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Effect of Chain Architecture on Adsorption from Dilute Solution: ω-Functionalized Linear and Mono-, Di-, and Tri-ω-functionalized Three-Arm Star Polybutadienes Denise F. Siqueira,† Marinos Pitsikalis,‡ Nikos Hadjichristidis,‡ and Manfred Stamm*,† Max Planck Institut fu¨ r Polymerforschung, Ackermannweg 10, 55021 Mainz, Germany, and Department of Chemistry, University of Athens, Panepistimiopolis-Zografou, 15771 Athens, Greece Received October 24, 1995. In Final Form: December 19, 1995X The adsorption behavior of ω-functionalized linear and mono-, di-, and tri-ω-functionalized three-arm star polybutadiene (PB) samples from the mixed solvent of cyclohexane and toluene (50% by volume) on silicon wafers is investigated by means of null-ellipsometry at 20.0 °C. Under these conditions no association of the sulfozwitterionic functional groups is detected in solution with dynamic light scattering, and there is sufficient contrast for in situ ellipsometric adsorption measurements. The adsorbed end-functionalized linear PB chains have a “brushlike” conformation. In the case of the functionalized star PB, the adsorbed amount increases when the number of functionalized arms increases from 1 to 3. However, the grafting density is more influenced by the molecular weight than by the number of functional groups. The adsorbed stars are less stretched than the linear chains. The adsorption energy is calculated as (9 ( 1)kT. The diffusion coefficient and hydrodynamic radius are determined with dynamic light scattering. The adsorption kinetics from time-resolved ellipsometric measurements show two regimes: (i) a diffusion-controlled process at the initial stages and (ii) at longer times, an exponential behavior, where the arriving chains must penetrate a barrier formed by the already adsorbed chains. The stars penetrate this barrier faster than the linear PB chains.
Introduction The adsorption of linear end-functionalized polymer chains has been extensively studied,1-10 since this is a subject of many practical and fundamental interest. However, there is scarce information about the adsorption of end-functionalized star polymers. Different adsorption behaviors may be expected between end-functionalized linear and star polymers, due to their different spatial architectures. The theoretical treatment of the adsorption of nonfunctionalized stars is well reported in the literature.11-15 In particular Halperin and Joanny11 studied the adsorption of stars on a flat solid surface and found three regimes as a function of the adsorption energy. In the strong adsorption limit the star is fully adsorbed. When the adsorption energy is smaller than a critical value, the adsorbed star assumes the “sombrero” structure, where just some arms are fully adsorbed, while the other * To whom correspondence should be addressed. † Max Planck Institut. ‡ University of Athens. X Abstract published in Advance ACS Abstracts, February 15, 1996. (1) Alexander, S. J. Phys. 1977, 38, 983. (2) de Gennes, P.-G. Macromolecules 1980, 13, 1069. (3) Milner, S. T.; Witten, T. A.; Cates, M. E. Europhys. Lett. 1988, 5, 413. Milner, S. T. Science 1991, 251, 905. (4) Ligoure, C.; Leibler, L. J. Phys. 1990, 51, 1313. (5) Kumacheva, E.; Klein, J.; Pincus, P.; Fetters, L. J. Macromolecules 1993, 26, 6477. (6) Murat, M.; Grest, S. G. Macromolecules 1989, 22, 4054. (7) Lai, P. Y.; Binder, K. J. Chem. Phys. 1991, 95, 9288. (8) Siqueira, D. F.; Breiner, U.; Stadler, R.; Stamm, M. Langmuir 1995, 11, 1680. (9) Tauton, H. J.; Toprakcioglu, C.; Fetters, L. J.; Klein, J. Macromolecules 1990, 23, 571. (10) Halperin, A.; Tirrell, M.; Lodge, T. P. Adv. Polym. Sci. 1992, 100, 31. (11) Halperin, A.; Joanny, J. F. J. Phys. II 1991, 1, 623. (12) Ohno, K.; Binder, K. J. Chem. Phys. 1990, 95, 5444. (13) Zhulina, E. B.; Vilgis, T. A. Macromolecules 1995, 28, 1008. (14) Carignano, M. A.; Szleifer, I. Macromolecules 1994, 27, 702. (15) Di Marzio, E. A.; Guttman, C. M.; Mah, A. Macromolecules 1995, 28, 2930.
