Reactive Adsorption of PS-PMMA Block Copolymers on Concave

Article pubs.acs.org/Langmuir

Reactive Adsorption of PS-PMMA Block Copolymers on Concave Alumina Surfaces Grady A. Nunnery,† Karl I. Jacob,† and Rina Tannenbaum*,‡ †

School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States Department of Biomedical Engineering, School of Medicine and the UAB Comprehensive Cancer Center, University of Alabama at Birmingham, Birmingham, Alabama 35294, United States

‡

ABSTRACT: The influence of pore size, relative block size, and solvent quality on the extent of diblock copolymer adsorption on alumina surfaces was determined. To this end, the block copolymer that was chosen was poly(styrene)-b-poly(methyl methacrylate) (PS-b-PMMA), in which the PMMA block strongly chemisorbs to the surface and the PS block weakly physisorbs. Several architectures (i.e., different ratios of M̅ nPMMA and M̅ nPS) of the PS-b-PMMA copolymers were adsorbed from various solvents onto porous alumina membranes with various pore sizes. It was determined that the diblock copolymer coverage decreased significantly as the pore size decreased, similar to the behavior of the PMMA homopolymer under the same conditions. However, the coverage decreased as the molecular weight of the anchoring block (PMMA) increased for all pore sizes, which is in contrast to the behavior of the PMMA homopolymer under the same conditions. The dependence of the coverage on the relative block size and solvent quality is analyzed on the basis of the anchor−buoy model and the deviation from it in a nonideal system. The results presented in this work are relevant to the study of block copolymer conformation in solutions and on surfaces, adsorption chromatography, and solvent sensors and controls.

1. INTRODUCTION The conformation of block copolymers in solution has attracted considerable interest from the scientific community in recent decades, with many accounts directed toward determining the extent of block segregation.1 The conformation of diblock copolymers in solution and at interfaces has also been studied extensively and reported in the literature.2−8 Three main solvent-dependent conformation possibilities have been proposed: (1) a conformation that consists of strongly segregated A and B regions, (2) a pseudo-Gaussian conformation in which only little block segregation occurs, and (3) a core−shell conformation in which one block surrounds the other block.9,10 The conformation of poly(styrene)-b-poly(methyl methacrylate), the chemical structure of which is shown in Figure 1, has been specifically addressed in the literature. Han and Mozer11 experimentally determined the radii of gyration for the PS and PMMA blocks in PS-b-PMMA (88 000 g/mol for the PS block and 203 000 g/mol for the PMMA) in toluene to be 21 and 8.5

nm, respectively. Although the degree of polymerization of the PMMA block in this case is more than twice as large as compared to that of the PS block (taking into account that the molar masses of the repeat units of PMMA and PS are quite similar, as are their characteristic sizes12,13), the measured radius of gyration of the PS block was found to be more than twice that of the PMMA block. A radius of gyration of 8.5 nm for a 203 000 g/mol PMMA homopolymer indicates near-θ conditions. Although toluene is a thermodynamically good solvent for PMMA, the authors explained this apparent paradox by considering that toluene is a much better solvent for PS than for PMMA; therefore, a core−shell conformation is adopted, with PMMA as the core and PS as the shell.14 The block architecture, specific block chemical reactivities, and conformations of block copolymers in solution directly impact the mechanism of adsorption of these materials onto various surfaces and the resulting morphologies of the adsorbed layers.15−22 For example, in the case of PS-b-PMMA diblock copolymer, the adsorption of the PS and PMMA blocks onto alumina surfaces occurs through distinctly different mechanisms. PS passively associates with the alumina surface by physisorption, whereas PMMA reactively chemisorbs. The chemisorption of a PMMA repeat unit occurs in the following manner: the acrylate side group undergoes de-esterification catalyzed by the presence of hydroxylic groups on the alumina surface (originating from the presence of AlO(OH) species), Received: August 8, 2012 Revised: September 16, 2012 Published: September 25, 2012

