Disjoining Pressure and Swelling Dynamics of Thin Adsorbed Polymer

In Final Form: August 10, 1999 ... swelling of thin hydrated films of such polysaccharides have been ... absolute film thickness as a function of disj...
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Disjoining Pressure and Swelling Dynamics of Thin Adsorbed Polymer Films under Controlled Hydration Conditions G. Mathe, A. Albersdo¨rfer, K. R. Neumaier, and E. Sackmann* Physics Department E 22, Biophysics Group, Technical University Munich, D-85748 Garching, Germany Received May 27, 1999. In Final Form: August 10, 1999 In this paper we study the static properties and the dynamical swelling behavior of thin spin-coated layers of natural polysaccharides on Si/SiO2 substrates: the neutral and slightly branched dextran and the negatively charged, linear hyaluronic acid, by ellipsometric observation of the film swelling in a humiditycontrolled environmental chamber. Equilibrium swelling ratios and disjoining pressures are measured as a function of the relative humidity of the surrounding atmosphere, which was varied from 4% up to 98%, with the former corresponding to intermolecular separation distances smaller than 6 Å. With increasing water uptake the disjoining pressure curves exhibit a crossover from hard-core repulsion to a regime dominated by hydration forces, which were recently recognized to dominate the interaction of polysaccharides at close distances. On the basis of the static measurements, the kinetics of swelling of the adsorbed polymers were determined by a sudden application of an osmotic stress. The kinetics of film thickening after stepwise increase of the humidity is discussed in terms of a simple diffusion model (generalized Maxwell-Stefan approximation). From this analysis we obtained an effective mesh size in the dry polymer film and a power law relating the mesh size to the volume fraction in the expanding network. We further demonstrate the possibility of controlling swelling behavior of laterally microstructured polymer layers by relative humidity and of measuring it locally by a recently developed quantitative imaging microellipsometer.

1. Introduction The swelling behavior of hydrophilic polysaccharides plays an important role in many biological systems. One example is hyaluronic acid, a charged mucopolysaccharide occurring in many living tissues. Confined between cells and the extracellular matrix, this giant macromolecule can generate high local disjoining pressure and thus create hydrated pathways for the transport of molecules by separating the cellular barriers.1 The disjoining pressure is a measure for the force per unit area within the wetting film and is the first derivative of the interfacial potential. The concept of disjoining pressure is essential to describe the physics of wetting of a surface with a fluid that is in equilibrium with its partial vapor pressure. A well-known example is the wetting of solid surfaces by liquid helium.2 In analogy to the situation of osmosis, the thickness and thus the local density of the wetting layer depend on the externally applied chemical potential µ of the solvent, which is related to the disjoining pressure by P ) µ/Vm, where Vm is the molar volume of the liquid.2 In recent years, thin hydrated polymer films on solid supports attracted much attention in biotechnical applications. Examples are the generation of biocompatible surfaces on transplants3 or of ultrathin, high electrical resistance layers on semiconductors for the fabrication of biosensors.4,5 However, only few studies of controlled * Author for correspondence. Tel: +49 (0) 89 289 12495; fax: +49 (0) 89 289 12469; e-mail: [email protected]. (1) Toole, P. Cell Biology of Extracellular Matrix; Plenum Press: New York, 1991. (2) Israelachvili, J. N. Intermolecular and Surface Forces. Academic Press: London, 1992. (3) Erdtmannn, M.; Keller, R.; Baumann, H. Biomaterials 1994, 15, 1043-1048. (4) Ra¨dler, J.; Sackmann, E. Curr. Opin. Solid State Mater. Sci. 1997, 2, 330-336. (5) Stelzle, M.; Weissmu¨ller, G.; Sackmann, E. J. Phys. Chem. 1993, 97, 2974-2981.

