Understanding the Force-vs-Distance Profiles of Terminally Attached

Jul 28, 2009 - In this work, we examine the interaction between thin films composed of terminally anchored poly(N-isopropyl acrylamide) (PNIPAAm) ...
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Understanding the Force-vs-Distance Profiles of Terminally Attached Poly(N-isopropyl acrylamide) Thin Films )

Sergio Mendez,*,† Brett P. Andrzejewski,†,‡ Heather E. Canavan,†,‡ David J. Keller,§ John D. McCoy, Gabriel P. Lopez,†,‡ and John G. Curro‡ Center for Biomedical Engineering and ‡Department of Chemical and Nuclear Engineering and §Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, and Department of Materials and Metallurgical Engineering, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801 )

†

Received January 21, 2009. Revised Manuscript Received July 6, 2009 In this work, we examine the interaction between thin films composed of terminally anchored poly(N-isopropyl acrylamide) (PNIPAAm) immersed in water and test surfaces. Understanding this force of interaction can be important when using PNIPAAm surfaces in biotechnological applications such as biological cell cultures. The two novel contributions that are presented here are (1) the use of a recently developed self-consistent field (SCF) theory to predict the force-vs-distance profiles, and (2) the use of a modified polymer scaling theory to estimate the wet film thickness from experimental force-vs-distance profiles. SCF theory was employed to model the equilibrium structure of the uncompressed PNIPAAm chains, and the force between a compressed polymer film and a test surface as a function of wall separation distance. The parameters that were varied include temperature, polymer molecular weight, and surface coverage. The force-vs-distance profiles obtained at low and high temperatures with the SCF theory were in qualitative agreement with the experimentally measured profiles reported in the literature. We also compared the results of our SCF theory to the Alexander de Gennes scaling theory and found agreement at large separation distance. We also propose a method to estimate the wet polymer film thickness from a force-vs-distance profile obtained from an atomic force microscope measurement. The main novelties of this approach are that we employed a density functional theory corrected version of scaling theory proposed by McCoy et al. [McCoy, J. D.; Curro, J. G. J. Chem. Phys. 2005, 122, 164905], and we provide equations to account for various geometries of AFM tips.

I. Introduction Poly(N-isopropyl acrylamide) (PNIPAAm) is an extensively studied thermally responsive polymer.1-3 This polymer exhibits a lower critical solution temperature (LCST ∼32 C) in aqueous solution, and the effects of temperature on the polymer structure and hydration are well documented in the literature.4 When PNIPAAm is synthesized in the form of a thin film, the surface properties can be reversibly altered by changing the temperature above and below the LCST.5 Interestingly, the temperature induced change in surface hydration of PNIPAAm films has been correlated to substantial changes in the adhesion of biological cells and proteins. Because the thermoresponsive behavior occurs around physiological temperatures, PNIPAAm has been utilized in biotechnological applications which include biosensors, drug delivery, and tissue engineering. In certain cases, cells and proteins will adhere to PNIPAAm films at physiological temperature (37 C), and they will become detached when the temperature is reduced to room temperature, i.e., below the LCST.6-8 This method of cell detachment is in stark contrast to adherent cells on traditional cell culture substrates (e.g., untreated glass dishes or Petri dishes), since the removal of cells requires * Corresponding author. (1) Katsumoto, Y.; Tanaka, T.; Sato, H.; Ozaki, Y. J. Phys. Chem. A 2002, 106, 3429. (2) Yoshida, R.; Sakai, K.; Okano, T.; Sakurai, Y. J. Biomater. Sci. 1994, 6, 585. (3) Maeda, Y.; Higuchi, T.; Ikeda, I. Langmuir 2000, 16, 7503. (4) Wang, X.; Qiu, X.; Wu, C. Macromolecules 1998, 31, 2976. (5) Maeda, Y.; Higuchi, T.; Ikeda, I. Langmuir 2001, 17, 7535. (6) Ista, L. K.; Perez-Luna, V. H.; Lopez, G. P. Appl. Environ. Microbiol. 1999, 65, 1603. (7) Akiyama, Y.; Kikuchi, A.; Yamato, M.; Okano, T. Langmuir 2004, 20, 5506. (8) Canavan, H. E.; Cheng, X. H.; Graham, D. J.; Ratner, B. D.; Castner, D. G. Langmuir 2005, 21, 1949.

10624 DOI: 10.1021/la9002687

harsh methods such as enzymatic digestion or mechanical dissociation.9 There remains a need in the literature to understand how a temperature induced change in the PNIPAAm conformation and hydration can result in such considerable changes in cell attachment and detachment. Therefore, to contribute to this knowledge base and to improve the performance of PNIPAAm in such applications, we have developed a theoretical method to examine the interaction between terminally anchored PNIPAAm and model surfaces (or “test” walls). In this study, we treat the relatively simple case of test walls with a purely repulsive potential; however, we envision using more sophisticated attractive potentials to mimic the temperature dependent force of adhesion of proteins or cells onto PNIPAAm films. We also experimentally measured the force-vs-distance profile of a simple system which was a bare solid surface approaching a PNIPAAm film immersed in water with the intention of using chemically or biologically treated surfaces in future studies. The main contribution is in the analysis of the data wherein we developed a simple method to estimate the wet film thickness from these profiles. The structure of terminally anchored PNIPAAm chains has been probed with experimental techniques as well as with computational modeling. Atomic force microscopy (AFM) has been used to measure the temperature induced change in thickness of PNIPAAm films immersed in water.10,11 For one of these AFM studies, laser ablation techniques were performed to remove a (9) Canavan, H. E.; Cheng, X. H.; Graham, D. J.; Ratner, B. D.; Castner, D. G. J. Biomed. Mat. Res. A 2005, 75A, 1. (10) Kidoaki, S.; Ohya, S.; Nakayama, Y.; Matsuda, T. Langmuir 2001, 17, 2402. (11) Jones, D. M.; Smith, J. R.; Huck, W. T. S.; Alexander, C. Adv. Mater. 2002, 14, 1130.

