J. Phys. Chem. 1995, 99, 1285-1291
1285
Effect of Electrolytes on Adsorption of Cationic Polyacrylamide on Silica: Ellipsometric Study and Theoretical Modeling Victor Shubint and Per Lime* Department of Physical Chemistry 1, Chemical Center, Lund University, P. 0. Box 124, S-221 00 Lund, Sweden Received: July 13, 1994; In Final Form: October 7, 1994@
Adsorption of cationic low-charge polyacrylamide on silica from LiC1, KC1, and CsCl solutions was studied by in situ null ellipsometry. The experimentally measured adsorbed amount (r),being essentially constant at low electrolyte concentrations, decreases at high salt contents. The onset of r decline depends on the type of counterion. Ellipsometric thickness ( d f )increases gradually with increase of electrolyte concentration (c,d,) and levels off at high c,dt. The experimental results are compared with model calculations within the framework of a self-consistent-field theory of polyelectrolyte adsorption. A constant surface potential condition and a random distribution of charge on the polymer were used throughout the calculations. A proper choice of parameters for polymer-surface and counterion-surface realistic surface potential and Flory-Huggins nonelectrostatic interaction provides accurate description of the experimentally observed r vs c,dt and df vs cSdtdependencies. The difference between counterions is reflected by assuming their attractive interaction with the surface to become stronger in the sequence Li+ < Kf < Csf. Structural characteristics of the polyelectrolyte adsorbed layers (size of, and fraction of segments in, trains, loops, and tails) obtained from the model calculations revealed that the molecular mechanisms behind the change of ellipsometric thickness with electrolyte concentration are the formation of larger loops and longer tails due to an increase of the ion-segment competition. For shorter polymer chains the theory predicts a qualitatively different behavior: insensitivity of ellipsometric thickness to the change in electrolyte concentration.
x
Introduction Interfacial behavior of polymers has been an important topic in colloid chemical literature over the past decades. An exhaustive overview of experimental and theoretical progress in the field has been given recently by Fleer et al.’ Despite undeniable achievements both in phenomenologicalunderstanding and in theoretical description of polymer adsorption at solid liquid interfaces, much remains to be learned about fine details of the molecular mechanisms involved. This is due to the complexity of the system under consideration, to the wide variety of polymers and substrates in terms of chemical composition, surface morphology, and electrochemical properties, and, finally, to the abundance of factors governing adsorption of polymers and their interfacial conformation. Hereafter, we will focus on one particular polymerhbstrate pair: polyelectrolyte on an oppositely charged surface. Apart from purely academic interest, these systems attract much attention due to their practical importance. Cationic polyelectrolytes are widely used in water treatment as flocculants and in papermaking as retention agents. In both cases the adsorbed amount of polymer and its interfacial conformation, which are the key characteristics determining polymer bridging efficiency, depend on a number of factors such as surface charge density, molecular weight of polymer, the manner of charge distribution along the chain and its stiffness, the strength of polymer-surface nonelectrostatic interaction, the presence of cosolutes (e.g., electrolytes or surfactants), etc. It is well recognized that electrolytes, which are always present in real systems, affect both polymer adsorptivity and adsorbed layer thickness via (i) screening of electrostatic + Permanent address: Department of Colloid Chemistry Chemical Faculty, St. Petersburg University, 198904 St. Petersburg, Russia. Abstract published in Advance ACS Abstracts, December 15, 1994. @
polymer-surface attraction and of electrostatic repulsion between charged segments, (ii) competition between polymer segments and small ions for the space near the surface, and (iii) competitive adsorption of counterions to the surface. All the above effects are well accounted for in the recent theory for polyelectrolyte adsorption by Bohmer et aL2 based on the model of Scheutjens and Fleer3,4 of polymer adsorption. According to the theory, an increase in electrolyte concentration c,dt can be accompanied by either increase (“screening enhanced” regime) or decrease (“screening reduced” regime) of polymer adsorption, depending on conditions, as was discussed recently by van de Steeg et aL5 Indeed, both regimes have been observed experimentally. The former one is more typical for highly charged polyelectrolytes, i.e., in the case when adsorption is limited by electrostatic repulsion between the segments. Screening of this repulsion leads to an increase in polyion adsorptivity, provided the nonelectrostatic polymer-surface interaction is strong enough to keep the screened polyelectrolyte adsorbed. However, salt screens not only repulsion between charged segments of polyelectrolyte but also segment-surface attraction. In the case when adsorption is dominated by this electrostatic attraction (relatively high surface charge, low polymer charge, and weak nonelectrostatic contribution), increase of electrolyte concentration results in decreasing adsorption. Naturally, a full range of situations intermediate between the above two regimes is feasible, and this often leads to the adsorbed amount r as a function of csdtdisplaying a Although the influence of salt on polyelectrolyte adsorption has been broached in a number of publications, a lack of systematic experimental studies of the electrolyte effect does not allow a complete picture to be drawn. The reports on the salt effect on interfacial conformation of polyelectrolytes are even more scarce. Wang and Audebert,*
QQ22-3654I95l2Q991285$Q9.QQIQ0 1995 American Chemical Society
Shubin and Linse
1286 J. Phys. Chem., Vol. 99, No. 4, I995
1-T
T
'CH3
Figure 1. Chemical structure of the cationic polyacrylamide molecule. t = 0.034.