arms dangle in the solution, and in the weak adsorption regime, thermodynamically stable and metastable structures may be found. In the metastable state the stars do not spread on the surface; they keep their spherical form, and this case perhaps may be compared to the adsorption of end-functionalized stars. Carignano and Szleifer14 compared the structural and thermodynamic properties of grafted linear and three-arm star polymer chains of the same molecular weights in a good solvent. Only one of the three arms has the end grafted to the surface, while the other two arms are free. The ratio of the arm lengths is varied. For low surface coverages both linear and branched chains present “mushroom” conformations. As the surface coverage increases, linear and branched chains show different density profiles and conformations on the surface, which are a function of the arm length and the length ratio among them. Zhulina and Vilgis13 predict the scaling laws for brushes formed by regularly branched (comblike and starlike) polymers as a function of the solvent quality. Ohno and Binder12 present a scaling theory for radial distributions of the star polymers in the bulk and at the surface. Some initial studies on the adsorption of stars by means of self-consistent field method are shown by DiMarzio and co-workers.15 In this work, we investigate the adsorption behavior (statics and kinetics) of linear and three-arm star polybutadienes, end-functionalized with the sulfozwitterionic group, on silicon wafers from the solvent mixture of cyclohexane and toluene (50% in volume) by means of null-ellipsometry. The solution properties of end-functionalized linear and star polybutadiene in the solvent mixture are investigated with dynamic light scattering. Experimental Section Materials. All the polybutadiene (PB) samples were prepared by anionic polymerization. All manipulations were performed in evacuated, n-BuLi-washed, and benzene-rinsed glass reactors equipped with breakseals and constrictions. First the dimethylamino group was introduced to the chain end by polymerizing butadiene with [3-(dimethylamino)propyl]lithium. Neutraliza-
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Table 1. Molecular Characteristics of ω-Functionalized Linear (L) and Mono-(1N)-, Di-(2N)-, and Tri-(3N)-ω-functionalized Polybutadienes
sample ZW-L-PB12 ZW-L-PB20 ZW-L-PB30 ZW-1N-PB111 ZW-2N-PB62 ZW-2N-Pb99 ZW-3N-PB67 ZW-3N-PB93
Mn arm nonfunctionalizeda (kg/mol)
34.8 22.1 35 23.2 33
Mn arm functionalizeda (kg/mol)
34.0 21.9 30.7 23.2 33
Mn stara (kg/mol)
Mb (kg/mol)
Mw/Mnc
NB
104 61.8 89 62.5 91.4
11.6 20 80 111 62.4 99 67.4 93.1
1.02 1.03 1.03 1.06 1.06 1.06 1.06 1.06
215 370 1481 2056 1156 1833 1248 1724
a Membrane osmometry (MO) in toluene at 37 °C. b Low-angle laser light scattering (LALLS) in THF at 25 °C. c Size exclusion chromatography (SEC) in THF at 30 °C. NB represents the degree of polymerization of the linear or the star PB samples calculated from Mw.
tion of the produced ω-functionalized PB with methanol gives the ω-functionalized linear PB, while reaction with methyltrichlorosilane leads to the tri-ω-functionalized three-arm star PB. The three-arm star PB with one and two dimethylamine end groups were prepared by controlled reaction of the ω-functionalized and nonfunctionalized living PB, obtained by using sec-BuLi as the initiator, with methyltrichlorosilane. The dimethylamine groups [-N(CH3)2] were transformed to the highly polar sulfozwitterionic [-(CH3)2N+(CH2)3 SO3-] by reaction with cyclopropanesultone. Details of the synthesis are given elsewhere.16 The molecular characterization was carried out on the dimethylamine-capped PB by size exclusion chromatography (SEC) in THF, low-angle laser light scattering (LALLS) in THF, and membrane osmometry (MO) in toluene. The results, also valid for the corresponding zwitterionic-capped PB, are given in Table 1. These results indicate a high degree of molecular and structural homogeneity. The functionalized and nonfunctionalized arms in the same star have almost the same molecular weight. The ω-functionalized PB samples are denoted here as ZW-L-PBm, while the three-arm star PB samples as ZW-nNPBm. The n stands for the number of end-functionalized arms, and m represents the molecular weight in kg/mol of the linear chain or the whole star. Reagent grade toluene and cyclohexane (Riedel-de Ha¨en) were distilled over sodium metal prior to use. Ellipsometry. Null-ellipsometry was used to measure in situ the adsorption of ZW-L-PBm and ZW-nN-PBm from dilute solutions on silicon wafers. The principles of ellipsometry as well as the experimental details are described elsewhere.8,17 All the adsorption measurements were made in a special built glass cell (Hellma), which has stress free entrance and exit windows fixed at 70.0°. The freshly cleaned silicon wafer was fixed on a support and placed in the cell. The cell was filled with ca. 80 mL of pure solvent (mixture of toluene and cyclohexane, 50% in volume), kept at a constant temperature of (20.0 ( 0.1) °C by a thermostat, and the ellipsometric angles were measured. Then the polymer solution was added and stirred for 2 min. Every 24 s a pair of ellipsometric angles, ∆ and Ψ, was recorded. The measurements last typically 3 h. For periods of time longer than 1 h, changes in the ellipsometric angles or adsorbed amount can no longer be resolved (Figure 1), indicating that the equilibrium in the adsorption process has been achieved. Solutions of ZW-L-PBm and ZW-nN-PBm were prepared in a mixture of toluene and cyclohexane (50% volume fraction in the mixture) in the concentration range of 0.009-0.8 mg/mL. Toluene and cyclohexane are good solvents for PB. Silicon wafers (kindly supplied by Wacker-chemitronics, Burghausen) were used as substrates. They are composed of Si (n ) 3.88 - i0.018)18 and a SiO2 layer typically 1600 Å thick with a refractive index of 1.462, determined through ellipsometric measurements. The increment of refractive index, dn/dc, was determined by means of a differential refractometer (λ ) 589.4 nm) at 20.00 °C as (0.050 ( 0.005) mL/g for ZW-L-PBm and ZW-nN-PBm in the (16) Pitsikalis, M.; Hadjichristidis, N. Macromolecules 1995, 28, 3904. (17) Motschmann, H.; Stamm, M.; Toprakcioglu Macromolecules 1991, 24, 3681. (18) Edward, D. P., Ed. Handbook of Optical Constant of Solids; Academic Press Inc.: London, 1985.