Published on Web 07/28/2009

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strip of polymer brush, thereby making it possible to measure a difference in height to ascertain the wet film thickness relative to the ablated substrate.10 In the other AFM study, microcontact printing of self-assembled monolayers (SAMs) was performed resulting in raised patterns of polymer brushes making it possible to measure the wet film thickness relative to the underlying SAM.11 Ellipsometric techniques, with a custom built environmental chamber, has also been used to report on the change of wet PNIPAAm film structure at low and high temperatures.52 The accuracy of the thickness values reported from spectroscopic ellipsometric data depends on the accuracy of the index of refraction of the solvent and swollen polymer film which is required as an input to fit the data. Previously, members of our research group used surface plasmon resonance to measure the change in refractive index as the temperature was varied continuously across the LCST.12 We abstained from reporting the corresponding change in wet film thickness, since we did not know with confidence the values of the temperature dependent index of refraction of the PNIPAAm brush. We also utilized neutron reflectivity (NR) to study the effects of molecular weight and surface coverage on the temperature induced film collapse.13-16 A minimization of least-squares algorithm was used to fit monomer volume fraction profiles to the NR data. These profiles suggested a substantial change in film thickness as the temperature was varied across the LCST. In this paper, we propose a novel fitting procedure to estimate wet film thickness from AFM data. Using self-consistent field (SCF) theory, we have previously studied how the equilibrium structure of tethered PNIPAAm depends on surface coverage, molecular weight, and temperature, and we found qualitative agreement with the aforementioned experimental studies.17 In that theoretical study, we predicted that confining the PNIPAAm to a flat surface can cause the phase diagram to deviate from that found in bulk solutions.17 The experimental and computational studies cited above indicate that the tethered PNIPAAm chains undergo a temperature dependent collapse in a manner analogous to the coil-to-globule transition of PNIPAAm chains in very dilute aqueous solution.4 Several theoretical methods have been used to model the structure of tethered polymers.18-20 Different implementations of SCF theory have been applied to tethered polymer systems by various researchers.21-30 Alexander31 and deGennes32,33 developed (12) Balamurugan, S.; Mendez, S.; Balamurugan, S. S.; O’Brien, M. J.II; Lopez, G. P. Langmuir 2003, 19, 2545. (13) Yim, H.; Kent, M. S.; Huber, D. L.; Satija, S.; Majewski, J.; Smith, G. S. Macromolecules 2003, 36, 5244. (14) Yim, H.; Kent, M. S.; Mendez, S.; Balamurugan, S. S.; Balamurugan, S.; Lopez, G. P.; Satija, S. Macromolecules 2004, 37, 1994. (15) Yim, H.; Kent, M. S.; Satija, S.; Mendez, S.; Balamurugan, S. S.; Balamurugan, S.; Lopez, G. P. Phys. Rev. E 2005, 7205, 1801. (16) Yim, H.; Kent, M. S.; Mendez, S.; Lopez, G. P.; Satija, S.; Seo, Y. Macromolecules 2006, 39, 3420. (17) Mendez, S.; Curro, J. G.; McCoy, J. D.; Lopez, G. P. Macromolecules 2005, 38, 174. (18) Halperin, A.; Tirrell, M.; Lodge, T. P. Adv. Polym. Sci. 1992, 100, 31. (19) Szleifer, I.; Carignano, M. A. Adv. Chem. Phys. 1996, 44, 165. (20) Milner, S. T. Science 1991, 251, 905. (21) Scheutjens, J. M. H. M.; Fleers, G. J. J. Phys. Chem. 1979, 83, 1619. (22) Cosgrove, T.; Heath, T.; van Lent, B.; Scheutjens, J. M. H. M. Macromolecules 1987, 20, 1692. (23) Shull, K. R. J. Chem. Phys. 1991, 94, 5723. (24) Baranowski, R.; Whitmore, M. D. J. Chem. Phys. 1998, 108, 9885. (25) Martin, J. I.; Wang, Z. G. J. Phys. Chem. 1995, 99, 2833. (26) Laradji, M.; Guo, H.; Zuckermann, M. J. Phys. Rev. E 1994, 49, 3199. (27) Muthukumar, M.; Ho, J. S. Macromolecules 1989, 20, 965. (28) McCoy, J. D.; Ye, Y.; Curro, J. G. J. Chem. Phys. 2002, 117, 2975. (29) Ye, Y.; McCoy, J. D.; Curro, J. G. J. Chem. Phys. 2003, 119, 555. (30) Carignano, M. A.; Szleifer, I. J. Chem. Phys. 1993, 98, 5006. (31) Alexander, S. J. J. Phys. (Paris) 1977, 38, 983. (32) de Gennes, P. G. Macromolecules 1980, 13, 1069. (33) de Gennes, P. G. R. Acad. Sci. Paris 1985, 300, 839.