swelling of thin hydrated films of such polysaccharides have been reported up to now despite their important role for the stabilization of tissues.6-8 The functionality of polysaccharides in these examples is expected to be due to their unique physical properties in aqueous environment. It is well-known that hydrophilic polysaccharides can store a large amount of water and form hydrogels with a distinct swelling behavior. During the continuous compression of the polymer network, several types of forces arise. Subsequently, these polymer-induced forces in these surface-grafted polymer films have been studied extensively, both theoretically and experimentally.2,9,10 For a better understanding of the complex biological functions and technical applications of these polysaccharide films it is also necessary and interesting to study the swelling kinetics, which is determined by the diffusion of solvent molecules into and through the polymer network. For example, in biosensors such as surface plasmon resonance devices it is necessary to achieve very short response times by using the fast diffusion through thin polymer films.11 Swelling kinetics of several polysaccharides such as dextran and hyaluronic acid and the solvent diffusion in such hydrogels has been subject to many studies.1,12-17 However, these studies have in common the fact that they (6) Elender, G.; Ku¨hner, M.; Sackmann, E. Biosens. Bioelectron. 1996, 11; 565-577. (7) Elender, G. Ph.D. Dissertation Institut fu¨r Kernphysik und Nukleare Festko¨rperphysik, Lehrstuhl fu¨r Biophysik E22. Mu¨nchen, Technische Universita¨t Mu¨nchen, 1996. (8) Rau, D. C.; Lee, B.; et al. Proc. Natl. Acad. Sci. U.S.A. 1984, 81, 2621-2625. (9) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (10) Israelachvili, J. N.; Wennerstro¨m, H. Nature 1996, 379, 219224. (11) Decher, G. Nachr. Chem. Techn. Lab. 1993, 41, 793-800. (12) Bisschops, M. A. T.; Luyben, K. Ch. A. M.; van der Wielen, L. A. M. Ind. Eng. Chem. Res. 1998, 37, 3312-3322. (13) Cukier, R. I. Macromolecules 1984, 17, 252-255. (14) Ogston, A. G. Trans. Faraday Soc. 1958, 54, 1754.

10.1021/la990658u CCC: $18.00 © 1999 American Chemical Society Published on Web 09/29/1999

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are based on simple assumptions on the thickness dependence of the disjoining pressure driving the swelling process. In this paper we present a method that allows the combination of both equilibrium measurements of the absolute film thickness as a function of disjoining pressure and time-dependent measurements of the swelling rate of thin solid-supported polymer films after application of an osmotic shock. For all experiments, thermally oxidized silicon is used as a substrate material because of its strong hydrophilic character necessary for polysaccharide adsorption and its superb surface quality with typical roughnesses on the angstrom scale. Furthermore, semiconductor surfaces offer a basis for possible applications of these experimental results in the field of biosensing. The thickness is measured by pointlike and imaging ellipsometry, and to achieve high sensitivity the swelling experiments are performed with surface-grafted polymer films exposed to a humid atmosphere. To control the partial water vapor pressure up to 98% relative humidity, the swelling experiments are performed in a closed humidity chamber. We further demonstrate that by using a recently developed microellipsometer,18 similar swelling studies can be performed with heterogeneously functionalized Si/ SiO2 substrates. Investigations of the swelling kinetics and interfacial potential measurements can be performed with a lateral resolution of ∼3 µm and a thickness resolution of 1-2 nm. 2. Materials and Methods 2.1. Materials. Dextran. Dextran from Leuconostoc mesenteroides (strain no. B-512) with a molecular mass of ∼500 kDa was purchased from Sigma (Deisenhofen, Germany). Dextran is a water-soluble weakly branched neutral polysaccharide. The average degree of polymerization of the blend used in our experiments is ∼2700 glucose monomers. Hyaluronic acid. Bacterial hyaluronic acid from Streptococcus zooepidemicus was purchased from Aldrich (Steinheim, Germany). It is a water-soluble polyanionic macromolecule consisting of up to 104 repeating disaccharide units of N-acetyl-D-glycosamine and D-glycuronic acid. The samples used had an average molecular mass of ∼106 Da, corresponding to ∼3000 monomers.19 Silicon wafers were gifts of the Wacker Chemitronic GmbH (Burghausen, Germany). These wafers are thermally oxidized with a thickness of the oxide layer of 147 ( 5 nm. 2.2. Sample Preparation. Aqueous solutions of hyaluronic acid and dextran with concentrations between 1.0 and 5.0 vol % were first prepared in ultrapure water (Millipore, Molsheim, France). To remove inhomogeneities in the bulk, such as insoluble dextran aggregates that exhibit typical diameters of the order of 10 µm, all solutions were centrifuged for 15 min at 5000g. The polymer films were deposited by spin-coating the substrates after deposition of polymer solutions of various concentrations. The thickness was varied by changing the concentration of polymer while keeping the spin speed constant at 2000 rpm. The samples prepared in this way were also structured laterally by photolithography. As masks we used EM grids (Plano, Marburg, Germany) with mesh sizes of 62 µm (width of the bars 20 µm, side length of the holes 42 µm). The micrometer pattern was finally generated by etching the layers selectively by UV irradiation. 2.3. Technical Setup and Data Evaluation. 2.3.1. Static swelling measurements. The equilibrium film thickness of (15) Ogston, A. G.; Sherman, T. F. J. Physiol. (London) 1961, 156, 67. (16) Ogston, A. G.; Preston, B. N.; Wells, J. D. Proc. R. Soc. London A 1973, 333, 297. (17) Vavruch, I. Kolloid Z. Z. Polym. 1965, 205, 32-39. (18) Albersdo¨rfer, A.; Elender, G.; Mathe, G.; Neumaier, K. R.; Paduschek, P.; Sackmann, E. Appl. Phys. Lett. 1998, 72, 2930-2932. (19) Meyer, K. Fed. Proc. 1958, 17, 1075-1077.