Figure 1. Chemical structure of poly(styrene)-b-poly(methyl methacrylate) (PS-b-PMMA). © 2012 American Chemical Society

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Figure 2. Mechanism of adsorption of PMMA onto alumina. The bonds between the COO− groups on the PMMA and Al3+ sites on the surface are formed as a result of three sequential reactions: (a) conversion of Al2O3 to AlO(OH) on the surface of the substrate in the presence of H2O; (b) deesterification of the methacrylate group in the presence of the surface OH groups to form the carboxylate group; and (c) coordination of the carboxylate groups on the Al3+ sites on the surface of the oxide substrate.

Figure 3. Mechanism of adsorption of PS onto alumina. Polystyrene interacts weakly with alumina through a transient dipole−dipole interaction between the π orbitals of the benzene ring bonding with the surface as opposed to the strong bonding observed in the PMMA-alumina system.

Table 1. Summary of the Solvents Used in This Study, Their Physical Characteristics, and Their Flory−Huggins Interaction Parameter, χ, with PS and PMMA solvent

Hildebrand solubility parameter4 (MPa1/2)

density at 25 °C (g/cm3)

intermolecular hydrogen bonding4

χPS

χPMMA

2-methoxy ethanol cyclohexanone toluene

21.5 20.3 18.2

0.930 0.948 0.867

moderate low to moderate poor

0.6321 0.2091 0.0179

0.0577 0.0105 0.4945

This is particularly important in a block copolymer such as PSb-PMMA where the affinity of the solvent for a particular block may become a dominant adsorption driver. (2) The strength of the chemisorption of the PMMA repeat unit onto the alumina surface as compared to that of the physisorbed PS. (3) The effect of surface curvature on the adsorption of polymer chains to concave surfaces. In this work, we studied the adsorption of PS-b-PMMA diblock copolymers from three different solvents onto concave alumina surfaces having various degrees of curvature (i.e., onto alumina mambranes with varying pose sizes). Clearly, the conformation of PS-b-PMMA depends upon solvent quality, as mentioned previously, and indeed, this work probes the effect of not only solvent quality but also block asymmetry and pore size on the adsorption of these block copolymers onto the porous alumina membranes. The anchor−buoy model1,15,34−36 was used here as an idealized theoretical framework for understanding the adsorption of this particular block copolymer system onto alumina substrates of various curvatures. In this model, one block strongly adsorbs onto the surface (in this case, PMMA), and the other block (in this case, PS) weakly

and the resultant conjugate base interacts with the positively charged aluminum centers on the surface in the presence of a minimal amount of water, as shown in Figure 2.23−27 Polystyrene, however, weakly associates with the surface via dipole−dipole interactions between the π orbitals of the styrene side groups and the surface cations, as shown in Figure 3. Previous studies of the adsorption of homopolymers to concave media and the adsorption of homopolymers and diblock copolymers to convex media28−31 had addressed the relationship between the characteristics of polymer adsorption as a function of surface curvature. It was shown that polymer coverage (i.e., the number of repeat units per unit surface area) increases significantly as curvature decreases. It was also shown by Manghi et al. and others,32,33 that the graft density and the conformation of the adsorbed polymer chains is dependent on the ratio between the number of segments and the degree of curvature and, in certain cases, on wheather the surface is concave or convex.31−33 Hence, the adsorption process of PS and PMMA homopolymers or PS-b-PMMA block copolymers occurs by the confluence of three independent phenomena: (1) The solvent-dependent conformation of the adsorbing polymer. 14961