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scaling theory, which describes how film thickness is related to polymer surface coverage and molecular weight. Scaling theory, although shown to capture the correct physics of polymer brushes, has some limitations that can be overcome by instead using SCF theory: (1) With SCF theory, we can define chain lengths, site diameters, and interaction potentials between the monomers and the grafting surface and/or the opposing test walls. (2) The solvent quality can be varied continuously between poor, theta, and good solvent conditions, and moreover, we can capture the effects of concentration and temperature on solvent quality as was done in this work. (3) SCF theory does not require the assumption of steplike monomer volume fraction profile, but rather calculates this profile self-consistently based on the external fields. To model thermoresponsive tethered polymers immersed in water, Baulin and co-workers developed a mean field theory which incorporates a concentration and temperature dependent Flory-Huggins interaction parameter, χ(φ, T), where φ is monomer volume fraction and T is temperature.34,35 Specifically, they utilized the χ(φ, T) that was obtained from the experimentally measured phase diagram of aqueous PNIPAAm solutions36 to predict the equilibrium structure of tethered PNIPAAm immersed in water. Baulin et al. limited their studies of tethered PNIPAAm to only one polymer molecular weight and surface coverage, and it was Mendez et al. who performed an exhaustive parametric study of this system using SCF theory.17 Several research groups have experimentally measured the force-vs-distance profiles of terminally anchored PNIPAAm immersed in water as a function of temperature. Huber et al. used an interfacial force microscope to measure the force exerted on a tethered PNIPAAm film by a hydrophobically modified glass tip.37 Cho et al. measured the force of approach between a PNIPAAm brush and a bare AFM tip and a tip coated with proteins.38 They found that one set of protein covered tips had repulsive interactions at temperatures below the LCST and attractive interactions above the LCST. A surface force apparatus (SFA) was used by Zhu et al. and Plunket et al. to measure the force encountered between tethered PNIPAAm and plain mica surfaces and mica surfaces coated with lipid bilayers.39,40 In general, most of these experimental studies have found that, at temperatures below the LCST, the force increases gradually with decreasing separation distance, while above the LCST, the force rises sharply at relatively short distance. This indicates that at low temperatures the terminally anchored PNIPAAm chains extend out into the solvent, whereas at high temperature, they collapse toward the wall, confirming the earlier conclusions of Balamurugan et al. (with surface plasmon resonance)12 and Yim et al. (with neutron reflectivity)14,16 and the conclusions our research group arrived at from modeling this system with SCF theory.17 In the SFA technique, the force of interaction between two perpendicular cross cylinders can be measured as a function of the distance between the two cylindrical surfaces. Plunkett et al. coated the surface of one cylinder with terminally anchored PNIPAAm and kept the surface of the other cylinder bare (i.e., untreated mica).40 Those authors compared the force-vs-distance data obtained from SFA measurements under good solvent conditions (T < LCST) with scaling theory of Alexander and (34) Baulin, V. A.; Halperin, A. Macrom. Theor. Sim. 2003, 12, 549. (35) Baulin, V. A.; Zhulina, E. B.; Halperin, A. J. Chem. Phys. 2003, 119, 10977. (36) Afroze, F.; Nies, E.; Berghmans, H. J. Mol. Struct. 2000, 554, 55. (37) Huber, D. L.; Manginell, R. P.; Samara, M. A.; Kim, B. L.; Bunker, B. C. Science 2003, 301, 352. (38) Cho, E. C.; Kim, Y. D.; Cho, K. J. Colloid Interface Sci. 2005, 286, 479. (39) Zhu, X.; Yan, C.; Winnik, F. M.; Leckband, D. E. Langmuir 2007, 23, 162. (40) Plunkett, K. N.; Zhu, X.; Moore, J. S.; Leckband, D. E. Langmuir 2006, 22, 4259.

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de Gennes. Equation 1 below is an adaptation of the expression for the force, f, of interaction for the geometry of opposed cross cylinders which was utilized by Plunkett et al. "   #   f ðDÞ 4 Lo 5=4 4 D 7=4 48 þ ¼ Ka D < Lo R 5 D 7 Lo 35

ð1Þ

where D is the radial separation distance between the cylinder surfaces, Lo is the uncompressed (i.e., no test wall present) film thicknesses, Ka is a constant of proportionality (“prefactor”), R is the radii of the cylinders, and the constant term 48/35 is included to ensure that the force goes to zero at Lo = D. The prefactor Ka includes the Boltzmann factor β = 1/kBT (kB is the Boltzmann constant and T is the temperature) and the polymer surface coverage, FA (number of chains per unit area). The value of Lo is the uncompressed thickness of polymer film while it is submerged in the solvent. Experimentally, with the SFA method, the film thickness can be defined as the separation distance where the force is measured as being nonzero upon approaching from a large distance where the force is zero. The process that Plunkett et al. employed to fit eq 1 to their experimental data involved adjusting the two parameters Lo and Ka until there was close agreement. The value of Lo obtained from the fit was then compared to the value of Lo that was measured with the SFA, and indeed, they reported excellent agreement. In this paper, we propose a fitting process similar to the one described above to allow for obtaining the thickness of a polymer film immersed in a good solvent with the AFM technique. This new fitting method can be desirable since AFM instruments are more widely used than SFA equipment due to cost limitations. On the basis of a density functional theory (DFT) study of tethered polymers, McCoy and Curro argued that in comparing scaling theory to experiments (or molecular models such as the one employed in this work) it is more valid to use the thickness of the compressed film, L, rather than the separation distance between walls, D.41 When experimentalists fit their data to eq 1, they usually have no other option than to use the separation distance between walls as shown schematically in Figure 1, rather than the compressed film thickness. To address this problem, McCoy and Curro proposed an empirical function for determining the ratio of L/Lo given the ratio of D/Lo (see eq 4.2 in ref 41 with D = H), and we refer to this as DFT-corrected scaling theory. Equation 2 is the expression for the force when the geometry is opposing parallel planar surfaces βf ðLÞ ¼ Kb FA

3=2

"   3=4 # Lo 9=4 L L < Lo Lo L

ð2Þ

where Kb is a proportionality constant. With SCF theory, the compressed film thickness, L, can be easily calculated at each wall separation distance. As mentioned previously, Lo is defined as the uncompressed film thickness, that is, when no opposing wall is present. The process that we employed to fit eq 2 to the SCF theory result was to adjust the two parameters Lo and Kb until there was agreement. The value of Lo obtained from the fit was then compared to the value of Lo that was obtained from SCF theory calculations with no wall present. In this paper, two contributions are made. First, SCF theory was used to model the force-vs-distance profiles between a film of terminally tethered PNIPAAm and a test wall as a function of (41) McCoy, J. D.; Curro, J. G. J. Chem. Phys. 2005, 122, 164905.

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Figure 1. Schematic diagram of the model system with parallel, planar walls where one wall is coated with a brush of end-tethered PNIPAAm (dark gray) and the opposing “test” wall (lightgray) is a bare surface separated by a distance D.

wall separation distance. From a SCF theory calculation of tethered PNIPAAm without an opposing test wall, we determined the unperturbed layer thickness, Lo. A test wall was then introduced and SCF theory was used to generate a force-vsdistance curve. The Lo in the scaling theory equation was adjusted until there was agreement between the curves from SCF and scaling theories. This allowed comparison of the Lo values obtained from the two theories. The parameters that were varied are polymer surface coverage and degree of polymerization at temperatures below and above the LCST. Second, we demonstrate how DFT-scaling theory can be used as a tool to analyze AFM force-vs-distance data. Specifically, we used this fitting procedure to reveal an estimate of the wet film thickness. This required a correction for the AFM tip geometry. In the next section, the theoretical and experimental methods are described. In the Results section, we present plots of the SCF theory calculations together with the fits from scaling theory, and we demonstrate the method used to fit the AFM data to DFTcorrected scaling theory.