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Figure 1. Experimental setup for static measurements consisting of an ellipsometer attached to a humidity chamber. The humidity inside the chamber is controlled by mixing a constant flow of dry filtered air with a flow of water-saturated air by a valve. With this technique the relative humidity inside the chamber can be adjusted to between 0.5% and 98%. spin-coated polymers on thermally oxidized silicon wafers was measured as a function of the relative humidity of the air by using a conventional ellipsometer (Plasmos GmbH Prozesstechnik, Mu¨nchen, Germany) equipped with a humidity chamber (as shown in Figure 1). Absolute values of the thickness and refractive index of the adsorbed polymer layers are obtained by measuring two ellipsometric angles ∆ and ψ, which are related to the complex reflection coefficients RP and RS of light polarized parallel (P) and perpendicular (S) to the plane of incidence, respectively

RP/RS ) tan ψ exp(-i∆)

(1)

where RP and RS are given as the ratio of the complex incident and evanescent electric fields, RP ) EP,evan/RS,incid and RS ) RS,evan/ ES,incid, respectively. The refractive indices and thicknesses can be evaluated by computer-assisted analysis of RP/RS in terms of the Fresnel equations of reflection for light of both S- and P-polarization.20 The equilibrium humidity inside the chamber was controlled by mixing a constant flow of dry filtered air with a flow of watersaturated air by means of a valve. With this technique the relative humidity inside the chamber can be adjusted between 0.5% and 98%. The humidity control device as well as the hygrometer used was described by Elender et al.6,7,21 Between two subsequent equilibrium thickness measurements the film was allowed to equilibrate for at least 10 min. For the evaluation of the swollen film containing increasing amounts of water, the refractive index was calculated by applying the well-known Garnet equation,22,23 which relates the refractive index nF of a homogeneous solution to the volume fraction Φ of the solute:

x

nF ) nM

1+

3Φ n20 + 2n2M

(

n20 - n2M

)

(2) -Φ

n0 and nM are the refractive indices of the pure solute and the pure solvent, respectively. The volume fraction Φ is simply related to the layer thickness h by Φ ) h0/h, where h0 is the dry film thickness measured at very low relative humidity (≈ 4%). For the evaluation of the ellipsometric data we used a value of the mean refractive index for dry polysaccharides of n ) 1.56.6,7 As (20) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland: Amsterdam, 1977. (21) Elender, G.; Sackmann, E. J. Phys. II 1994, 4, 455-479. (22) Garnet, M. Philos. Trans. R. Soc. London, Ser. A 1904, 203, 385-420. (23) Garnet, M. Philos. Trans. R. Soc. London, Ser. A 1906, 205, 237-288.