studying hydrodynamic layer thickness (dhd) of low-charged cationic polyacrylamide on silica, observed a decrease of d h d in the region of salt concentrations where r also decreases, and this shows a proportionality (to some extent) between dhd and r. In the case of hydrolyzed polyacrylamide on weakly-charged cationic polystyrene latex, the layer thickness also followed the change in adsorbed amount: both dhd and r increased with increasing ionic ~trength.~ A completely different picture was observed by Takahashi et al.,1° who conducted an ellipsometric study of sodium polyacrylate adsorption onto platinum plates from NaBr solutions and found a substantial increase in ellipsometric thickness df of the adsorbed layers with dilution while r decreased. This effect was interpreted as electrostatic swelling of the polyelectrolyte layers. Among the techniques which can be used for characterization of adsorbed layers of polymers,' ellipsometry has a number of advantages: it is a nondestructive method and allows in situ investigation of adlayer characteristics; flat substrates with nearly atomic smoothness can be used which excludes complications related to adsorbate roughness and curvature; very small amounts of substance are required for adsorption measurements; the method provides information on both adsorbed amount and interfacial conformation (average layer thickness) in one experiment; and the kinetics of adsorption/desorption processes can be easily followed. In the present paper we report on ellipsometric studies of adsorption of a low-charged cationic polyacrylamide on silica plates from LiC1, KC1, and CsCl aqueous solutions. Equilibrium characteristics of the system, r and df,have been modeled within the framework of a self-consistent-field theory using realistic model parameters, and consistency between experimental findings and theoretical predictions is discussed.
Experimental Section Materials and Chemicals. Cationic polyacrylamide (CPAM) used in this study is a copolymer of acrylamide (AM) and (3(methacry1amido)propyl)trimethylammonium chloride (MAPTAC) (see Figure 1) with mean molecular weight M , = lo6 as specified by the manufacturer (Allied Colloids Ltd, Bradford, U.K.). The polymer was used as supplied, without further purification. The fraction of cationic MAF'TAC units, t = 0.034, was determined by titration of C1- counterions. This value is in good agreement with results obtained by polyelectrolyte titration.12 Polymer solutions (0.25% w/w) for ellipsometric experiments were prepared on freshly distilled water and stored at 5 OC for no longer than a week. Si/SiOz plates with a silica layer of about 30 nm thick were prepared by oxidation of polished silicon wafers in dry oxygen at 900 "C and were cleaned prior to use as described e1~ewhere.l~ Water used throughout the experiments was purified by the following consecutive steps: distillation, percolation through Millipore Water System, and final double distillation in an allPyrex apparatus. It had a typical pH of 5.6 f 0.2 and a