II. Method: Theory The SCF theory that was used in this work was adapted from the DFT that was originally developed by McCoy, Ye, and Curro.28,29 These authors utilized DFT to model tethered, athermal polymers immersed in an explicit solvent and benchmarked their results to molecular dynamics (MD) simulations and single-chain mean field theory.30 They also applied DFT to tethered polymers in a continuum solvent and reported excellent agreement with results from MD simulations.28 With this theoretical approach, the density profiles of polymer, Fp(z), and solvent, Fs(z), are determined from the coupled functional equations: FR ðzÞ ¼ F½Up0 ðzÞ, Us0 ðzÞ UR0 ðzÞ ¼ G½Fp ðzÞ, Fs ðzÞ

ð3Þ

where z is the distance away from the wall and U0R(z) is the external field for polymer or solvent (R = p, s) which is used to account for the effects of solvent and other chains on a tethered polymer or solvent molecule. The density of a single tethered chain or solvent molecule, in general, will vary with distance away from the wall, Langmuir 2009, 25(18), 10624–10632

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and the first equation represents how this depends on the external field. The second equation represents how the external field can be determined given Fp(z) or Fs(z), and to do this, we used a modified form of the method developed by Chandler, McCoy, and Singer.42 The details of how this method can be applied to polymer systems are provided in several publications.28,43 In our previous publication, we elaborated on the arguments that were made to arrive at the polymer and solvent fields.17 To summarize, we first performed a Taylor series expansion of the free energy difference between the tethered chain system and an ideal system about a reference system of untethered molecules in bulk solution. The density profiles of ideal chains in the external field should have the same profiles as the fully interacting chains with no external field. Obviously, the closer the ideal system is to the real system, the more accurate the Taylor series expansion will be. For our purposes, we choose the ideal system to consist of noninteracting solvent sites and freely jointed chains tethered to a surface in the presence of the ideal fields U0p(z) and U0s (z). Then, we minimized the grand potential free energy to derive an expression for the ideal polymer and solvent fields. Since we are primarily interested in the density profiles on long length scales, we approximated the direct correlation functions as being shortranged, allowing us to further simplify the equations for the fields. Finally, the expressions for the direct correlation functions were obtained by taking the appropriate derivatives of the Helmholtz free energy of mixing from Flory-Huggins theory. Recall that this form of the free energy includes an interaction parameter; thus, we used the experimental concentration and temperature dependent χ(φ, T) χðφ, TÞ ¼

2 X

ðAi þ Bi TÞφi

ð4Þ

i ¼0

The empirically determined Ai and Bi parameters are provided in ref 36. Following the procedure discussed above, that was presented in detail in our previous publication,17 we finally obtained the polymer and solvent fields βUp0 ðzÞ ¼ βUp ðzÞ þ ½ 1 -

1 - 2ðχ0 þ 2χ1 þ 3χ2 ÞÆφs æ N

þ 6ðχ1 þ 3χ2 ÞÆφs æ2 -12χ2 Æφs æ3 ½φp ðzÞ -1 þ λðzÞ βUs0 ðzÞ ¼ βUs ðzÞ þ ½ 1 -

1 - 2ðχ0 - χ1 ÞÆφp æ N

þ 6ðχ1 - χ2 ÞÆφp æ2 þ 12χ2 Æφp æ3 ½φp ðzÞ -1 þ λðzÞ

ð5Þ

where λ(z) is a Lagrange multiplier used to enforce incompressibility, N is the degree of polymerization, and φR = FR/FT is the volume fraction of polymer or solvent. In eqs 5, we write the reference system volume fraction as Æφpæ = ÆFpæ/FT, which can be evaluated from the density profile from eq 6 Fp;ref

R¥ 2 Fp ðzÞ dz ¼ ÆFp æ ¼ R0¥ 0 Fp ðzÞ dz

Fs ðrÞ ¼ Fs;ref expð-βUs0 Þ

ð7aÞ

Due to chain connectivity, the functional F for the tethered polymer is not a simple expression and can be written as N X Æδðri - rÞæ Fp ðrÞ ¼ i ¼1

R Æδðri - rÞæ ¼

Zðri Þ ¼ e -βUi

0

Z

Z :::

δðri - rÞZðri Þ dri R Zðri Þ dri

~ 1 :::rN Þ expðδðr1 - r0 ÞSðr

X

ð7bÞ

βUj0 Þ Π drj

j6¼i

j6¼i

where the first site of the polymer is constrained to be attached to the surface at r0. The intramolecular interactions and chain connectivity constraints are contained in S~ (r1...rN). Recall that our ideal system is a freely jointed chain of bond length σ which allows us to write ~ 1 :::rN Þ ¼ δðr1, 2 - σÞ:::δðrN -1, N - σÞ Sðr

ð8Þ

Equation 7b is solved numerically using Fourier transforms as described in earlier publications.28,29 An iterative scheme was used to solve for the density profiles of tethered PNIPAAm immersed in water. In this scheme, an initial profile was used to calculate the external fields, Uo(z), with eq 5. This field was then used to calculate new profiles with eqs 7. Convergence was established when the maximum difference between the Fp(z) in consecutive iterations was less than 0.1%. If the convergence criteria was not satisfied, the density profiles were updated using a mixing coefficient (0.10), and then, they were used to recalculate the external fields. By this method, we obtained a self-consistent solution for the density profiles and the external fields. To perform the numerical solutions, the z-axis was divided into a grid with spacing of 0.25σ, and 600 Fourier components were used. The total density, FTσ3, was arbitrarily set equal to 1 for the sake of convenience. The inputs to the SCF theory are temperature, T, number of statistical segments per chain, N, dimensionless surface coverage, FAσ2 (i.e., the number of chains per unit area), and the interaction potential between monomers and the grafting surface, which we defined with a “hard” purely repulsive potential.

III. Method: Experimental ð6Þ

We chose the reference system to be a bulk polymer solution at a (42) Chandler, D.; McCoy, J. D.; Singer, S. J. J. Chem. Phys. 1986, 85, 5971. (43) McCoy, J. D.; Teixeira, M. A.; Curro, J. G. J. Chem, Phys. 2001, 114, 4289.