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described by Elender7 the film thickness can be calculated selfconsistently by starting from the refractive index of the dry layer and by application of Garnet’s formula successively. The forces operating within the film can be analyzed in terms of the disjoining pressure p, defined as the negative derivative of Gibbs free energy G with respect to h, that is, -∂G/∂h,24 where G is the free energy of the film as a function of the thickness h, which can be evaluated from the following equation25-27

p ) -(RT/Vm) ln(X)

(3)

Here Vm is the molar volume of water, T is the temperature, R is the molar gas constant, and X is the relative humidity defined by the ratio of vapor pressure to the saturation pressure of water in the surrounding atmosphere. p simply measures the change of the chemical potential of water µ ) -RT ln(X) within the film, and no structural features are involved at this stage. 2.3.2. Dynamic Swelling Measurements. The dynamic swelling experiments were performed as follows: After equilibration at low relative humidity (≈4%) the investigated part of the sample was exposed to a steady flow of air of high relative humidity (typically ∼90%). The following thickening of the polymer film, driven by the abrupt change in osmotic pressure, was monitored by the time evolution of the reflected intensity, which was measured by a high-sensitivity cooled CCD chip (Hamamatsu, Herrsching, Germany) with a time resolution of 10 images per second. The intensity I(t) was then converted to the layer thickness h(t) by comparing measured and calculated intensity curves. The theoretical curve was determined by applying the Fresnel equations of the optical reflection and transmission coefficients of planar surfaces for all layers involved, following Azzam and Bashara20 and by considering Garnet’s relation (section 2.3.1, eq 2). To achieve fast switching times between air of low and high humidity the pipes guiding the gas flow were placed close to the investigated region of the sample (Figure 2). To ensure thermal equilibrium conditions at the end of the measurement and to monitor also possible long-range relaxation phenomena, the data acquisition was carried out for at least 20 s after removing the high-humidity air flow despite the fact that more than 90% of the swelling took place within 2-3 s after an abrupt increase in the humidity. An advantage of our experimental setup is the possibility of determining the difference in reduced chemical potential independently in an equilibrium measurement for all swelling ratios. Therefore the effective driving force of film thickening can be given for all states of the polymer layer during the swelling process. 2.3.3. Quantitative Imaging Ellipsometry. The structured samples were analyzed by high-resolution imaging microellipsometry. The measuring device as well as the evaluation procedure has been described in detail by Albersdo¨rfer et al.18 In brief, a polarized beam of a He-Ne laser (wavelength λ ) 632.8 nm) is reflected at the vertically mounted sample and collected by a microscope objective (numerical aperture NA ) 0.4, magnification Mn ) 20). After determining the degree of polarization with an analyzer, the image is projected by a tube lens on a cooled high-sensitivity CCD camera. The ellipsometric parameters ∆ and ψ, which determine the absolute film thickness, are obtained locally by applying the rotating analyzer principle20 for each pixel on the image. In previous work18 we demonstrated that with this technique quantitative thickness measurements of laterally patterned “hairy-rod” systems with a lateral resolution of 3 µm and a thickness resolution of 5 Å are possible. In the present case of adsorbed dextran and hyaluronic acid layers this absolute thickness resolution is not fully reached because of the much higher thickness of the initial layer and a grade of surface homogeneity that is not completely comparable with the perfectly smooth hairy-rod system. These facts lead to a decreased resolution of ∼1-2 nm. (24) Landau, L. D.; Lifschitz, E. M. Lehrbuch der theoretischen Physik, Band V, Statistische Physik Teil1; Akademie-Verlag: Berlin, 1987. (25) Parsegian, V. A.; Fuller, N.; Rand, P. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 2750-2754. (26) Pashley, R. M.; Kitchener, J. A. J. Colloid Interface Sci. 1979, 71, 491-500. (27) Rand, R. P. Annu. Rev. Biophys. Bioeng. 1981, 10, 277-314.

Figure 2. Principle of dynamic swelling measurement. At times t e tstart the adsorbed polymer layer is kept at constant low relative humidity by exposing the investigated parts of the sample to a steady flow of dry air (X = 4%). The measured intensity I(t) takes a constant value. At t ) tstart the chemical potential of the water molecules in the polymer is changed within 100 ms by switching to a steady flow of humid air (X = 90%). The swelling of the polymer layer leads to a timedependent intensity, from which the thickness curve h(t) is evaluated as described in the method section.

3. Theoretical Background of Dynamic Swelling Measurements The theoretical analysis of the swelling dynamics studied in this paper is based on the generalized MaxwellStefan approach (GMS approach),28 which was successfully used in previous work.12 The general GMS equation is given by

Fdr,i(r b,t) ) Ffr,i(r b,t)

(4)

b,t) is the time-dependent net driving force on where Fdr,i(r a test molecule of the component i, located at position b r, b,t) stands for the frictional force exerted on that and Ffr,i(r molecule by all other components involved at any time t.12 The net driving force is due to the gradient of the chemical (28) Wesselingh, J. A.; Krishna, R. Mass Transfer; Ellis Horwood: Chichester, UK, 1990.