conductivity of around 1 pS cm-' after saturation with COz from the air. The analytical grade salts from Merck were used without purification. Ellipsometry. The adsorbed amount of the polymer and the layer thickness were measured by means of in situ null ellipsometry. This technique is based on detection of the change in the state of polarization of light upon reflection from the surface bearing an adsorbed film with refractive index differing from that of the surrounding medium.14 It can be used for accurate determination of the amount of material in the interfacial film. A separate determination of the mean refractive index (nf) and the average thickness (df) of the film is a more difficult task. To make it possible, one has to satisfy the following conditions: (i) sufficient sensitivity of both ellipsometric angles and A to the changes in nf and df, which can be achieved by choosing a substrate with suitable optical properties, (ii) a proper determination of the substrate optical characteristics, and (iii) high accuracy of measurements. A detailed description of our experimental setup and measurement procedure has been given recently by Landgren and Jons~on.'~ The equipment allows measurements of ellipsometric angles with a typical accuracy of 0.002' and 0.005' for Y and A, respectively. Moreover, in order to eliminate systematic errors due to imperfections of the ellipsometer optical components, four-zone measurements were performed at the beginning of every experiment. All measurements were conducted at the wavelength A = 401.5 nm and the angle of incidence 4 = 67.2" in a thermostated cuvette at 25.0 f 0.1 "C. The substrate (Si/SiO2 plates) consists of bulk silicon, with complex refractive index n2 jk2 (n2 and k2 being the real and imaginary parts, respectively) and a layer of silica with refractive index nl and thickness dl, surrounded by a transparent medium with refractive index no (no = 1.3424 for water at 25 'C and A = 401.5 nm). Thus, the four parameters n2, k2, nl, and dl are to be determined. This was achieved by ellipsometric measurements in air and in water, which were performed at the beginning of every experiment and yielded the following mean optical characteristics: nl = 1.480 f 0.002, dl = 32 f 2 nm, n2 = 5.50 f 0.01, and kz = 0.35 f 0.03. After the measurements on the bare substrate in water, the desired electrolyte concentration and pH were adjusted in the cuvette. After thermal equilibration a certain amount of polymer was injected into the cuvette, and the ellipsometric angles Y and A were recorded continuously until an equilibrium (or quasiequilibrium) was reached. All measurements were conducted under continuous stirring by a magnetic stirrer at about 300 rpm. The results of Y and A measurements were interpreted within the framework of an optical four-layer model, assuming isotropic media and planar interfaces. The mean refractive index nf and the average thickness df of the adsorbed layer were calculated by solving numerically the Drude equations as described in ref 16. The adsorbed amount r was calculated from nf and df according to de Feijter et a1.l'
+
nf - no T=d dnldc
using dnldc = 0.169 cm3 ggl as was measured for the polymer solutions. It is notable that the results of r calculation using the Cuypers formula,18 based on the Lorenz-Lorentz equation for a two-component mixture (polymer/electrolyte) with specific molar volume and molar refractivity of the polymer calculated assuming additivity of structural components, agree with those deduced from eq 1 to within less than 5%. A somewhat more elaborate treatment proposed by Takahashi et d . 1 ° which takes into account Donnan exclusion of electrolyte from the poly-
Effect of Electrolytes on Polyelectrolyte Adsorption electrolyte layer gives no correction to these values. This is due to the low charge density of our polymer and relatively low electrolyte concentrations studied.