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32, 100, and 220 nm, respectively, as shown in Figure 4. These discs were determined to be amorphous by X-ray diffraction, and their specific surface areas were calculated by an analysis of the scanning electron micrographs. SEM imaging of the uncoated discs was accomplished by mounting them to a conductive stage with conductive powder and analyzing them with a Zeiss SEM Ultra60 at 5 kV with an in-lens secondary electron detector. It is important to note that the convex (disk circumference) and flat (disk faces) surface areas are negligible because they account for less than 0.3% of the entire surface area on the disk. Therefore, at least 99.7% of all of the surface area on the disk resides in cylindrical pores and is concave.31 The block copolymers used in this study are summarized in Table 3. Four different PS and PMMA block combinations were used in this

associates with the surface. According to the anchor−buoy model, the block that preferentially binds the surface is referred to as the anchor, and the weakly adsorbing block that extends outwardly from the surface into the solvent is referred to as the buoy. The suitability of this model to this particular PS-bPMMA block copolymer and the associated deviation imposed by the nature of the blocks will dictate the adsorptive behavior of the system.

2. EXPERIMENTAL SECTION The solvents used in this study were purchased from Sigma-Aldrich Chemical Co. and used without further preparation unless otherwise noted. Relevant physical data can be found in Table 1. Solubility parameters alone should not be used as guaranteed predictors of solubility; rather, dipoles, hydrogen bonding, and π bonding, among other inter- and intramolecular forces, must be considered as well.37,38 The Flory−Huggins interaction parameter χ was also calculated;39,40 however, the way we have chosen to analyze this system is through the polarity of the solvent, shown in Table 2.38,41 Poly(methyl

Table 3. Diblock Copolymers That Were Used in the Study polymer system designation PS−PMMA low−low (ll) high−low (hl) high−high (hh) low−high (lh)

Table 2. Partial Contributions to the Hansen Solubility Parameter for Solvents Used in This Study solvent

δpolar (MPa1/2)

δH bond (MPa1/2)

2-ethoxy ethanol cyclohexanone toluene

1.4 6.3 9.2

2.0 5.1 14.3

PS block molecular weight, M̅ n (g/mol)

PMMA block molecular weight, M̅ n (g/mol)

total molecular weight (g/mol)

fraction of PMMA block (%)

PDI

25 000

26 000

51 000

51

1.06

166 200

42 000

208 200

20

1.07

201 500

152 000

353 500

43

1.09

29 200

285 100

314 300

91

1.08

work, comprising both symmetric and asymmetric copolymers. The PS25 000−PMMA26 000 block copolymer used had a polydispersity index of 1.06 and was designated as low−low (ll), the PS201 500− PMMA152 000 block copolymer used had a polydispersity index of 1.09 and was designated as high−high (hh), the PS166 200−PMMA42 000 block copolymer used had a polydispersity index of 1.07 and was designated as high−low (hl), and finally, the PS29 200−PMMA285 100 block copolymer used had a polydispersity index of 1.08 and was designated as low−high (lh). Solutions having concentrations of 0.1% (w/v) copolymer were prepared by adding the appropriate masses of dry copolymer to volumetric flasks, filling to the to-contain line with a particular solvent (toluene, cyclohexanone, or 2-ethoxy ethanol), and allowing at least 2 days for complete dissolution.

methacrylate) is much more polar than polystyrene. As such, nonpolar toluene prefers the PS block over the PMMA block, and experimental evidence supports this conclusion, as previously mentioned.14 Likewise, polar 2-ethoxy ethanol is expected to be a good solvent for PMMA and a poor solvent for PS, which experiment also supports.42 Cyclohexanone, a good solvent for both blocks, is more polar than toluene yet less polar than 2-ethoxy ethanol. Anodized aluminum oxide discs (Anodisc), having a diameter of 13 mm, were purchased from Whatman (a unit of GE Healthcare). The membranes featured open cylindrical pores with a narrow size distribution and differences in pore size. The pore diameters as reported by the manufacturer were 20, 100, and 200 nm. Independent SEM analysis has determined the mean diameters of these pores to be

Figure 4. SEM images of the alumina porous membranes used.30 (a) Membrane with 32-nm-diameter pores. (b) Membrane with 100-nm-diameter pores. (c) Membrane with 220-nm-diameter pores. (d) Setup of the experimental procedure. 14962