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potential of species i.12,28 Because of our stratified and laterally homogeneous sample geometry for the dynamic swelling experiments, only variations of the observable quantities in z-direction, that is, perpendicular to the surface, are considered. Furthermore, we restrict our investigations on the swelling behavior of adsorbed polymer films to times after the application of an osmotic shock. Therefore, no explicit time dependence of the net b,t) driving force must be taken into account, that is, Fdr,i(r ≡ Fdr,i(z) and Fdr,i(z) can be expressed as

Fdr,i(z) ) -

d ∆µ (z) dz i

(5)

∆µi(z) is the difference in chemical potential of component i within the adsorbed layer at height z and of its vapor in the surrounding atmosphere. In the following we restrict our consideration to the solute molecule water and consider only a mass flow perpendicular to the surface. The frictional force between water molecules and polymer network can be written as12

Ffr )

RT Φ(uS - uP) Deff

(6)

where Φ is the volume fraction of the polymer in the polymer-water solution, uS - uP is the velocity difference between water and polymer during the swelling process occurring in the z-direction, and Deff is an effective diffusion coefficient for water molecules in the polymer network. Deff is in general a function of Φ and therefore implicitly time-dependent because both water and polymer are nearly incompressible. uS, uP, and Φ are related by a simple volume conservation law according to: us(1 - Φ) - uPΦ ) 0. Therefore the velocity difference uS - uP can be expressed as a function of the velocity of film thickening uP ) dh/dt, which is directly accessible by our experimental setup. The conservation law yields

(1 -1 Φ)u

uS - uP ) -

P

(1 -1 Φ)dhdt

)-

(7)

To relate the observed swelling kinetics to microscopic properties, one needs a model for the dependence of Deff on Φ, which holds for all states of swelling. A large variety of approaches are described in the literature. These include heuristic models based on analogies between the viscous hydrodynamic flow through a bed of fibers on a macroscopic scale and diffusion of solvent inside a gel bead on a molecular scale28,29 or semiempirical relations, such as proposed by Ogston et al.14-16 More sophisticated microscopic models are proposed by Vrentas and Vrentas30 which take into account the ratio between the molecular volume of the diffusing solvent molecules and the free volume inside the polymer, the glass transition temperature TG, and other parameters related to TG, especially the constant pressure heat capacity difference CP(TG) CP(T). In our approach we apply a semiempirical model proposed by de Gennes9 and De Smedt et al.31 that contains the Ogston model as a special case. The basic assumption is that the transport of a probe molecule through a network is an activated process involving an activation energy. By (29) Coulson, J. M.; Richardson, J. F. Unit Operations; Pergamon Press: Oxford, 1976. (30) Vrentas, J. S.; Vrentas, C. M. J. Polym. Sci., Part B: Polym. Phys. 1992, 30, 1005-1011. (31) De Smedt, S. C.; Lauwers, A.; Demeester, J. Macromolecules 1994, 27, 141-146.

assuming that the activation energy is determined by the elastic energy associated with the expansion of the local mesh size during the passage of a molecule, the effective diffusion coefficient is given by the following scaling law9,31

Deff ) D1 exp[-β(d/ξ)δ]

(8)

where D1 is equal to the self-diffusion coefficient in the pure solvent at temperature T. d represents the size of the diffusing solvent molecule and ξ is the effective mesh size of the polymer network, which is a function of the polymer volume fraction Φ. ξ can be related to the volume fraction by a power law υ′9,31

ξ ) ξ0Φ-υ′

(9)

where the parameters β and δ are assumed to be approximately 1.32 ξ0 is the minimum mesh size for the dry polymer network. In the following we introduce the swelling ratio F ≡ 1/Φ, which is the measured quantity in our experiment, and the molecular parameter λ ) β(d/ ξ0)δ, and eq 8 becomes (υ ≡ υ′δ)

Deff ) D1 exp(-λF-υ)

(10)