Theoretical Model The adsorption of polyelectrolyte to a planar and oppositely charged surface was modeled on the basis of a self-consistentfield theory, initially developed by Scheutjens and Fleer3-4and later extended to polyelectrolytes.2 (A more recent treatment is given by I~raels.'~)We will here only give the main features of the theory; for more details we refer the reader to the original publications. Briefly, the space adjacent to a planar surface is divided into layers, and each layer is further divided into lattice cells of equal size. Within each layer the Bragg-Williams approximation of random mixing is applied, and thus all sites in a layer are equivalent. One lattice cell contains either solvent, a solvated ion, or a polymer segment. The model contains five different species: neutral polymer segment, positively charged polymer segment, cation, anion, and solvent. The polyelectrolyte is considered to be a completely flexible chain consisting of rpolymer segments of which the fraction z is positively charged and (1 - z) is neutral. In general, the distribution of polymer charges along the chain can be described as being uniform, regular, random, or blocky. The uniform distribution ascribes an equal fractional charge to every polymer segment and is the most widely encountered distribution in lattice modeling. In the regular arrangement, the charged segments are evenly distributed and separated by neutral segments. In this work a random charge distribution along the polymer chain was adopted. The adsorption of charged block copolymers has been modeled by 1~raels.l~ In a simple description, the surface is modeled as either having a fixed surface charge density or having a fixed surface potential. The latter approach was selected here in agreement with the surface potential measurements by ISFET (ion-selective field-effect transistors) technique.20 There are two different types of interactions in the model: electrostatic (charge-charge) and nonelectrostatic(the rest). The nonelectrostatic interaction between species in adjacent lattice sites is described by Flory-Huggins parameters.2' The same description is used for the interaction with the surface. The relation to the adsorption parameter xs is given, e.g., for the polymer by X S = -A1,001polymer,suface - Xsolventmrface), Ai,o being the fraction of all neighbors of a site in layer 1 which resides in the surface layer. Here, AI,O= 1/4, since a hexagonal lattice was selected. In line with the random mixing approximation, the charged species (charged polyelectrolyte segments and salt species) are assumed to interact with a potential of mean force, vi, which depends only on the distance to the surface (layer number i). The potential of mean force is related to the charge density through Poisson's equation, - E O E r V v i = ei, where EOEr is the dielectric permittivity of the medium and ei is the total charge density in layer i. The charges of the species are located to planes in the middle of each lattice layer, and the space in between the charged planes is free of charge. A uniform dielectric permittivity is used. From the set of volume fraction profiles of the species, { + ~ i } , and the interaction parameters, a nonelectrostatic potential U A ~ could be calculated for species A in layer i. There is also a layer-dependent but species independent hard-core potential, u'i, acting on each species. This potential is essentially the lateral pressure and is responsible for making the volume fraction in each layer sum up to one. Given the nonelectrostatic potential
x
J. Phys. Chem., Vol. 99, No. 4, 1995 1287
TABLE 1: Parameters of the Model value
quantity
temperature
T=298K relative dielectric constant = 80 lattice spacing d = 0.6 nm surface potential q o = -100mV bulk polymer volume fraction &Iymcr= 5 x 10-5 degree of polymerization rpolymer = 10 005 fraction of charged segments t = 1/29 RZ 0.034 random distribution of polymer charges Interaction Parameters" RT~po~ymer.water = 0SRT
RTXpolymer.cation = 0SRT RTXpolymer,anion = 0.5RT CsadM
= 7.7 h
r
= -2 kJ mol-' RTXpolymer+.surface = -5 kJ mol-' RTXcation.surfwe = -5 kJ mol-' Conversion Factorsb r/(mg m-*) = 0 . 3 5 r c d c RTXpolynet0,surface
Other interaction parameters are zero. Subindex polymer0 and polymer+ refer to neutral and to charged polymer segments, respectively. Obtained from the size of a lattice cell and equalization of a polymer segment in the model with a monomer of CPAM with an average mass. U A and ~ the electrostatic energy q A V j of species A in layer i as well as the hard core potential u'i of layer i, the distribution of unconnected segments of type A is given by the Boltzmann weight of the sum of the three terms, + ~ i exp[-(uai U'i q A v i ) / k r ] . For polymers, the matter becomes more complex since the connectivity has to be taken into account. Finally, and { UAi} and {vi}are Since {@Ai} depends on { UAi} and {vi}, functions of { $ ~ i } as indicated above, {+Ai}, {UAi}, and {vi} have to be solved self-consistently. The numerical solution of this set of implicit and nonlinear equations was carried out on an IBM RS 6000l590 workstation. Parameters used in the model calculations of the adsorption of the cationic polyacrylamide on the silica surface are compiled in Table 1. Some of the parameters (T, E ~ +polymer, , ~ - ~and~ t) are known characteristics of the experimental system. The values of some other parameters ( d , Xpolymer,watcrt Xpolymer,cation, and Xpolymer,anion) are less obvious, and some reasonable assignments were used. The results are not strongly sensitive to the precise values of these parameters. Finally, the rest (VO, Xpolymfi,surface, Xpolymert,siirface, and Xcation,s&ze) were used a~ fitting parameters, although the values of these parameters were not allowed to be unrealistic. As a first approximation, all parameters were assumed to be independent of electrolyte concentration.