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The adsorption of the copolymer to the surfaces was achieved by the following process: Each disk was exposed to 3 mL of polymer solution after the alumina disk and the glass sample vial were rinsed twice with clean solvent. The vials were placed in a laboratory oven at 343 K, sealed after their temperature equilibrated, and tilted so that both faces of the disk would be accessible to the polymer solution. Each trial was repeated in triplicate. Before data acquisition, copolymer-rich discs were rinsed in order to remove unbound polymer. Each disk was cooled, removed from its vial, and rinsed at least five times with at least 5 mL of pure solvent in a Soxhlet extraction apparatus. The disk was removed and examined visually upon drying. If the disk dried unevenly or showed shiny spots on its surface, then it was rinsed again in the apparatus in order to remove all unbound polymer. Discs with dirt or other contaminants were discarded. After ensuring that all discs were viable and free of unbound polymer, their decomposition profiles were measured in a TA Instruments Q50 thermogravimetric analyzer (TGA). Each disk was heated at 20 K/min from room temperature to 720 K in dry air. The decomposition profile of the very thin adsorbed PMMA layer matched the decomposition profile of bulk PMMA well. A typical decomposition plot is shown in our previous work.9 The polymer adsorption was determined by the mass loss between 373 and 720 K. In this temperature range, the substrate’s mass was shown to be constant in a separate experiment.

3. RESULTS AND DISCUSSION Two values were calculated from the experimental data: the chain density (Ψ) and the repeat unit density (Γ). The repeat unit density, sometimes referred to as the coverage, is defined as the total number of repeat units in all polymer chains that are adsorbed on the surface divided by the total surface area. Chain density refers to the total number of adsorbed block copolymer chains (through both physical and chemical interactions) divided by the entire surface area. The Ψ value can be calculated by dividing Γ by the total molecular weight of the block copolymer. Clearly, this is an average quantity that is a function of molecular weight distributions and anchoring distributions in the chains comprising the sample. In previous work, it was reported that the coverage of PMMA homopolymer on porous alumina substrates generally increases with molecular weight up to a certain threshold, after which it becomes independent of the polymer molecular weight.31 Therefore, there are two main questions to be addressed in this context: (1) How does coverage vary with the block copolymer molecular weight? (2) How is this different from the adsorption of a homopolymer, and what would be the reason for this difference? A plot of the polymer coverage as a function of the molecular weight of the PS block, the PMMA block, and the total molecular weight of the diblock copolymer (i.e., PMMA block + PS block) is presented in Figure 5. It shows that contrary to trends observed for homopolymers, the maximum coverage is not achieved for the highest total molecular weight of the block copolymer. The copolymer designated hl has a greater surface coverage than the copolymer that is designated as hh, even though the combined molecular weight of the former is approximately only 60% of the latter. Furthermore, copolymer lh does not exhibit a coverage that is commensurate with its relatively high total molecular weight. Hence, the adsorption of block copolymers on these porous media does not scale with the combined molecular weights of the two blocks, and hence this behavior differs significantly from that observed with homopolymer adsorption.

Figure 5. (Top) Total coverage, (middle) PS contribution, and (bottom) PMMA contribution as a function of the total molecular weight of the block copolymer.

Another way of presenting this information, providing additional insight into the adsorption behavior of the diblock copolymer, is presented in Figure 6. The lines in this plot represent the weighted relative block sizes of the copolymers. The heavy lines represent PMMA block adsorption, and the overall height of up to the top of the lighter line is the total block copolymer adsorption. Therefore, it is acceptable to think of the heavy line as the PMMA block adsorption and the visibly lighter line as the PS block adsorption. Thus, this graphical presentation summarizes all of the relevant data: relative block sizes, coverage and pore sizes. The x axis represents the total molecular weight of the two blocks (PS + PMMA). The various solvent systems are arranged left to right in order of increasing polarity. It is also possible to plot the same data as a function of 14963


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Figure 6. Effects of pore size, solvent quality, and total molecular weight on coverage. The heavy lines represent PMMA block adsorption, and the ultimate height of the lighter line is total adsorption. Therefore, it is acceptable to think of the heavy line as PMMA block adsorption and the lighter line as PS block adsorption. Lighter + heavier bars = total (PMMA + PS) adsorption.

