higher (x,= 0.38) than that from the Flory-Huggins EOS. These two xs values are rather low compared to xs found e1~ewhere.l~ Often, pretreated silica particles containing a mixture of hydrophobic and hydrophilic surface sites are dispersed in aqueous solution for the measurement of the adsorption isotherm.39 The silica particles used in our experiment23 are tiny colloidal particles with a relatively low concentration of silanol groups on the surface at pH 7, which are believed to act as the adsorption sites via hydrogen bonding with the ether oxygen in the PEG backbone. This is also verified by the low affinity adsorption isotherm40 observed at low concentrations. The low affinity adsorption isotherm is consistent with the low xs value, as illustrated in Figure 4a when the Flory-Huggins EOS is used. The xs for the van der Waals EOS must be raised to 0.38 to reach a comparable surface concentration since the rearrangement of tracer chains on the surface largely depends on the surface concentration of the displacer chains. After determining the parameters xsand R,, we are able to compare the theoretical predictions and the experimental data. This comparison is made in Figure 9 for two molecular weight tracer chains (Nt = 100, 200). Figure 9 shows a qualitative agreement between the theoretical predictions and the fluorescence data. At a particular xs, the relative excimer to monomer intensity ratio, (Ie/ Im)/(Ie/I&, for the shorter tracer chain (Nt = 100) initially rises very rapidly to a displacer concentration of 2 x lo4 M and levels off when the displacer concentration is further increased. For the longer tracer chain of Nt = 200, (Ie/Im)/(Ie/I,,J0increases sharply at low equilibrium concentrations of displacer, followed by a maximum where
(Ie/Im)/(Ie/I,,J0exceeds unity before reaching a plateau. These general features predicted from the theory correspond very well to the fluorescence e ~ p e r i m e n t .The ~~ theory predicts exactly the same displacer concentration giving the maximum in ( I e / I m ) / ( I e / I , J 0for the longer tracer chain. However, there exist notable differences between the predictions and the experimental data in the plateau region for both molecular weight tracer chains. The discrepancies are due to the fact that the preadsorbed tracer chains are not completely desorbed into bulk solution, even at a high displacer concentration. Approximately 35% of the initially adsorbed tracer chains remains oh the surface, as determined from the optical densities of the supernatant solution.23 If the tracer chains had desorbed completely, the theoretical predictions and experimental data would have coincided as Cd gets large. The theory predicts that the tails of the remaining tracer chains are folded at first and then stretched into a direction normal to the surface at a high displacer concentration, yielding a smaller mean square end-to-end distance and, consequently, an enhanced fluorescence signal. We speculate that what actually happens is that the tracer chains are entrapped on the surface by displacing polymer. Since the size of the displacer used in the experiment (end-to-end distance 120 A) is comparable to the silica particle size (150 A), the displacer chain can wrap around the spherical particles, a process not described by the planar surface assumed in the theory. When the displacer concentration is increased, it is possible that some tracer chains remain pinned to the surface by the many bound segments of displacer and are unable to rearrange despite the equilibrium tendency to be displaced. Thus, excimer formation is sterically hindered by this process, causing (Ie/Im)/(Ie/I,,J0 to be less than unity. The mechanism for the entrapment of the tracer chains a t a high displacer concentration is not accounted for in the theory, consequently giving a discrepancy in the numerical values of
-
(39) Rubio, J.; Kitchener, J. A. J. Colloid Interface Sci. 1976,57,132. (40) Unpublished results.
(41)Note Added in Proof This & represents the total amount adsorbed within the first blob. Use of the average concentration within the blob, @, = (a/()J&/"@(z)dz, serves to lower &, requiring a larger x. to effect the same result. The trends and semiquantitative results remain unaltered while the numerical value of xB would change.
-
Ie/Im*
It is difficult to determine which EOS describes our experimental system better since xs is left as an adjustable parameter. As shown in Figure 9, once the xs is determined for each EOS, they both show the same qualitative feature. The xs determined from the van der Waals EOS is slightly larger than that from the Flory-Huggins EOS since the van der Waals treatment predicts a lower adsorbed amount at the same than does the Flory-Huggins approach. The probe in our experimental system is more localized than layer thickness measurements; however, sensitivity to the details of the EOS is lacking.