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concentration equal to the average concentration within the polymer brush. With expressions for the ideal polymer and solvent fields, we consider the functional F in eq 3 for the determination of the polymer and solvent density profiles. For a single-site solvent in the ideal system, we obtain the solvent profile Fs(z) from the ideal solvent field

Materials. N-Isopropyl acrylamide (NIPAAm), toluene, methanol (MeOH), Cu(I)Br, and N,N,N0 ,N00 ,N00 -pentamethyldiethylenetriamine (PMDETA) were purchased from SigmaAldrich Corporation. 2-Bromo-2-methyl-N-(3-triethoxysilylpropyl)-propionamide (initiator) was purchased from Gelest. Silicon wafers were purchased from Silicon Inc. Deionized water (18.3 MΩ cm-1) was produced in-house with a Nanopure reverse osmosis system. DOI: 10.1021/la9002687

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Polymer Synthesis. PNIPAAm was prepared following a two-step in situ polymerization scheme.44 The first step resulted in the functionalization of a silicon surface with an initiator, and the second resulted in the formation of a film composed of terminally anchored PNIPAAm via atom transfer radical polymerization (ATRP). Silicon wafers were cleaned with concentrated HCl/MeOH (1:1 by vol) for 30 min followed by concentrated H2SO4 for 30 min. Wafers were then rinsed with copious amounts of DI water and dried with nitrogen. A self-assembled monolayer (SAM) of the initiator was attached to the silicon wafer by immersion in a 4 mM toluene solution at room temperature overnight. The wafer was then rinsed 3 times with toluene and dried in a stream of nitrogen. Polymerization was performed in a 1.7 M NIPAAm solution of NIPAAm (5.0 g, 44 mmol) where the solvent was 25 mL of a MeOH/H2O mixture (1:1 by vol). Cu(I)Br (7 mg, 3 μmol) and PMDETA (30 μL, 25 mg, 140 μmol) were added to the NIPAAm solution and deoxygenated by bubbling nitrogen for 30 min and then sealed for transfer to a glovebox. Inside the glovebox, the wafers were immersed in the polymerization solution. The polymerization was performed at room temperature for a prescribed time. To stop polymerization, wafers were removed from the polymerization solution and rinsed three times with methanol, removed from the glovebox, rinsed with methanol and then water, and dried in a stream of nitrogen. Ellipsometric thickness, contact angle, and XPS elemental composition data were taken to verify SAM and polymer formation (see Supporting Information). AFM Measurements. Force measurements were carried out with a modified Veeco Nanoscope IIIa atomic force microscope on ATRP grown PNIPAAm films in a standard fluid cell filled with deionized water. Tip movements and data collection were automated with custom-written Labview software. Spectral densities of the AFM cantilever were acquired in air before the experiment. PNIPAAm coated wafers were cut and placed on a J-type scanner. An O-ring and fluid cell containing the AFM cantilever was then set on top of the sample. Degassed DI water was injected into the fluid cell, and the film was allowed to equilibrate with the water for 30 min. The AFM cantilever was moved toward the sample surface in discrete 2 nm steps with a dwell time of 100 ms per step. Cantilever deflection was recorded and averaged at each step until tip-sample forces caused a deflection by 10 nm, after which the cantilever was withdrawn from the surface in the same manner (discrete 2 nm steps with average deflection recorded at each step). The deflection detector was calibrated by taking force curves on a bare silica surface, and the piezoelectric positioners were calibrated against known standard samples. The vertical position data were transformed to true tip-sample distance by adding the value of the vertical position to the value of the tip deflection at each point. Tip-sample force was calculated using a spring constant of the cantilever of 0.02 N/m as provided by the manufacturer. The “MSCT” AFM silicon nitride tips were purchased from Veeco Probes. The shape of these tips was a square pyramid.

IV. Results and Discussion In our model, PNIPAAm chains are terminally anchored to a surface. For the sake of keeping the model simple, we use a “hard core” completely repulsive interaction between the monomer and the surface. Making a direct comparison between the SCF theory and an experimental system would require knowledge of the empirically measured interaction between the monomers and the surface; however, this is beyond the scope of the work presented in this paper. We begin our discussion by modeling the unperturbed system, that is, tethered polymers immersed in a solvent (with no test wall present), and demonstrate how the PNIPAAm structure (44) Mulvihill, M. J.; Rupert, B. L.; He, R.; Hochbaum, A.; Arnold, J.; Yang, P. J. Am. Chem. Soc. 2005, 127, 16040.

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Figure 2. Volume fraction profiles, φ(z), from SCF theory with no test wall present at temperatures below and above the LCST. φ(z) at 20 C (solid curve) and at 40 C (dashed curve).

is affected by temperature. Wang et al. probed the effect of temperature on free PNIPAAm chains in dilute solutions with light scattering experiments.4 They reported that, below the LCST (good solvent condition), the PNIPAAm chains were in a swollen coil conformation, while above the LCST (poor solvent condition), the chain conformation was a compact globule. Yim et al. later confirmed that a similar temperature-induced change in conformation occurs for end-tethered PNIPAAm.14 Here, we use SCF theory to model this behavior. Volume fraction profiles for chains with N = 50 and FAσ2 = 0.03 at two temperatures (T = 20 and 40 C) are presented in Figure 2. Clearly, the model illustrates that, below the LCST, the chains extend out into the solvent, while above the LCST, the chains are collapsed as expected. We define the film thickness, Æzæ, as twice the first moment of the volume fraction profile, φ(z), which is the output of the SCF theory R 2 zφðzÞ dz Æzæ ¼ R φðzÞ dz

ð9Þ

Using eq 9, we found the dimensionless film thickness at 20 and 40 C to be Æzæ/σ = 11.9 and =3.7, respectively; and the ratio of the thickness below and above the LCST is 3.2. It was found through the experimental measurements of Yim et al.16 and the computational modeling of Mendez et al.17 that this ratio can depend on both the polymer molecular weight and surface coverage. Our goal was to model the force of interaction between a film of tethered PNIPAAm immersed in water and a test wall as shown in Figure 1. Again, for the sake of simplicity, we introduce a test wall where the interactions between the monomers and the test wall were hard core and purely repulsive. At large separation distance, D, the test wall will have no effect on the structure of the tethered polymer as noted in the volume fraction profiles (not shown). However, at smaller D, the film will become perturbed and the force of interaction can be calculated by using the wall contact theorem as was reported by McCoy et al.41 and others.45-47 In Figure 3, we show how this force of interaction expressed in the dimensionless units Pσ3/kBT (where P is pressure in the zdirection) varies as a function of dimensionless wall separation distance, D/σ. For a tethered polymer with N = 50 and FAσ2 = 0.03, we note in Figure 3a that upon decreasing D the dimensionless force always rises and is positive (i.e., there is repulsive interaction as expected). At a temperature below the LCST, the force is nonzero at long distance and gradually increases with a (45) Lebowitz, J. L. Phys. Fluids 1960, 3, 64. (46) Percus, J. K. J. Stat. Phys. 1976, 15, 423. (47) Dickman, R.; Hall, C. K. J. Chem. Phys. 1988, 89, 3168.