By combining eqs 4 to 10 we finally obtain an equation for the time dependence of the solvent density F(z,t) in the adsorbed film:

dF(z,t) Deff d ) [F(z,t) - 1] ∆µred[F(z,t)] dt h0 dz

(11)

where ∆µred ≡ ∆µ/RT is the reduced difference of the chemical potential. Equation 11 is in general a nonlinear differential equation because of the complex relation between swelling ratio and chemical potential of the solvent and can only be solved numerically. For the interpretation of our data we use a simplified approximation of this relation, called linear driving force approach.28,12 The main assumption of this approximation is that the entire mass transfer occurs within a thin layer at the polymer-air boundary. In the special case of ultrathin adsorbed films this layer comprises approximately the whole polymer layer of thickness h. Satisfying the boundary condition ∆µred(z ) h) ) 0, |∆µred| increases as z approaches the substrate surface. In the linear driving force approximation F(z,t) is assumed to vary linearly with the position z inside the polymer layer. In this approach, the position-dependent swelling ratio F(z,t) is replaced by the mean value Fj(t) ) [F(z ) h,t) + F(z ) 0,t)]/2 that is related to the measured layer thickness h(t) by h(t) ) h0Fj(t). In analogy to that the reduced chemical potential ∆µred(F) is represented by the only two values ∆µred[F(z ) h,t)] and ∆µred[F(z ) 0,t)]. By means of this the gradient of ∆µred(F) can be replaced by its differential quotient

∆µred(z ) h) - ∆µred(z ) 0) d [∆µred(z,t)] ≈ ) dz h 0 - ∆µred(z ) h0Fj) ∆µred(Fj) ) (12) h0Fj h0Fj Finally, the average value Fj(t) is replaced by F(t) ) h/h0. The kinetic equation describing the increase of the solvent (32) Langevin, D.; Rondelez, F. Polymer 1978, 19, 875.

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Figure 3. Static swelling curve of an adsorbed dextran layer with an initial dry thickness of 1657 Å. On the left ordinate the absolute layer thickness (circles) is plotted versus relative humidity, whereas the right ordinate shows the refractive index (triangles) of the polymer-water mixture due to Garnet’s relation.

density in the polymer film can then be expressed as:

D1 1 dF/dt ) 2 1 - exp(-λF-υ) F ∆µred(F) h0

(

)

(13)

4. Results and Discussion 4.1. Equilibrium Swelling Behavior. The swelling of adsorbed layers of dextran and hyaluronic acid with several dry thicknesses was investigated. In Figure 3 the swelling behavior of adsorbed dextran with a dry layer thickness of 1657 Å is shown as an example. On the left ordinate the absolute thickness of the swollen layer is plotted against the relative humidity, whereas the right ordinate shows the corresponding refractive index of the polymer-water mixture corresponding to Garnet’s relation. Typical for the investigated polymers is the very small swelling ratio in the low-humidity regime and the rapid thickness increase at humidities greater than 90%. The swelling behavior turned out to be completely reversible for dextran films as well as for hyaluronic acid films. This was controlled by measuring several swelling and condensation cycles for all investigated samples (data not shown). In Figure 4 (top and bottom) the disjoining pressures as calculated from the relative humidity according to eq 3 are plotted versus the absolute layer thickness h for dextran layers with dry thicknesses of 174.5, 376.2, 939.2, and 1657.6 Å and for hyaluronic acid layers with dry thicknesses of 140.0, 360.0, and 2260.0 Å, respectively. In Figure 5(top and bottom) the disjoining pressures of the layers in Figure 4 (top and bottom) are plotted versus the swelling ratio F ) h/h0. The normalized curves overlap to a large extent, suggesting a universal swelling behavior that is essentially independent of the initial dry layer thickness. However, there are some subtleties in the high disjoining pressure regime: thus the dextran layer with the thinner dry thickness exhibits a trend to a higher disjoining pressure than the thicker dry layers. The opposite holds for the hyaluronic acid layers. We do not have an explanation for this difference in the behavior of the two types of polymers. Moreover, because of the limited thickness resolution of ∼1-2 nm we were not able yet to study these systematic deviations from the universal law in more detail. Furthermore, all plots of the disjoining pressure as a function of swelling ratio exhibit a crossover from a regime with a steep slope to a regime with a smaller slope. Figure

Figure 4. Plot of disjoining pressure p versus absolute film thickness h for dextran layers with dry thicknesses of 174.5 Å, 376.2, 939.2, and 1657.6 Å (top) and hyaluronic acid layers with dry thicknesses of 140.0, 360.0, and 2260.0 Å (bottom).