Figure 8. Effect of pore size, solvent quality, and PMMA molecular weight on coverage. The heavy lines represent PMMA block adsorption, and the ultimate height of the lighter line is total adsorption. Therefore, it is acceptable to think of the heavy line as PMMA block adsorption and the lighter line as PS block adsorption. Lighter + heavier bars = total (PMMA + PS) adsorption.

the molecular weight of the PS block alone, shown in Figure 7, and the PMMA block alone, shown in Figure 8. It is obvious from these plots that adsorption from toluene gives rise to the largest overall polymer coverage on the surface.

PMMA is likely to constitute the anchor on the surface whereas PS would constitute the buoy. In a commonly good solvent, the adsorption would then be driven by the favorable and preferential interactions between the PMMA block and the surface. Let us assume that the PMMA block adsorbs onto the surface in a sequence of blobs, as proposed by Rubinstein,43 and that the PS block extends outward into the solvent as a buoy. This type of system can be represented schematically by a 1D illustration, as shown in Figure 9. It is obvious, therefore,

Figure 7. Effect of pore size, solvent quality, and PS molecular weight on coverage. The heavy lines represent PMMA block adsorption, and the ultimate height of the lighter line is total adsorption. Therefore, it is acceptable to think of the heavy line as PMMA block adsorption and the lighter line as PS block adsorption. Lighter + heavier bars = total (PMMA + PS) adsorption.

Figure 9. Schematic representation of the anchor−buoy adsorption of the PS-PMMA block copolymer from a good solvent for the buoy as a function of the molecular weight of the adsorbing block (surface shown as a flat surface, i.e., Rpore ≫ Rg). If the molecular weight of the buoy (red) block remains the same and the molecular weight of the anchor (blue) block increases (NPMMA2 > NPMMA1), as it does from the left image to the right image, then the distance between the PS blocks is expected to increase (d2 > d1) as well, and as a result, the coverage is expected to decrease.

The reasons that these block copolymers do not behave similarly to the PMMA homopolymer can be explained by considering the impact of the adsorption mechanism, block asymmetry, and solvent quality on the conformation and dynamics of the polymer chains. First, we will discuss this result in light of the different mechanisms of adsorption of PS and PMMA onto alumina. Whereas PS forms weak, transient bonds with alumina via π-orbital−cation interactions between the benzene group of PS and the Al3+ centers on the surface, PMMA is known to form stronger direct coordination bonds through its carbonyl group, as previously explained and as illustrated in Figure 3. Therefore, if we approach this problem from the viewpoint of the de Gennes anchor−buoy model,34−36

that if the molecular weight of the PS block is kept constant (NPS = const) and we assume that only the number of blobs changes with the PMMA block molecular weight but not their size, then an increase in the molecular weight of the PMMA block (NPMMA2 > NPMMA1) should lead to a larger area occupied by each BCP chain and hence the overall coverage will decrease (d2 > d1). This result is contrary to the situation observed with 14964


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homopolymer adsorption,31 where the adsorption increased with an increase in PMMA molecular weight up to a critical value, after which it remained constant. Such an occurrence would be evident in a plot of chain density as a function of PMMA block molecular weight. For these reasons, we expect the chain density to decrease as the PMMA block molecular weight increases, and indeed this is what we observe, as shown in Figure 10. Note that the same cannot be said when the

Figure 12. Effect of pore size, solvent quality, and total molecular weight on the chain density. Note the change in the z axis from the previous plots. No heavy/light lines are required because each copolymer consists of one PS chain and one PMMA chain.