Langmuir 1989, 5, 1105-1111
1105
distance of longer tracer chains varies over a broad range so that the distance of tracer chain on the surface can even be smaller than that in bulk solution a t a high displacer concentration. To make a direct comparison with the fluorescence experiment, the attraction between hydrophobic pyrene ends attached to a hydrophilic polyethylene glycol (PEG) chain in water has been considered by using a capture process where pyrene ends within twice the capture radius are combined to form excimers. Corrections for the displacement of tagged chains have also been taken into account. Comparison of the theoretical prediction with the fluorescence experimental data shows qualitative agreement for tracer polymers of two different molecular weights (4250,8650). The quantitative discrepancy in the plateau region may be due to nonequilibrium entrapment of some tracer chains by the higher molecular weight displacers before their rearrangement on the surface. One purpose of this work is to point out the compatiSummary bility between fluorescence experiments on specifically A simple model considering the rearrangement of tracer labeled polymer chains and a simple model of polymer chains due t o the presence of displacing polymer is dechain trajectories. Both approaches offer detailed inforveloped, and results from the model are compared with mation regarding polymer conformations. Such an apthe fluorescence experimental data obtained p r e v i o u ~ l y . ~ ~ proach could be applied to tagged chains in a variety of We assume a Gaussian chain as a tracer polymer adconditions such as those due to external fields, polymer sorbing on a planar surface and that the rearrangement blending, surface boundaries, or chain chemistry. of tracer chains on the surface is affected only by a field Acknowledgment. This work was supported by the due to displacing chains using a modified diffusion equaNSF-MRL program through the Center for Materials tion. The displacer field is separately calculated from the Research a t Stanford University. A.P.G. gratefully acself-consistent equation developed by Ploehn et al." The knowledges the support of the Xerox foundation, GE approximate analytic expression derived here shows a Corporate Research, and IBM for a faculty development qualitative agreement with our observations from award. We thank Dr. H. Ploehn and Prof. W. Russel for fluorescence experiment^:^^ a higher molecular weight making their manuscript available. displacer changes the mean square end-to-end distance of tracer chains more effectively; the mean square end-to-end Registry No. PEG, 25322-68-3.
While the analytic solution derived in this paper shows qualitative agreement with the fluorescence e ~ p e r i m e n t , ~ ~ there remain limitations of this treatment. First, the self-consistent field created by the tracer chain itself is neglected. This might be important when displacer concentration is rather low. Second, although the use of scaling theory for the lateral distribution of tracer chain is a simple, indirect approach, it does not give a correct behavior at the 0 condition. This is because even at the 0 condition, when the displacing polymer is adsorbed on the surface a t a high surface concentration, the tracer chains are also expected to stretch in a direction normal to the surface simply due to intermolecular packing constraints. A more general self-consistent field theory or mean field lattice theory can improve these limitations. Thus, it is worthwhile to compare the results from this paper with the results obtained from more general theories.
Ellipsometry Studies of Cleaning of Hard Surfaces. Relation to the Spontaneous Curvature of the Surfactant Monolayer Martin Malmsten and Bjorn Lindman* Physical Chemistry 1, Chemical Center, Lund University, P.O. Box 124, S-221 00 L u n d , Sweden Received November 14, 1988. I n Final Form: April 18, 1989 By means of a previously developed in situ ellipsometric exhibited the removal of triglycerides from hard surfaces by surfactants is investigated for different classes of surfactants. In addition, the fat removal efficiency of different surfactants is investigated as a function of temperature, salinity, added cosurfactant or hydrocarbon, etc. Different surfactants show very different cleaning efficiency, and even more striking is the strong influence of the parameters mentioned. In a number of cases, a nonmonotonic variation is observed. These different findings are discussed in relation to phase diagrams and microemulsion structure. While the cleaning is a complex process, it is suggested that cleaning efficiency can mainly be referred to the optimal, or spontaneous, packing of the surfactant molecules under the conditions given. It is postulated that maximal removal is related to the optimal surfactant packing into planar layers, i.e., zero curvature toward water and soil. For all systems investigated, this simple model is shown to give a good rationalization of the experimental observations. Particular emphasis is put on nonionic oligo(ethy1ene oxide) surfactants where a nonmonotonic behavior with respect to temperature, hydrocarbon concentration, and salinity is observed. These findings are discussed in relation to other phenomena exhibited by these surfactants and in particular in relation to recent work concerned with temperature-dependent head-group conformations leading to a decreased polarity at higher temperature.
Introduction Applications of surfactants are related to the self-association of surfactant molecules either in the bulk phase, at interfaces, or at macromolecules. While this self-asso0743-7463/89/2405-llO5$01.50/0
ciation is influenced by the characteristics of the system, there are also important general features that govern self-assembly. Because of that, much can be learned from studies of simple, well-defined, systems, and theories 0 1989 American Chemical Society