6 shows the swelling ratios obtained for both polymers at the two regimes. In the high-pressure regime close to F ) 1, no significant difference between hyaluronic acid and dextran can be observed. At p ) 108 Pa, for instance (open and closed circles), the swelling ratio lies in the range of 1.1 to 1.2 for both dextran and hyaluronic acid. However, different swelling ratios are obtained in the lower-pressure regime of about 107 Pa (open and closed squares). The swelling ratio of hyaluronic acid is about F ≈ 2.7, whereas dextran swells only up to about F ) 2.0 for a similar disjoining pressure. Finally, the maximum swelling ratios observed at a relative humidity of about 98% (as shown in Figure 5) show that the maximum water uptake in hyaluronic acid films (maximum swelling ratio ∼6.0) is systematically higher than in dextran films (maximum swelling ratio ∼3.7). In Figure 5 a power law p ∼ F-n was fitted to the disjoining pressure curves of dextran and hyaluronic acid at pressures between 6 × 108 Pa and 6 × 107 Pa. For the swelling behavior of the dextran layers, values for n between 9 and 10 and for the hyaluronic acid layers a value of 9.0 are found, reflecting the strong similarities between the interactions of the involved monosaccharides (glucose in the case of dextran, N-acetyl-D-glycosamine and D-glycuronic acid in the case of hyaluronic acid) on molecular distances. In this high disjoining pressure regime with typical intermolecular distances r comparable with the Bohr radius (∼0.5 Å), the swelling behavior should be mainly dominated by short-range repulsive interaction caused by overlapping molecular orbitals. The hard-core repulsion of the Lennard-Jones potential scales as r-12,

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Figure 5. Double-logarithmic plot of the disjoining pressure p versus swelling ratio F for the same dextran layers (top) and hyaluronic acid layers (bottom) presented in Figure 4 (top and bottom). The drawn lines show fits of the data to the power law p ∼ p-n in the high-pressure regime of hard-core repulsion for dextran and hyaluronic acid, respectively.

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Figure 7. Logarithmic plot of the disjoining pressure versus distance L between neighboring monosaccharides for dextran (top) and hyaluronic acid (bottom) (as shown in Figure 4). L is calculated by using the relation L(F) ) a0(F1/3 - 1) assuming a monomer diameter of a0 ≈ 7.5 Å. Also shown are the fits of the data to the exponentially decaying hydration force given in eq 15.

films step by step and therefore generate a situation in which hydration effects can dominate the swelling behavior. However, the hydrophilic polysaccharides are still in a highly compressed state (p >106 Pa) corresponding to very small intermolecular distances. To discuss this aspect, we introduce a new parameter L for the free distance between two neighboring monosaccharides within the polymer network. In a cubic lattice model, L is given by

L(F) ) a0(F1/3 - 1)

Figure 6. Swelling ratios as obtained for dextran (open squares and circles) and hyaluronic acid (filled squares and circles) with different initial dry thicknesses (as shown in Figure 4) at two different disjoining pressures 107 Pa (squares) and 108 Pa (circles).

which corresponds to a scaling law of p ∝ F-9.2 This agrees fairly well with the exponents obtained from our experimental data in the highly condensed state. In the low-pressure region between 3 × 106 Pa and 4 × 107 Pa the disjoining pressure decays more slowly with the swelling ratio (as shown in Figure 5). Because of the increased mesh size of the polymer network the water molecules begin to fill up the growing “voids” in the polymer

(14)

where a0 is the molecular size of a monosaccharide unit, approximately given by a0 ≈ 7.5 Å.33 Figure 7 shows plots of the disjoining pressure of the hyaluronic acid and dextran layers (as shown in Figure 4) as a function of L. In the lower-pressure regime, corresponding to intermolecular separation distances between 1 and 4 Å, the force decay is essentially exponential. This behavior is consistent with predictions by Rau and Parseglan,34 who provided strong evidence that the interactions between polysaccharides at close separation are dominated by exponentially decaying hydration forces according to (33) Aspinall, G. The Polysaccharides; Academic Press: New York, 1982. (34) Rau, D. C.; Parsegian, V. A. Science 1990, 249, 1278-1281.