will be driven not only by the affinity of the reactive (and more polar) block for the surface but also by the unfavorable interactions of this block with the solvent. We then expect that this adsorption would lead to increased coverage and a tighter surface conformation of the adsorbing block. The chain density of an adsorbing block copolymer from a selective solvent on a flat surface is given by Ψ = (σa−2) = Rg−2, where σ is the dimensionless surface density defined as the number of grafted chains per unit area times the area taken up by a single monomer segment,48 a is the area occupied by a repeating segment, and Rg is the radius of gyration of the block and is given by Rg = aNυ(where 1/3 ≤ υ ≤ 3/5 depending on the solvent quality, with υ = 1/3 for a bad or θ solvent and υ = 3/5 for a good solvent).47−49 For the PS-PMMA system under study, toluene constitutes a relatively poor solvent for the PMMA block but an excellent solvent for the PS block, and hence under these conditions the block copolymer will exhibit classic anchor−buoy adsorption behavior. As a first-order approximation, the chain density can be evaluated as Ψ ≅ Rg,PMMA−2 ≅ aPMMA−2NPMMA−2/3, where υPMMA = 1/3 and Rg,PMMA = aPMMANPMMA1/3. Figure 13a shows a plot of the theoretical and experimental values of the chain density, adsorbed from toluene, as a function of the PMMA block molecular weight for three different sizes of alumina pores. For the larger pores (i.e., low-curvature surfaces that from the standpoint of the polymer Rg can be viewed as approximately flat surfaces), the conformation of the PMMA anchor chains fits well with the anchor−buoy model, as evidenced by the experimental υPMMA = 0.341. This agrees with the results obtained by several theoretical approaches31,32 that indicate that for curvatures lower than a specific value inwardly grown chains of homopolymers behave similarly to those on flat surfaces. For the smallest pore, for which Rpore ≈ Rg (i.e., the highest-curvature surface), the overall chain density is smaller by almost an order of magnitude as compared to that of the larger pores and υPMMA = 0.382, indicating a more relaxed conformation. This would be consistent with a limited number of PMMA block anchoring points, dictated by the constraints imposed by the geometry with the higher curvature.28−30 As the solvent becomes more polar (note the partial contributions of the Hansen solubility parameter presented in Table 241), the adsorption behavior of the system deviates from that of the classic anchor−buoy model because the polystyrene

Figure 10. Effect of pore size, solvent quality, and PMMA block molecular weight on the chain density. No heavy/light lines are required because each copolymer consists of one PS chain and one PMMA chain. Notice the general trend and its relation to the PMMA molecular weight (as opposed to the PS molecular weight, previous plot).

adsorbed chain density is plotted as a function of the PS block molecular weight, shown in Figure 11 or as a function of the total adsorbed polymer (PS + PMMA) molecular weight, as shown in Figure 12.

Figure 11. Effect of pore size, solvent quality, and PS block molecular weight on the chain density. No heavy/light lines are required because each copolymer consists of one PS chain and one PMMA chain.

Let us now discuss the role of the solvent quality on the adsorption of the block copolymers. The anchor−buoy model assumes that one of the blocks is more strongly attracted to the surface than the other block, leading to phase segregation, with one block close to the surface and another block extending outward.44−52 Under the conditions of a commonly good solvent, the only driving force determining the adsorption profile is the attraction of the more reactive block to the surface. As the solvent polarity decreases, the adsorption profile 14965


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Figure 13. Plots of the theoretical (dashed line) and experimental values of the chain density, adsorbed from two different solvents, as a function of the PMMA block molecular weight for three different sizes of alumina pores. (a) Adsorption from toluene, a good solvent for the PS block and a moderately bad solvent for the PMMA block. (b) Adsorption from 2-methoxy ethanol, a bad solvent for the PS block and a good solvent for the PMMA block.