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Figure 4. Semilog plot of the dimensionless force, Pσ3/kT, vs compressed PNIPAAm film thickness, L/σ, from SCF theory with N = 50 and various FAσ2 at T = 20 C (solid curves), and from scaling theory (long-dashed curve), i.e., eq 2 with Kb = 2.5 and values of Lo, which are summarized in Table 1.

Figure 3. (a) Dimensionless force, Pσ3/kT, vs dimensionless wall separation distance, D/σ, of PNIPAAm films from SCF theory with N = 50, FAσ2 = 0.03 at T = 20 C (solid curve) and 40 C (dashed curve); (b) free energy, A(D/σ), from numerical integration of the plots in (a) from D/σ to infinity; (c) force vs distance from SFA measurements reported by Plunkett et al. at T = 26 C (solid circles) and 36 C (open circles).40

sharp rise at short distance. At high temperature, the force is zero at long distance and rises very sharply at short distance. These force-vs-distance profiles affirm that the polymer is in a swollen state below the LCST and compacted above. To make a qualitative comparison with experimental SFA data reported in the literature,40 we numerically integrated the curves in Figure 3a from D/σ to infinity to produce curves that represent the surface free energy, A(D/σ), shown in Figure 3b. This must be done since the SFA data was presented as F/R (force between the cross cylinders divided by the radius of the cylinders), which can be considered as the interaction energy between two parallel surfaces. Qualitatively, there is a similarity between the free energy curves from SCF theory (Figure 3b) and the experimental SFA data (Figure 3c) at low and high temperatures. We refrained from making a direct, quantitative comparison between the force-vsdistance profiles obtained from SCF theory and experimental measurements because of uncertainties in the statistical segment length, σ, and the interaction potentials between the monomer and the grafting surface and the test wall. However, as will be Langmuir 2009, 25(18), 10624–10632

presented later, we benchmark both SCF theory and the experimental results to scaling theory which, although useful, is an intermediate step toward reaching our ultimate goal which is to develop the SCF theory to the level of getting quantitative agreement with experimental data. In the synthesis of thin films composed of terminally anchored polymers, there are well-known techniques to control the polymer molecular weight and surface coverage. It seems reasonable to hypothesize that these two tunable parameters can have an effect on the performance of PNIPAAm films in biotechnological applications such as protein and cell adhesion. Therefore, we use SCF theory to predict the effect of these parameters on the force-vs-distance profiles. We chose to model PNIPAAm films at T = 20 C with a few values of surface coverage (FAσ2 = 0.01, 0.03, and 0.06) while keeping the degree of polymerization constant (N = 50). For the sake of comparison with scaling theory, we plot in Figure 4 the log of the force vs perturbed film thickness, L, which was calculated using eq 9 with the volume fraction profiles obtained at each wall separation distance. This semilog plot indicates that, at a given value of L, the magnitude of the force increases dramatically as the amount of tethered polymer on the surface is increased. We expected this behavior because decreasing the spacing between chains (i.e., raising FAσ2) causes them to stretch away from the surface to minimize steric repulsions between monomers. A similar effect of surface coverage on the force was reported by McCoy et al.41 in their theoretical study of bead-spring chains immersed in a good solvent. Since we lack a complete set of experimental data to compare against, we instead compare our SCF theory to the scaling theory of Alexander and de Gennes.31,48-50 In trying to match the results of SCF theory to eq 2, we treated both Kb and Lo as fit parameters. For a given pair of surface coverage and degree of polymerization, thermodynamics will dictate the equilibrium wet film thickness of a polymer brush. Scaling theory provides a relationship which states that, for a good solvent, the polymer film thickness should scale linearly with number of monomers per chain and to the onethird power with the surface coverage.32 In performing our fit, it is instructive to note that the N from SCF theory (number of statistical segment lengths per chain) is not the same as the N defined in scaling theory. Since the y-axis is logarithmic, the parameter Kb served to shift eq 2 up or down on the y-axis, and Lo served to change the curvature of the scaling theory equation. (48) de Gennes, P. G. Macromolecules 1981, 14, 1637. (49) de Gennes, P. G. Adv. Colloid Interface Sci. 1987, 27, 189. (50) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1953.

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Table 1. Noncompressed PNIPAAm Film Thickness, Lo, Calculated from the First Moment of the Volume Fraction Profiles from SCF Theory at T = 20 C with No Test Wall Presenta N

FAσ2

Lo, SCF theory

Lo, scaling theory

25 50 75 100 50 50

0.03 6.8 8.0 0.03 12.2 13.5 0.03 17.4 18.8 0.03 22.5 24.5 0.01 10.2 13.5 0.06 13.2 14.2 a Scaling theory was fit to the SCF theory force-vs-distance curves by keeping Kb constant (2.5) and by varying Lo in eq 2 until there was agreement. N is the number of statistical segments in a polymer chain with diameter of σ. FA is the number of polymer chains per unit area.