Figure 1. Typical curve of adsorbed amount as a function of time measured for a solution containing 0.0092 mg/mL of ZW3N-PB93 in cyclohexane/toluene (50% in volume) at 20.0 °C.
Figure 2. Multilayer model used for ellipsometric data interpretation. The adsorbed layer is assumed to be isotropic and homogeneous. solvent mixture and did not depend on molecular weight or number of functional groups in the investigated range. Data Analysis. For the data interpretation, a layer model of an adsorbed homogeneous isotropic polymer layer on a silicon wafer is proposed (Figure 2). In this layer model the substrate can be first well characterized by means of ellipsometry; the refractive index of the medium can be measured with an Abbe refractometer, and the remaining optical parameters, n1 and d1, corresponding to the adsorbed polymer film can be obtained from ellipsometric measurements.8,19 The adsorbed amount A (mg/m2) can be calculated using the following equation:
A)
d1(n1 - n0) (dn/dc)
) d1c1
(1)
where n1 and d1 are polymer layer parameters obtained from the values of ∆ and Ψ measured at the equilibrium, n0 is the index of refraction of the solution measured with an Abbe refractometer, dn/dc is the increment of refractive index determined with a (19) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North Holland Publication: Amsterdam, 1987.
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differential refractometer, and c1 is the mean polymer concentration within the layer. Although a separate determination of n1 and d1 is difficult due to the small differences in index of refraction of the polymer and solution, the product n1d1 is an invariant of the adopted layer model. The adsorbed amount determined by means of ellipsometry proves insensitive toward whichever type of concentration profile near the wall is assumed: 17 step, parabolic, or exponential. Dynamic Light Scattering (DLS). DLS measurements were performed on an ALV 3000 commercial digital correlator equipped with a 400 mW krypton ion laser (λ ) 647 nm). Autocorrelation functions, g1(t), were measured for the solutions of ZW-L-PB80 and ZW-3N-PB93 in a solvent mixture of toluene and cyclohexane (50% vol) at 22 °C for concentrations of 4.3, 0.86, and 0.43 mg/mL at scattering angles of 30°, 60°, 90°, 120°, and 150°. The results can be well represented by the following single exponential function, which is typical for monodispersed spheres:20
gq(t) ) exp(-2Dq2t)
(2)
where t is the time delay, D is the diffusion coefficient, and q is the magnitude of the scattering vector. The diffusion coefficient and the hydrodynamic radius Rh of particles are interrelated by the Stokes-Einstein relation
Rh ) kT/6πηD
(3)
where k is the Boltzmann’s constant and η is the viscosity of the solvent.