-
+ +
Results Experiment. In preliminary experiments we established that the adsorption isotherm of CPAM on silica is (as expected) of a high-affinity type and reaches a plateau at a bulk polymer concentration somewhat below 30 ppm. All experimental results presented in this paper refer to the plateau region. In Figure 2 we show the amount l? of the polyelectrolyte adsorbed from a 50 ppm solution in the presence of LiCl, KCl, or CsCl as a function of the electrolyte concentration at pH = 5.6. As one can see, the adsorbed amount, being essentially M), constant at low electrolyte concentrations (c,dt -= decreases substantially at high electrolyte contents. Such behavior is indicative of the "screening reduced" regime of polymer adsorption and agrees well with corresponding results for weakly-charged polyelectrolytes reported in the literat~re.7~8~22-25 This regime is typical in the case when electrostatics are the main driving force for adsorption. This, however, does not exclude nonelectrostatic forces from being operational simul-
l
~
~
~
Shubin and Linse
1288 J. Phys. Chem., Vol. 99, No. 4, 1995
0
:I
'
1.5
5
8 f P
E
0
1.0
8
01 10.4
I
103
102
10-1
100
0
Electrolyte concentration, M Figure 2. Adsorbed amount of CPAM on silica at pH = 5.6 f 0.2 as a function of electrolyte concentration: LiCl (open squares), KCl (filled squares), and CsCl (open diamonds). Data from two independent sets of experiments are shown. T
5v; 4 .f
.-B. 3
0
q
301
B ?
IO! U '
104
102 10' Electrolyte concentration, M
103
100
Figure 3. Ellipsometric thickness of adsorbed CPAM layers at pH = 5.6 f 0.2 as a function of electrolyte concentration. The symbols are the same as in Figure 2. Data from two independent sets of experiments
are shown. taneously. Indeed, the ability of polyacrylamide to adsorb on silica oxide at neutral pH has previously been demonstrated by Lecourtier et a1.26 In a separate experiment we investigated the feasibility of CPAM adsorption from acid solutions. In accord with Lecourtier et al., we found that even at pH below 4, where the silica surface charge is small,*' r remained substantial: 0.4-0.8 mg m-2 depending on electrolyte concentration. In the theoretical modeling of the polyelectrolyte adsorption (see next subsection), the ability of polyacrylamide to adsorb on the surface is taken into account. The effect of electrolyte on CPAM adsorption clearly depends on the type of cation (see Figure 2). This feature indicates unequivocally that, apart from nonspecific electrostatic screening of polyelectrolyte-surface interaction and space competition between ions and polymer segments, cations affect polyelectrolyte adsorption via competition for the surface sites. The higher affinity of a cation to the surface, the lower the electrolyte concentration for the onset of the decline in r. In this respect the cations studied form a sequence Li+ < K+ < Cs+ which replicates that of binding constants typically found for alkali ions on oxides.28 Figure 3 shows the dependence of the ellipsometric thickness df of adsorbed CPAM on electrolyte concentration. Ellipsometric thickness increases gradually with increase in ionic strength and levels off at the highest studied electrolyte concentrations. Over 3 orders of magnitude in electrolyte concentration df increases from about 10 nm at c,dt = M to 35-40 nm at c,dt = lo-' M. It is notable that the type of
10
20 30 layer number
40
50
Figure 4. Calculated polymer volume fraction profiles as a function of the layer number for = (dotted curve), (short-dashed (solid curve). The inset curve), (long-dashed curve), and
shows the same data on a semilogarithmicscale, and the bulk polymer volume fraction is also indicated. Other parameters are according to Table 1. cation has no pronounced effect on ellipsometric thickness within experimental error (&lo%). In the following subsection we will present the results of the modeling of the polyelectrolyte adsorption using the selfconsistent-field approach. Model Calculations. One of the primary results of the model calculations is the distribution of the polymer segments adjacent to the surface. Examples of polymer volume fraction profiles calculated for different electrolyte concentrations are presented in Figure 4. As shown, the increase of electrolyte concentration leads to an expansion of the adsorbed polymer layer. Thus, at the lowest = the segments density decays rapidly and reaches the bulk level of $polymer = 5 x within the first 40 layers, while at high the theory predicts slowly decaying segment density profiles. Calculated excess amount of adsorbed polymer rcdc can be obtained from the volume fraction profile by simple summation:
is the polymer volume fraction in layer i and is the bulk polymer volume fraction. Figure 5 shows rcdcvs $salt obtained with different sets of model parameters. All curves exhibit the same qualitative feature: constant or slightly increasing rcdcat low salt contents followed by a decrease of the excess amount at high This behavior correlates well with our experimental observations (cf. Figure 2). An explanation of the maximum in rcdcas a function of $sd, was indicated in the Introduction. In order to mimic the difference between the cations, calculations were performed with different cation-surface interaction parameter ~ ~ ~ ~(Figure i ~ 5 , ~curves , ~ a). ~ More r f negative ~ ~ ~results ~ in i the shift ~ of ~ the, onset ~ of d rcdc ~ decline toward lower electrolyte concentrations, in full agreement with experiment. A reduction of the absolute value of the surface potential to +O = -50 mV (curve b) or of the chain length to rpolymer = 1,015 (curve c) both lead to decreased values of the excess amount, but with similar dependence on The calculated polymer volume fraction profiles can also be tested against their consistency with the results of ellipsometric thickness measurements. To do this, one should find a way to estimate the ellipsometric thickness from a given volume fraction profile. In this work we used two approximate formulas where
$polymer,i
$polymer
~
~
~
~
~
J. Phys. Chem., Vol. 99, No. 4, 1995 1289
Effect of Electrolytes on Polyelectrolyte Adsorption 50
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0 ~ " ~ ' " ' ~ ' " " ~ " ~ ' " ' ' " ~ ' ' ~ ' ~ ' ' -4 -3 -2 -5 -4 -3 -2 log @salt log @salt Figure 5. Calculated excess amount of polymer as a function of the Figure 6. Thickness of adsorbed polymer layer as a function of the ~ , ~ ~of f the i ~ electrolyte ~ logarithm of the electrolyte volume fraction at different R T ~ ~ ~ ~ i ~logarithm volume fraction. The thickness was for the conditions given in Table 1 (curves a), V O= -50 mV (curve calculated according to eq 3 (dashed curves) and eq 4 (solid curves) b), and rpalymer = 1015 (curve c). Other parameters are according to for the conditions given in Table 1 (curves a), & = -50 mV (curves Table 1. b), and rpolymcr= 1015 (curves c). Other parameters are according to Table 1. "
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for this purpose:
and
deff
=
(4)
Equation 3 was proposed by McCrackin and C o l ~ o nand , ~ ~for a number of profiles (linear, Gaussian, and exponential) eq 3 gave a good agreement with the thickness of an equivalent uniform layer, i.e., the uniform layer which would produce the same ellipsometric angles as the stack of isotropic sublayers representing the anisotropic film. The second formula was given by Charmet and de Gennes30 as a means of calculation of an effective layer thickness. It is notable that for rapidly decreasing profiles both formulas give very similar or even identical (e.g., for exponential refractive index distribution) results. For slowly decreasing profiles, such as a power law, the equivalent ellipsometric thickness, determined as described above, always lies in between the values calculated using eqs 3 and 4. Thus, del and deff can be used as guidelines for estimation of ellipsometric thicknesses. In Figure 6 the results of numerical summation of theoretical volume fraction profiles using eqs 3 and 4 are shown. As expected, the two formulas give very similar results at low &at where the segment density decays roughly exponentially (see the inset of Figure 4). At high salt contents, where the density profiles decay more slowly, the discrepancies between the formulas can be substantial. However, both of them give the same trend of the layer thickness change with electrolyte concentration. For rpolymer = 10 005 the simulated ellipsometric thickness shows an increase with increasing &dt (curves a and b). It is remarkable that Xcation,surface has only minor influence on the calculated effective thickness (data not shown). Note also a pronounced leveling off (or even decrease when using eq 4)of
d vs #salt at high salt concentrations. All these features are in excellent accord with our ellipsometric results (cf. Figure 3). The decrease in the magnitude of the assumed surface potential does not affect the qualitative trend of the d vs dependencies, but the increase of the thickness becomes less pronounced (see Figure 5, curves b). By contrast, when the calculation is performed for the shorter polymer chain rpolymer = 1015, the result is qualitatively different, exhibiting no salt concentration dependence (curves c). Summarizing the comparative analysis of the results of model calculations presented in this section, we can conclude that the model reproduces well all main qualitative features of adsorbed amount and ellipsometric thickness dependencies on the concentration of supporting electrolyte solution. The same applies to the influence of the type of counterion. Moreover, although the use of the theoretical model in its present form for quantitative description of real systems is hardly justified, applying the conversion factors given in Table 1 to express theoretical results in metric units one obtains reasonable agreements between measured and calculated values of adsorbed amount and thickness of adsorbed layer.