block begins to associate with the surface. When adsorption occurs from a more polar solvent, the competition between the solvent and the surface for the PMMA block is still dominated by the strong affinity that the PMMA block has for the surface, and hence PMMA is still the anchor. However, in this case, polystyrene adsorbs on the surface as well, at least to some extent, because it has a greater energy incentive to avoid the solvent and instead associate with the surface and hence can be viewed as a pseudoanchor. Therefore, the result is no longer an anchor−buoy system but rather an anchor−pseudoanchor system in which both blocks associate with the surface, albeit to different extents and for different reasons. Clearly, this anchor− pseudoanchor system would inevitably lead to lower values of both Γ and Ψ as compared to an anchor−buoy system, as indeed observed experimentally. For the PS-PMMA system under study, 2-methoxy ethanol constitutes an excellent solvent for PMMA but a poor solvent for PS. From the standpoint of the solvent alone, the conformation of the PMMA block should scale as Rg,PMMA ≅ aPMMANPMMA3/5 (where υPMMA ≈ 3/5 in a good solvent), and the chain density can then be evaluated as Ψ ≅ Rg,PMMA−2 ≅ aPMMA−2NPMMA−6/5. Figure 13b shows a plot of the theoretical and experimental values of the chain density, adsorbed from a 2-methoxy ethanol solution, as a function of PMMA block molecular weight for three different sizes of the alumina pores. For the larger pores, the experimental values of υPMMA were 0.317 for the 100 nm pores and 0.312 for the 220 nm pores. This would again be consistent with an anchor−buoy conformation, even though the fact that the solvent is a bad solvent for the PS block directly impacts the conformation of the PMMA block on the surface. This is most likely due to the crowding effect of having both the PMMA and the PS blocks adsorbed on the surface at the same time (as shown in Figure 14).28,47,48 For the smallest pore, the overall chain density is also considerably smaller as compared to that of the larger pores, similar to the previous case, but υPMMA = 0.234, indicating a greater deviation from the anchor−buoy model. The υPMMA values for both solvent systems are summarized in Table 4. Given the additional geometric constraints imposed by the high curvature of the surface, fitting both the anchor and

Figure 14. Pictorial representation of the dependence of polymer adsorption on the solvent quality (surface shown as a flat surface, i.e., Rpore ≫ Rg). (Left) An adsorption scheme that occurs from a solvent that is a good solvent for the buoy block (toluene, which is a good solvent for the PS block), according to the anchor−buoy model. (Right) If the solvent is a poor solvent for the buoy block (2-ethoxy ethanol, which is a poor solvent for PS), then the buoy block no longer behaves as a buoy but rather associates with the surface in order to escape the solvent.

Table 4. Summary of the Exponential Values (υPMMA) in the Expression for Chain Density (Ψ, Given by Ψ ≅ NPMMA−2υPMMA) for Both Solvent Systems pore size (nm)

υPMMA (adsorbed from toluene)

υPMMA (adsorbed from 2ethoxy ethanol)

theoretical 32 100 220

0.333 0.382 0.341 0.341

0.600 0.234 0.317 0.313

the pseudoanchor on the surface gives rise to low coverage and a very compressed conformation.

4. CONCLUSIONS The solvent quality, pore size, and block asymmetry all contribute to the extent of diblock copolymer coverage on curved surfaces. As the solvent becomes more polar, there is an increase in competition for the surface from the apolar block, 14966


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and the coverage decreases as a result of deviation from the ideal anchor−buoy model and an increase in the anchor block adsorption blob size. As the anchor block decreases in size, adsorption generally increases, as was also shown with the anchor−buoy model. The chain density was shown to increase as the anchor block size decreased, as expected from the model. As observed in this system for homopolymers, the block copolymer coverage was seen to decrease significantly as the pore size decreased, and a simple geometric model was proposed to explain this phenomenon, as well as a similar phenomenon observed for adsorption to convex media (particles).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by a research grant from the Institute of Paper Science and Engineering (IPST) at the Georgia Institute of Technology and a Paper Science and Engineering (PSE) Graduate Fellowship from the Institute of Paper Science and Engineering (IPST) at the Georgia Institute of Technology (to G.A.N.).

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