Results and Discussion Adsorption Isotherms. Null-ellipsometry is a very accurate technique to investigate adsorption phenomena. However, it requires sufficient contrast between the layers in the model presented in Figure 2. Toluene is a good solvent for the functionalized PB samples, while cyclohexane is a bad one. The association behavior of these polymers in cyclohexane was recently reported.16 The difference in refractive indices between toluene and PB at the wavelength of 632.6 nm is too low. Therefore the solutions were prepared in the mixture of toluene and cyclohexane (50% in volume), which provides enough contrast. Up to a concentration of 2.0 mg/mL of polymer in this mixed solvent, no aggregation process is detected by means of DLS (see below). Nonfunctionalized PB in this solvent mixture does not adsorb on the substrate surface, since no changes in the ellipsometric angles can be observed in a corresponding adsorption experiment. The adsorption behavior of the end-functionalized PB in pure toluene is the same as that in the solvent mixture of cyclohexane and toluene. The use of a mixed solvent, however, allows in situ ellipsometric investigations due to the available contrast, while experiments with toluene are only possible by using films which have been dried after the adsorption is complete. However, the adsorbed amount in pure cyclohexane is much lower. This is probably due to strong intermolecular association of the chains in the solution,16 making free chains available only at very low concentration. In Figure 3 the adsorption isotherms obtained for the linear chains of different molecular weight, ZW-L-PB12, ZW-L-PB20, and ZW-L-PB80, are shown. The samples ZW-L-PB12 and ZW-L-PB20 present practically identical plateau values (2.47 ( 0.01) and (2.41 ( 0.25) mg/m2, respectively, which are higher than that obtained for the high molecular weight sample, ZW-L-PB80, (1.69 ( 0.18) mg/m2. All samples carry the same functional group; therefore the adsorption energy for the three samples is (20) Pecora, R.; Berne, B. J. Dynamic Light Scattering; John Wiley & Sons: New York, 1976.
Figure 3. Adsorption isotherms for the linear ZW-L-PB12, ZW-L-PB20, and ZW-L-PB80 samples from solutions prepared in the solvent mixture of cyclohexane and toluene (50% in volume) by means of ellipsometry. All the measurements were performed at 20.0 °C.
the same. Thus the observed differences in the adsorbed amount at the plateau are due to different PB block lengths. This behavior can be understood with the following argument: the longer the butadiene blocks, the bigger the space they occupy and the stronger the repulsion between them. The concentration behavior is indicative for a Langmuir-type adsorption, where an equilibrium between adsorbing and desorbing chains is achieved at a given concentration. Because of the large uncertainties at very low concentrations, a more detailed fit was not performed. The grafting density σ can be obtained from
σ ) ANA/Mw
(4)
where A is the adsorbed amount, NA the Avogadro’s number, and Mw the molecular weight of the PB. The interchain distance Dinter can be calculated from the grafting density:
Dinter ) 1/xσ
(5)
On the other hand, the space needed to accommodate a swollen polymer coil in a good solvent in its unperturbed state on the surface, Dover, can be calculated as
Dover ) (πRPB2)0.5
(6)
where RPB is the Flory radius (R ) aNν) for linear PB. In cyclohexane the values of ν and a can be found in the literature21 as 3/5 and 0.15 nm, respectively. For the solvent mixture used, the same values are assumed, as an approximation. The ratio δ ) Dinter/Dover may be used to give a measure on the degree of stretching of the adsorbed chains. A δ value of 1 indicates that the chains are essentially not stretched and assume a “mushroom” conformation on the surface, while lower δ values indicate stretching with the tendency to form “brushes”, as the other extreme. The δ values obtained for the three linear samples are shown in Table 2 and indicate that the adsorbed chains are stretched and that their conformation is between a truly unperturbed mushroom conformation and a truly extended brush. We use for this conformation the notation brushlike. The adsorption isotherms obtained for the star PB samples are shown in Figure 4. In the case of strong (21) Roovers, J.; Martin, J. E. J. Polym. Sci., Polym. Phys. Ed. 1989, 27, 2513.
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Table 2. Various Parameters of ω-Functionalized Linear (L) and Mono-(IN)-, Di-(2N)-, and Tris-(3N)-ω-functionalized Polybutadienesa sample
Aplateau (mg/m2)
σ (chains/nm2)
Dinter (nm)
Dover (nm)
δ ) Dinter/Dover
RPB (nm)
ZW-L-PB12 ZW-L-PB20 ZW-L-PB80 ZW-1N-PB111 ZW-2N-PB62 ZW-2N-PB99 ZW-3N-PB67 ZW-3N-PB93
2.47 ( 0.01 2.41 ( 0.25 1.69 ( 0.18 1.77 ( 0.17 1.86 ( 0.06 1.90 ( 0.12 2.14 ( 0.18 2.3 ( 0.2
0.125 0.07 0.012 0.0096 0.0179 0.0128 0.0191 0.0148
2.8 3.8 9.1 10.2 7.5 8.8 7.2 8.2
10.5 14.5 33.3 25.2 19.1 25.2 19.7 24.3
0.27 0.26 0.27 0.4 0.39 0.35 0.37 0.34
5.9 8.2 18.8 14.2 10.8 14.2 11.1 13.7
a A plateau denotes the adsorbed amount corresponding to the plateau region in the adsorption isotherm and σ is the grafting density. Dinter is the experimental average interchain distance, Dover is the calculated chain spacing necessary for unperturbed coils on the surface to being to touch, and δ ) Dinter/Dover is the parameter indicating chain stretching. RPB is the calculated Flory radius, for details, see text.