Discussion Having established a good consistency between theory and experiment,we can explore in more detail the information which can be obtained from the model calculations in order to elucidate molecular mechanisms for the electrolyte effect on adsorbed layers of polyelectrolyte. A detailed discussion of the influence of salt ions on adsorptivity of polyelectrolytes has been given recently by van de Steeg et aL5 Hereafter we will focus instead on the salt effects on structural characteristics of adsorbed layers. To understand the conformational rearrangements behind the changes in the average (ellipsometric)thickness of CPAM layers on silica, we have analyzed the probability of a polymer segment to be part of different structural entities (trains, loops, and tails) as well as the average length (average number of segments) of these en ti tie^.^ Typical results are presented in Figure 7. Over the whole electrolyte concentration range more than 80% of polymer segments reside in loops, reflecting an extended interfacial conformation, a characteristic of weakly charged polyelectrolytes. At low electrolyte concentrations the loops contribute most to the average thickness of the adsorbed layer since contribution of tails is negligible as could be expected
1290 J. Phys. Chem., Vol. 99, No. 4, I995
Shubin and Linse
a 50
1000
40
r W
30 5
U
tails
...... ?5
loops -4
-3
-2
20
..........
in trains -5
-3
-4
.i
-2
log %all
Figure 7. Calculated average fraction of segments being in tails, loops, and trains as a function of the logarithm of the electrolyte volume fraction. The inset shows the calculated average number of segments per tail and loop as a function of the logarithm of the salt volume
fraction. Parameters are according to Table 1. for a strongly attached high molecular weight polymer. As a consequence, the ellipsometric thickness is nearly one half of the average contour length of loops. The average train length of about three is almost insensitive to the change in 4sdt. At low ionic strength, 12.5% of the polymer segments are in immediate contact with the surface (in trains). Taking into account the average train size, this implies that at these conditions every polymer molecule has more than 400 groups of segments attached to the surface (attachment points). This multipoint attachment renders the polymer adsorption virtually irreversible. The conformation of a part of an adsorbed polymer molecule at low &It is schematically depicted in Figure 8a. Upon increase of electrolyte concentration, the fraction of polymer segments in trains decreases gradually which, for a given = constant, means progressively fewer attachment points of the polymer molecule to the surface. Increase of the concentration of the small ions makes their competition with the polymer segments for the place in the first layer more and more successful and causes the gradual detachment of the polymer chains. This appears to be a key factor responsible for the effect of electrolyte on conformation of the adsorbed macromolecules. The above process is accompanied by (i) an increase of the polymer fraction in tails from 2% to about 15% and (ii) a substantial increase of the average length of both loops and tails. As a result, at the highest 4$dtonly 5% of segments remain in trains, which brings the number of the polyelectrolyte contacts with the surface down to about 160. At the same time the loop length doubles and the tail size increases by a factor of 7 compared to that at low electrolyte concentration. The average tail size reaches almost 1/10 of the total chain length. A conformation of the polyelectrolyte at high &dl is schematically presented in Figure 8b. Now the calculated ellipsometric thickness d e l (see Figure 6) exceeds even one-half of the stretched loop length. Taking into account that the latter is a clear overestimate of the average extension of loops (because of the coily conformation of the relatively large loops), we conclude that at high tails contribute substantially to the average layer thickness. These long dangling tails are responsible for the slow decay of the polymer volume fraction profiles at high salt concentrations(see Figure 4). Thus, a self-consistent picture of the macromolecular conformation of adsorbed polyelectrolyte emerges from the above analysis. A similar analysis applied to the case of shorter-chain polymers helps to clarify the reasons for the peculiar insensitivity of calculated ellipsometric thickness to the change in electrolyte