Our intention was to find a single value of Kb which would allow us to fit eq 2 to the SCF theory results over the range of surface coverage and molecular weight that was used in this study. Indeed, we found that fixing Kb = 2.5 and adjusting Lo in eq 2 allowed us to obtain reasonable fits as noted in the plots. For most cases, there was better agreement at large L than at small L as expected, since eq 2 is known to be less reliable at short distances. We can now compare the Lo values used to fit eq 2 to the Lo values we obtained from the corresponding SCF theory calculations when no test wall was present, i.e., the uncompressed film. The values of Lo from the fits and from SCF theory are summarized in Table 1. There is remarkably good agreement between the two values of Lo indicating that a single value of Kb in eq 2 is sufficient to characterize our SCF theory results. To understand the effects of polymer molecular weight on the force, we chose to model PNIPAAm films at T = 20 C with a few values of N (=25, 50, 75, and 100) while keeping the surface coverage constant (FAσ2 = 0.03). In Figure 5, a semilog plot of dimensionless forces vs L, we observe that, for a given value of L, increasing the chain length results in a large increase in the repulsive force. This behavior is plausible because increasing the molecular weight leads to an increase in the film thickness, therefore a rise in the force of approach. Again, we compare our SCF theory to scaling theory with the same value of Kb = 2.5 and by varying Lo in eq 2. In Table 1, we summarize the values of Lo from the fits and those obtained from SCF theory when no test wall was present. For the profiles obtained with low N, there is excellent agreement over all values of L. However, we note from Figure 5 that, at large N (=75 and 100), there seems to be disagreement at the lower values of L. We speculate that perhaps this might be due to the occurrence of a compression-induced phase transition, but this speculation will be the subject of a future study. In trying to understand the phenomena of bioadhesion (e.g., cell attachment) onto PNIPAAm surfaces, our ultimate goal is to develop our version of SCF theory such that there is quantitative agreement with experimental force-vs-distance data. The inputs to SCF theory are the polymer molecular weights (N) and surface coverage, and since the output of theory is in dimensionless units, a direct comparison to experiments would require knowing the value of the statistical segment length, σ. Although in principle it is feasible to reproducibly synthesize PNIPAAm films with wellcharacterized molecular weights and surface coverage, in practice this can be a difficult task. As an intermediate step toward our final goal, we begin by analyzing experimental AFM data with a novel method that employs DFT-corrected scaling theory to estimate the thickness of a swollen PNIPAAm brush immersed in water. In this paper, we propose a convenient method to estimate the wet film thickness from a set of AFM force-vs-distance data. 10630 DOI: 10.1021/la9002687

Figure 5. Semilog plot of the dimensionless force, Pσ3/kT, vs compressed PNIPAAm film thickness, L/σ, from SCF theory with FAσ2 =0.03 and various N at T = 20 C (solid curves), and from scaling theory (long-dashed curve), i.e., eq 2 with Kb = 2.5 and values of Lo which are summarized in Table 1.

To illustrate this method, we begin with the force, f, between a polymer-coated and an uncoated parallel surface found from DFT-corrected scaling theory. We are interested in the total force, Ftot, exerted on an AFM tip. To account for the shape of the tip, we integrate f over the tip surface. Butt and co-workers reported such integration for AFM tips with parabolic shapes; however, they used an exponential approximation for the force rather than the equation from scaling theory.54 By fitting their AFM data, they estimated the wet film thickness and the surface coverage for tethered polystyrene immersed in cyclohexane (solvent). We conduct a similar analysis for PNIPAAm. A general expression for the total force exerted on a rotationally symmetric AFM tip can be written as Z

¥

Ftot ¼

2πx f ðyÞ dx

ð10Þ

0

where the coordinates x and y are defined in Figure 6 for the case of a cone-shaped tip with the origin located at the tip. For convenience, we rescale all the length variables coordinates by dividing by Lo and represent them with over bars Z Ftot ¼ 2πL2o

¥

x f ðyÞ dx

ð11Þ

0

Since we are interested in the force in the y-direction, we rewrite eq 11 as Z Ftot ðHÞ ¼ 2πL2o

x H

Z ¼ πL2o

¥

¥ H

dx f ðyÞ dy dy

dx2 f ðyÞ dy dy

ð12Þ

This is a general expression that can be used to calculate the total force exerted on a rotationally symmetric AFM tip. For illustrative purposes, we first treat a cone-shaped AFM tip. The linear relationship between x and y can be written as y = mx+H where m is the slope of the cone. This leads to an equation for the total force exerted on the cone Ftot ðHÞ ¼

2πL2o m2

Z

¥

ðy -HÞ f ðyÞ dy

ð13aÞ

H

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Figure 6. Schematic diagram of a cone-shaped AFM tip. H is the distance between the cone tip and the flat surface.

If an AFM tip had a parabolic shape, the equation y = mpx2 + H can be written where mp is a coefficient. The total force on the parabolic tip can be expressed as Ftot ðHÞ ¼

Z πL2o ¥ mp

f ðyÞ dy

ð13bÞ

H

In our AFM experiments, we used a regular square pyramidshaped AFM tip. From simple geometric relationships, we get Z Ftot ðHÞ ¼ 8L2o tanðθÞ

¥

ðy -HÞ f ðyÞ dy

ð14Þ

H

where θ (=35 from manufacturer) is half the angle of the pyramid’s tip as viewed from a side projection. The integral in eq 14 was solved numerically with f from eq 2. All of the constants in eq 14 were lumped together into a value we call Kp. To fit the experimental data to DFT-corrected scaling theory, we followed a procedure that has some similarities to the method reported by Plunkett et al.40 They estimated the wet film thickness by adjusting Ka and Lo in eq 1 until there was good agreement between their SFA data and the theoretical curve. The Lo from their fit (274 nm) was found to be in reasonable agreement with the measured onset of steric repulsions (269 nm). This methodology was suggested by the work of Taunton et al. where they plotted force vs D/Lo data for polymer brushes with various molecular weights and found the plots to collapse to a master curve upon shifting the vertical axes (i.e., by multiplying the force data by a constant).51 To estimate the wet film thickness at 24 C, we started by generating an array of numbers from 0 to 1 to represent the ratio of D/Lo. By comparing the results from density functional theory to scaling theory, McCoy and Curro41 provided an empirically fit relationship (see eq 4.2 in ref 41) that allows the determination of L/ Lo for a given value of D/Lo. Thus, we used these computed values of L/Lo to calculate the force with eq 2. Equation 14 (without the prefactor constant, Kp) was then numerically integrated to generate (51) Taunton, H. J.; Toprakcioglu, C.; Fetters, L. J.; Klein, J. Nature 1988, 332, 712. Macromolecules 1990, 23, 571. (52) Tu, H.; Heitzman, C. E.; Braun, P. V. Langmuir 2004, 20, 8313.