Figure 4. Adsorption isotherms for the star ZW-1N-PB111, ZW-2N-PB62, ZW-2N-PB99, ZW-3N-PB67, and ZW-3N-PB93 samples from solutions prepared in the solvent mixture of cyclohexane and toluene (50% in volume) by means of ellipsometry. All the measurements were performed at 20.0 °C.
adsorption the chains loose entropy when they stick, but this loss is compensated by the high enthalpic gain due to the favorable interactions between surface and functional group. The adsorption energy per end functional group calculated for this system is high (about 9 kT), as will be shown in the next section. Thus a considerable difference in the adsorption behavior would be expected when the number of functional groups varies between 1 and 3 for samples with the same molecular weight. Experimentally a systematic increase in the plateau values can be observed when the number of functionalized arms increases from 1 to 3 and the molecular weight is approximately the same. Comparing the plateau value obtained for the linear and star end-functionalized PB chains, we observed that the plateau value obtained for the linear chains ZW-L-PB80 is approximately the same as those obtained for the stars ZW-2N-PB99, ZW-2N-PB62, and ZW-1N-PB111. It is, however, lower than those obtained for the stars with three functionalized arms (ZW3N-PB67, ZW-3N-PB93), although they have approximately the same molecular weight. The surface density σ can be calculated for the stars using eq 4 and the molecular weight of the whole star. The results for the plateau values are shown in Figure 5. In this figure one can observe the trend that the dependence of σ on the molecular weight seems to be stronger than its dependence on the number of functionalized arms, although only a limited number of experiments are available. The σ values obtained for ZW-2NPB62 and ZW-3N-67 are very close. It indicates that although the adsorption energy is high, the entropic loss involved in the attachment of a third arm when two arms are already attached may be very high. The adsorbed end-functionalized stars may assume different conformations on the surface, where the probability of occurrence
Figure 5. Variation of the chain grafting density σ as a function of the molecular weight of the whole star.
Figure 6. Schematic representation of the possible conformational states of the adsorbed end-functionalized stars and linear molecules. Different conformational states may contribute very differently to the total adsorbed amount as discussed in the text.
may significantly decrease with increasing number of adsorption sites. All the possibilities of attachment of the chains with different architectures are schematically shown in Figure 6. Thus for entropic reasons configurations in part f and in particular in part g of Figure 6 should be less favored as compared to those in part e for the stars with three functionalities.
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From the values of the surface grafting density, Dinter can also be calculated for the stars by means of eq 6, as shown in Table 2. Dinter represents the experimental average distance between two adsorbed stars. The values are practically the same for stars with two or three endfunctionalized arms, again indicating that the configuration shown in Figure 6g practically may not play a significant role in the adsorption process. Dinter increases weakly with increasing molecular weight of the stars. For the sample ZW-1N-PB111, Dinter is larger. Due to the chain branching, the steric hindrance close to the surface caused by adsorbed stars seems to be bigger than that caused by linear chains. The stars have clearly a reduced freedom for chain stretching as compared to linear chains (see Figure 6), which results in an enhanced steric repulsion between neighboring chains. The relative contribution of this conformational restriction should depend on molecular weight and should be negligible in particular for very high molecular weights. As a control experiment, the adsorption of nonfunctionalized stars was investigated. Neither the center of the stars (which is chemically different from the arms) nor the PB arms adsorb onto the silicon wafer from the solvent. The radius of the star in a good solvent can be calculated as22
Rstar ) af1/5N3/5
(7)
where f is the number of arms, or functionality, of the star. In Table 2, Rstar is represented as RPB. In the star the mean segment density in the coil is higher than that in the linear chain, and the segment density distribution becomes narrower. Dover can thus be calculated by means of eq 6, using RPB from eq 7. The stretching parameter δ indicates that the adsorbed star PB chains are less stretched than the adsorbed linear ones. Calculation of Adsorption Energy. In the previous section it was shown that neither the PB segments nor the core of the stars adsorbs on the silicon wafers from the solvent mixture of toluene and cyclohexane. The adsorption of the end-functionalized PB on the hydrophilic surface of silicon wafers is due to the favorable interactions between SiO2 and the zwitterionic groups. Ligoure and Leibler4 developed a theoretical study which permits one to calculate the adsorption energy for end-functionalized linear chains. They consider equilibrium conditions, i.e., the chemical potential of free chains in the solution is equal to that of the adsorbed chains and a parabolic profile for the brush. The dimensionless surface density of chains Σ, Σ ) (ak2σ, where aK is the Kuhn statistical length), is a function of the degree of polymerization N, the free energy gain when an end group is anchored, γkT, and the volume fraction of polymer in the bulk, φb:
N(v/aK3)φbR ) γ + ln(φb/ΣN)
(8)
The logarithmic term in eq 8 represents the entropic contributions, while the left-hand side term represents the excluded volume contribution, where v is the excluded volume parameter and R the relative excess of monomer concentration at the interface with respect to φb. R can also be expressed in terms of the height of the brush h, as well as aK, N, φb, and v: (22) Daoud, M.; Cotton, J. P. J. Phys. France 1982, 43, 531.