Figure 8. Schematic representationof an end fragment of an adsorbed CPAM molecule at low (a) and high (b) electrolyte concentration. The polymer charges as well as the bulk electrolyte ions are omitted for simplicity. Note that only ca. 1/30 of the train-loop part of the adsorbed polymer molecule is shown. The dashed lines correspond to the ellipsometric thickness,
concentration (see Figure 6, curves c). Indeed, if ion-segment competition for surface sites is still operational and, as in case of long-chain molecules, results in eventual desorption of polymer at high (cf. Figure 5 ) , why does it cause almost no conformational changes in terms of train, loop, and tail characteristics? The theory predicts the constancy of both average length and average number of trains, loops, and tails. In this case, the average lengths of tails and loops are 150 and 14 segments, respectively, and the number of trains is only 40 per molecule. The disappearance of a fraction of the trains with increase of the salt concentrationapparently leads to the situation when the entropical penalties for the polymer molecule being close to the surface are not overcompensated any more by the energy gain due to electrostatic and nonelectrostatic polymersurface interaction. Then the whole molecule leaves the surface while the configuration of the remaining molecules is virtually unperturbed. Experimentally,this effect can be observed if only polydispersity of the polymer is low. Finalizing the discussion, we would like to make one more comment. This concerns the choice of model parameters. In the present work a number of them, e.g., surface potential and some interaction parameters, were used as free fitting parameters and were assumed to be independent of solution composition. To make the model calculation of a real polymer/substrate system more rigorous and substantiated, one should employ a wider variety of experimental data obtained over a broad range of experimental conditions for fitting the values of model parameters. An altemative or, rather, complementary way is to rely on independent information about these model parameters. Thus, surface charge and surface potential of substrate in the presence of polyelectrolyte at varied solution conditions ( i e . , pH and electrolyte concentration) can be determined by conventional colloid chemical methods of potentiometric titration and the ISFET technique, respectively. Information about surface chemical composition (e.g., surface concentration of hydroxyl groups [SOH]) can be obtained via spectroscopic methods and can be used for estimation of x parameters (e.g., Xplyme&,sdace [SOH] can be assumed). Unfortunately, to date such data are scarce in the literature.
-
Conclusions The combination of ellipsometry, which provides two important characteristics of the adsorbed polyelectrolyte layerthe
J. Phys. Chem., Vol. 99, No. 4, 1995 1291
Effect of Electrolytes on Polyelectrolyte Adsorption adsorbed amount and the average thickness-and model calculations within the framework of the self-consistent-field theory of polyelectrolyte adsorption proved to be successful in elucidating the molecular mechanisms of the electrolyte effect on the structure of adsorbed polyelectrolyte layer. Ion-segment competition is shown to cause conformational changes of adsorbed polyelectrolyte molecules. h experiments these changes manifest themselves in electrolyte concentration dependence of the average layer thickness. The model calculations predict qualitatively different behavior for shorter-chain polymers. Verification of the theoretical predictions as well as progress in further development of the theory is mainly restricted by the lack of versatile experimental information on interfacial behavior of polyelectrolytes, including their influence on surface properties such as surface charge, potential, and surface chemical composition of solids. This calls for continuation of experimental work in the field.
Acknowledgment. R. Israels is gratefully acknowledged for valuable suggestions regarding numerical algorithm involving electrostatic potential and A. Panasjuk for his participation in ellipsometric measurements. We are thankful to the Swedish Research Council for Engineering Science (TFR), Karlshamn’s Research Foundation, and Bo Rydin Foundation for financial support of this work. References and Notes (1) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman & Hall: London, 1993; p 502. (2) Bohmer, M. R.; Evers, 0. A,; Scheutjens, J. M. H. M. Macromolecules 1990, 23, 2288. (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) van de Steeg, H. G. M.; Cohen Stuart, M. A.; de Keizer, A,; Bijsterbosch, B. Langmuir 1992, 8, 2538.
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