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Figure 7. Semilog plot of force vs the ratio between the wall separation distance, D, and the uncompressed PNIPAAm film thickness, D/Lo. The solid curve is from eq 14 with f from eq 2 and Kp = 1200. The empirical relationship from ref 41 was used to convert from D/Lo to L/Lo. Experimental AFM data (x’s) taken from a PNIPAAm film immersed in water at T = 24 C. These data were fit to the scaling theory curve by adjusting two parameters: a constant (yoffset = 220 nm) was added to the AFM vertical displacement data (yafm) to give D (yoffset þ yafm); and this D was divided by the other fit parameter, Lo (275 nm). The inset is a plot of the AFM force vs D as defined previously.

a curve for the function, Ftot(Hh). In Figure 7 we show, on a semilog, Ftot(H) where Kp was adjusted (1200) until this curve matched the range of AFM force data. The next step was to perform a two-parameter fit of the AFM data to the aforementioned curve. Unlike the SFA technique which allows for knowing the wall separation distance, D (since direct contact between the cross cylinders is possible), in our AFM experiment the distance coordinate that was measured was tip displacement and not the absolute distance between the tip and the surface at the base of the PNIPAAm film. The separation distance, D, was not measured directly because the fragile AFM cantilever could not be pressed into the underlying solid surface. Therefore, the fitting procedure required that we add an offset (yoffset) to the y-axis AFM data (yafm) where D = yafm + yoffset. Since we wanted to plot the AFM force data as a function of D/Lo, we adjusted the fit wet film thickness, Lo,fit, to shrink or expand the horizontal range. Thus, yoffset and Lo,fit were manipulated independently until the AFM data were found to be in close agreement with a section of the curve from eq 14: we found, through probing the parameter space, best fit values of yoffset = 220 nm and Lo,fit = 275 nm. To obtain a more reproducible fit, a statistical algorithm could be implemented to find these parameters by minimization of the errors. Obviously, this fit procedure would benefit greatly if D were measured directly. The semilog plot of the AFM data shows a sharp drop at large distances which we suspect is due to slight attractive interactions between the bare silicon nitride AFM tip and the NIPAAm monomers as was reported by Goodman et al.53 As scaling theory cannot account for attractive forces, we expect some disagreement at large separation distances. The inset to Figure 7 shows a plot of the AFM force data as a function of D as defined previously. This shows a gradual rise in the force as expected from SFA data as well as SCF theory predictions. (53) Goodman, D.; Kizhakkedathu, J. N.; Brooks, D. E. Langmuir 2004, 20, 3297. (54) Butt, H.-J.; Kappl, M.; Mueller, H.; Raiteri, R.; Meyer, W.; Ruhe, J. Langmuir 1999, 15, 2559.

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As described above, the AFM data was fit to get an estimate of the thickness (Lo,fit) of the wet film at 24 C. For this PNIPAAm film, the dry thickness was measured with ellipsometry to be 48 ( 4 nm making the dry to wet thickness swell ratio 1:4.6. We can compare this estimated swell ratio to other PNIPAAm brush systems reported in the literature with the important caveat that, since the swell ratio depends on polymer surface coverage and molecular weight (as predicted by Mendez et al.17), we do not expect quantitative agreement. Plunkett et al.40 with SFA techniques found a swell ratio of 1:4.8, and Tu et al.,52 who synthesized terminally anchored PNIPAAm films in a manner similar to us, used environmental ellipsometry to find the dry to wet swell ratio of 1:4.0. The closeness of these swell ratios provides evidence that our fitting method provides reasonable wet film thickness values. In summary, we have demonstrated that SCF theory can be used to model the force of interaction between end-tethered PNIPAAm and an opposing bare test surface. We also proposed a method to estimate the wet film thickness of a PNIPAAm brush from AFM force-vs-distance data. The enhanced understanding from this modeling can be used to impact further experimental work, primarily if there is an application that requires specific control of the force of interaction, for example, to stabilize colloidal suspensions. We found that large polymer molecular weight or high surface coverage can result in high force of interaction. In this work, the test surface was made to have a purely repulsive potential of interaction with the NIPAAm monomers. We are currently in the preliminary stages of implementing test walls that have attractive interactions for the sake of mimicking biological cell walls. These nascent studies indicate that, with attractions, there can be a minimum in the force-vsdistance profile, thus providing the capability to offer some guidance to the future optimization of bioadhesion applications. We envision that the ability to estimate the wet film thickness from AFM measurements using our proposed fitting process may lead to the possibility of generating topographical maps of a wet film area.

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V. Conclusions The purpose of the research reported in this paper is to contribute to the understanding of the force of interaction between films composed of end-tethered PNIPAAm and test surfaces. We employed a self-consistent field theory to study the effects of temperature, degree of polymerization, and surface coverage on the force of interaction between PNIPAAm and a repulsive test wall. We found qualitative agreement with the experimentally measured force-vs-distance profiles reported in the literature, which indicates that, at temperatures below the bulk solution LCST, the chains are well-solvated, while above the LCST, the chains collapse to the surface. We found that a single value of the prefactor Kb (2.5) in the expression for the surface force (eq 2) could be used to adequately fit our SCF theoretical results to scaling theory. There was very good agreement between the unperturbed film thickness values calculated with SCF theory and those obtained from the fit to scaling theory. We also reported a method to estimate the thickness of tethered PNIPAAm immersed in water from force-vs-distance data measured with atomic force microscopy. A general expression for the total force on a rotationally symmetric AFM tip was derived. A density functional theory corrected version of scaling theory41 was used to represent the force at a given tip height. From the proposed fitting procedure, a wet film thickness value was estimated, and the ratio of dry to wet film thickness was in agreement with ratios published in the literature. Acknowledgment. This work was supported by NSF-Partnerships for Research and Education in Materials (PREM) program grant no. DMR-0611616, the Office of Naval Research grant no. N00014-08-1-0741, and the Defense Threat Reduction Agency (DTRA) grant no. HDTRA-07-1-0034. Supporting Information Available: A copy of the experimental characterization of the polymer surface is provided. This material is available free of charge via the Internet at http://pubs.acs.org.

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