π2h2aK R)
8N2φbv
(9)
Substituting eq 9 in eq 8 we obtain
π2h2 ) γ + ln(φb/ΣN) 8Na2
(10)
The height h of the adsorbed layer in the brush regime can be expressed as
h ) (12/h)1/2Σ1/3ν1/3N
(11)
Substituting eq 11 in eq 10 we obtain
( )()
π2 12 8 π2
2/3
ν a3
2/3
Σ2/3N ) γ + ln(φb/ΣN)
(12)
The parameter (ν/a3) in the left-hand side of eq 12 is the same for the samples ZW-L-PB12, ZW-L-PB20, and ZWL-PB80. The dimensionless Σ and the chain length N are known. In order to calculate the adsorption energy γ, we take the ratio of eq 12 for the two samples ZW-L-PB12 and ZW-L-PB80 for the same concentration
(ΣZW-L-PB12)2/3NZW-L-PB12 ) (ΣZW-L-PB80)2/3NZW-L-PB80 γ + ln φb - ln ΣZW-L-PB12 - ln NZW-L-PB12 (13) γ + ln φb - ln ΣZW-L-PB80 - ln NZW-L-PB80 All the parameters involved in eq 13 are known except for the adsorption energy parameter γ, which is the quantity we want to determine. For both samples ZWL-PB12 (NB ) 215) and ZW-L-PB80 (NB ) 1481), we take the same bulk concentration of 0.4 mg/mL, which corresponds to φb of approximately 4 × 10-4 and the experimental Σ values of 6.9 × 10-3 and 6.6 × 10-4, respectively. The adsorption energy obtained corresponds to about 9 kT per functional group. This is a high value compared to the adsorption energy involved in the adsorption of segments of nonfunctionalized homopolymers. The calculation of γ was also done for other bulk concentrations in the region of the adsorption plateau, obtaining the value of (9 ( 1)kT. Moreover, similar calculations as shown in eq 12 were performed involving the ratios between ZWL-PB12 and ZW-L-PB20 and between ZW-L-PB20 and ZW-L-PB80. The results are consistent, and the value of the mean adsorption energy γ obtained is (9.1 ( 0.7)kT. It compares to values obtained for other end-functionalized polymers reported in the literature.5 Dynamic Light Scattering. The apparent diffusion coefficients obtained from DLS measurements for solutions of ZW-3N-93 in the toluene/cyclohexane mixture at concentrations of 0.86 and 0.43 mg/mL are DDLS ) (1.12 ( 0.06) × 10-7 and (1.2 ( 0.1) × 10-7 cm2/s, respectively, as shown in Table 3. Light scattering does not exhibit any angular dependence up to 150°. For the higher concentration (4.3 mg/mL) two relaxation processes are observed, indicating association between the functionalized stars. In this case, the autocorrelation functions are treated as bimodal exponential ones, yielding two different diffusion coefficients and therefore two different hydrodynamic radii. The faster process indicates the diffusion of particles with the same velocity as found in the more dilute range, DDLS ) (1.4 ( 0.2) × 10-7 cm2/s, while in the slower process the aggregates diffuse approximately 10 times slower. This behavior has not been found for the
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Table 3. Diffusion Coefficients (DDLS) and Hydrodynamic Radii (Rh) Determined from Dynamic Light Scattering Measurements sample ZW-L-PB80 ZW-3N-PB93
concentration (mg/mL)
DDLS (10-7 cm3/s)
Rh (nm)
4.4 0.87 4.3
2.03 ( 0.05 2.1 ( 0.1 1.4 ( 0.2 (fax) 0.161 ( 0.008 (slow) 1.12 ( 0.06 1.2 ( 0.1
12 ( 1 11.5 ( 0.9 19 ( 3 (fast) 167 ( 8 (slow) 22 ( 2 20 ( 2
0.86 0.43
same polymer in pure cyclohexane, where the highest concentration investigated was approximately 1.0 mg/ mL.23 Differences are due to the different solvents and concentrations. DLS measurements were also performed for solutions of ZW-L-PB80 in the toluene/cyclohexane mixture at concentrations of 4.4 and 0.87 mg/mL, and again up to 150° there is no angular dependence. In both concentrations only one relaxation process is detected, and the mean apparent diffusion coefficient obtained is DDLS ) (2.06 ( 0.04) × 10-7 cm2/s, which is comparable with literature data.21,24 Contrary to the results obtained for the stars ZW-3N-93, no aggregation was detected in solutions of the linear ZW-L-PB80 at the concentration of 4.4 mg/mL. It indicates that intermolecular association is favored when the number of end-functionalized arms increases. There is evidence of gel formation of functionalized stars in pure cyclohexane. The concentration, at which the gelation process begins, decreases with the increase of the number of functionalized arms.16 As a result of the DLS experiments, one thus can exclude aggregation, micelle formation, or gelation in the mixed solvent at the utilized concentrations for the adsorption experiments. Parameters obtained from DLS are compiled in Table 3. Adsorption Kinetics. The adsorption kinetics of endfunctionalized polymer chains is usually discussed as a two-regime process.4,17,25 At the initial stages, the substrate surface is bare and the kinetics of adsorption is governed by the diffusion of the chains from the bulk solution to the surface. All chains that arrive at the surface are considered to be immediately adsorbed. Desorption may be neglected. The mass transport can be interpreted as a Fickian diffusion. The diffusion coefficient D is obtained from the slope of the curve A(t) as a function of xt which depends on the bulk concentration c0:
2 c0xDt A(t) ) xπ
Figure 7. Adsorbed amount as a function of xt obtained for (a) ZW-L-PB80 at the concentration of 0.0095 mg/mL and (b) ZW-3N-PB93 at the concentration of 0.0092 mg/mL. Solid lines indicate the fits, from which the diffusion coefficients Delli are obtained.
quite different for stars and linear chains and desorption may not be negligible. After the initial regime, an activation barrier of adsorbed chains is formed and governs the kinetics because the chains arriving from solution have to diffuse across this barrier. Ligoure and Leibler considered a simplified model where the adsorbed amount (or the surface coverage) approaches exponentially an equilibrium adsorbed amount Aeq with time, introducing a characteristic penetration time τ
A(t) ) Aeq[1 - exp(-t/τ)]
(15)
(14)
From the slope of the curves A(t) as a function of xt shown in Figure 7a,b for the solutions of ZW-L-PB80 and ZW-3N-93 at the bulk concentrations of 0.0095 and 0.0092 mg/mL, the diffusion coefficients are determined as Delli ) (1.1 ( 0.2) × 10-7 and (2.0 ( 0.2) × 10-7 cm2/s, respectively. These diffusion coefficient values are averages of experiments made in duplicates and take into account mean errors in the concentration and in the determination of t ) 0. These results are in reasonable agreement with those obtained from the DLS measurements, shown in Table 3. Absolute values may be difficult to compare due to the limited applicability of eq 14, where several assumptions have to be made. Thus, for instance, rearrangement times of segments at the surface might be (23) Pitsikalis, M.; Hadjichristidis, N.; Mays, J. W. Macromolecules 1996, 29, 179. (24) Pitsikalis, M.; Siakali-Kioulafa, E.; Hadjichristidis, N. J. Polym. Sci., Polym. Phys. Ed. 1996, 34, 249. (25) Semenov, A. N. Macromolecules 1992, 25, 4967.
From eq 15 we see that this second process under those conditions at later times has an exponential nature, and the penetration rate may be obtained from the slope of [ln(Aeq - At)] as a function of time, where Aeq is the adsorbed amount obtained in equilibrium at infinite times. The exponential behavior obtained for ZW-L-PB80 and ZW3N-93 in the bulk concentrations of 0.0095 and 0.0092 mg/mL with Aeq being 1.25 and 1.6 mg/m2, respectively, is shown in Figure 8. From the slope of the straight line for longer times in Figure 8, the penetration rate constants (1/τ) are calculated as (0.46 ( 0.06) and (0.30 ( 0.09) h-1 for ZW-L-PB80 and ZW-3N-93, respectively. This small difference may be due to the fact that one arm of a star molecule is much shorter than the linear chain, and stars are smaller in size as compared to the corresponding linear chains. Moreover, the stars have three end-functionalized arms, leading to a higher probability for the adsorption. τ involves the adsorption and desorption rate constants ka and kd, respectively. By replacing the polymer solution by pure solvent, no desorption is observed. Therefore, kd is probably very small, although it contains the replace-
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Effect of Chain Architecture on Adsorption
Langmuir, Vol. 12, No. 6, 1996 1637
these arguments, it would be interesting to compare several samples with the same molecular weights and a different number of end-functionalized arms. Conclusions
Figure 8. Long time behavior of the adsorption of ZW-L-PB80 at c ) 0.0095 mg/mL and ZW-3N-PB93 at c ) 0.0092 mg/mL. Aeq is the mean adsorbed amount in the plateau region at very long times. For times longer than 0.2 h, the data Aeq - A(t) are the average of 10 data points. The standard deviations are indicated by error bars, which increase with time.
Figure 9. Long time behavior of the adsorption of ZW-L-PB80 at c ) 0.097 mg/mL, ZW-3N-PB93 at c ) 0.094 mg/mL, and ZW-1N-PB111 at c ) 0.093 mg/mL. Aeq is the mean adsorbed amount in the plateau region at very long times. For times longer than 0.2 h, the data Aeq - A(t) are the average of eight data points. The standard deviations are indicated by error bars, which increase with time.
ment of one adsorbed chain by another one, a process on which we do not have any detailed information. A linear dependence of ka on the concentration is expected. In order to verify the influence of the concentration on τ, the exponential law was also applied to solutions of ZW-LPB80 and ZW-3N-PB93 at the bulk concentrations of 0.097 and 0.094 mg/mL with Aeq being 1.54 and 2.4 mg/m2, respectively, as shown in Figure 9. The corresponding penetration rate constants are 0.65 and 3.4 h-1, respectively. The same increment in the concentration causes different increases in the penetration rate constants. Surprisingly for ZW-3N-PB93 the increase is much more pronounced than for ZW-L-PB80. The same arguments discussed in the more dilute region can be used in the more concentrated region. The effects are stronger for the more concentrated solutions because in this case the number of adsorbing species is much higher. The higher the concentration, the bigger is the probability that more molecules hit the surface. The dependence of the penetration rate constant on the concentration is reported in the literature15 for asymmetric block copolymers. For comparison, the data obtained for the solution of ZW1N-PB111 at the same concentration (c ) 0.093 mg/mL) and Aeq ) 1.6 mg/m2 are also plotted in Figure 9. Although this sample has a molecular weight higher than that of ZW-L-PB80 and just one functionalized arm, the penetration rate constant calculated is 1.25 h-1, 2-folds the value obtained for the linear chain. In order to be sure about
The adsorption behavior of end-functionalized linear and star PB from the solvent mixture of cyclohexane and toluene (50% in volume) on silicon wafers is investigated by means of null-ellipsometry. Under these conditions, no aggregates are detected with dynamic light scattering and there is sufficient contrast for the ellipsometric measurements. The end-functionalized linear PB chains carry one sulfozwitterionic group each but have different molecular weights. The adsorbed amount is controlled by the length of the PB chains; the adsorption of short chains results in higher plateau values than those for the longer ones. The adsorbed linear PB chains are stretched and assume a brushlike conformation on the surface, which is situated between the limiting conformations of a mushroom and a true brush. The plateau values measured for the end-functionalized star PB samples show that they increase as the number of functionalized arms is increased, for approximately the same molecular weight. However, the grafting density depends more strongly on the molecular weight than on the number of functional arms. The free energy gain for the adsorption of a zwitterionic group on the silicon wafer from the solvent mixture of cyclohexane and toluene (50% in volume) is calculated based on theoretical models4 as (9.1 ( 0.7)kT. This value indicates a strong binding of the sulfozwitterionic groups to the surface and is consistently obtained for all materials investigated. The diffusion coefficients and hydrodynamic radii for linear and star PB materials were measured with dynamic light scattering. The linear chains show smaller hydrodynamic radii than the star chains. For solutions of the star PB at low concentrations, just one relaxation process is detected. For higher concentrations, two relaxation processes are detected, indicating association among the stars. In the case of the linear PB chains, in the whole investigated concentration range, no aggregation is detected. The adsorption kinetics show two processes. In the beginning, the adsorption is diffusion controlled. From plots of the adsorbed amount as a function of xt, diffusion coefficients are estimated for linear and star PB chains. These values are of the same magnitude as those measured with dynamic light scattering. At longer times, the chains must penetrate through a barrier formed by the previously adsorbed chains. The penetration rate constants calculated for star chains are much higher than those calculated for the linear chains. The faster penetration of the star chains might be due to the different conformations assumed by the stars, which facilitate the penetration through the barrier. While this study gives an indication of the effect of chain architecture on the adsorption behavior, much more detailed investigations are needed for the rigorous evaluation of power laws and kinetics. Acknowledgment. We acknowledge stimulating discussions with Dr. J. Reiter. The authors thank Dr. W. Theobald and V. Erb for their help with the ellipsometry experiments and C. Rosenauer for the dynamic light scattering measurements. This work was funded within EC Framework Contract CI1-CT93-0351. LA950929A