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P ) P0 exp(-L/λ0)

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(15)

where λ0 is the decay length, which is typically about 3 Å for separation distances in the range of 10 to 30 Å.34 The internal pressure generated by the hydration forces is of the order 107-109 Pa.34 Fitting eq 15 to the pressure curves of hyaluronic acid and dextran (as shown in Figure 7) yields an internal pressure of about 1.5 × 107 Pa and a decay length of 2.0 and 1.1 Å, respectively. Although the value for a0 had to be estimated, our results agree well with those of Rau and Parsegian.34 This pressure characteristic confirms the interpretation of hydration forces as the dominant interaction within the polysaccharide layers investigated here. However, in the lower-pressure regime (p < 3 × 107 Pa) we observed a considerably lesser swelling of dextran than of hyaluronic acid, resulting in a significantly smaller decay length. Dextran is a slightly branched polymer, exhibiting on average one short branch at every third backbone monomer. It probably exhibits a comblike structure.33 These short branches may lead to enhanced internal friction between neighboring or already entangled polymer backbones, resulting in an impeded swelling and therefore smaller values for λ0.35-37 However, the distinct swelling behavior of dextran is not yet fully understood and our explanation is tentative. In principle, some other forces exhibiting a similar distance dependence exist that are able to influence and modify the observed swelling behavior. However, by trying to fit alternative force models to the measured data we found that none of them is able to explain our results both qualitatively and quantitatively: (A) (Attractive) van der Waals forces are too weak to explain the magnitude of the disjoining pressure (we calculated the Hamaker constants and measured the separation distances). They play only a role in the regime of high disjoining pressure in which the hard-core repulsion is dominant, as discussed in the text. Also, the theoretically predicted power law for attractive van der Waals forces cannot fit our data. (B) Electrostatic interactions turned out to be negligible for dextran because of its charge neutrality. For hyaluronic acid we also expect that the condition of charge neutrality is fulfilled for the following reasons: At the externally applied humidities the water content inside the layer is so low that the counterions are expected to remain condensed to the polysaccharide backbone. Therefore, this theoretical approach is also not able to reproduce both magnitude and functional dependence of the measured disjoining pressure. (C) Polymer-induced forces lead to a power law-like behavior (thus the Flory-Huggins theory would yield an exponent of 2) that may be fitted to the measured data for hyaluronic acid (but not for dextran), exhibiting a power law exponent in the vicinity of 2. This suggests that for this case a polymer theory would in principle be able to describe the observed behavior. On the other hand, we found that the fitting of the Flory-Huggins model to the data does not reach the quality of the fitting of the hydration force model. This is a strong indication that the latter model describes the present physical situation best. 4.2. Nonequilibrium Swelling Behavior. In the dynamic measurements adsorbed layers of dextran with a dry thickness of 1657.6 Å and hyaluronic acid with a dry thickness of 2260.0 Å were investigated using the pro(35) Flory, P. J.; Rehner, J. J. Chem. Phys. 1943, 11, 521-526. (36) Flory, P. J.; Rehner, J. J. Chem. Phys. 1943, 11, 512-520. (37) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953.

Figure 8. Example of an intensity plot I(t) versus time in arbitrary units for a swelling dextran layer. Starting from a constant value of I for t < tstart at low humidity (≈4%), the observed intensity oscillates when the film thickness increases because of interference effects. The number of maximum and minimum values depends on the dry thickness of the layer and the swelling ratio F of the final swollen state. At longer times the curve approaches slowly a constant value due to the saturation of the layer with water.

Figure 9. Swelling ratios F versus time t for hyaluronic acid (filled squares) and dextran (open squares) as evaluated from I(t).

cedure described in the experimental section. In Figure 8 the time dependence of the intensity I(t) is shown for dextran as an example. The sample was initially kept at low humidity (≈4%) to start from a constant value of the intensity at times less than tstart (which is set to zero in the following). The humidity is then suddenly increased to a value of 90%. The observed intensity shows first a sharp drop and then rises again steeply because of interference effects during increasing film thickness. The number of observed maxima and minima of I(t) depends on the difference between the initial dry thickness and the final thickness. At least one pair of maximum and minimum values is necessary as reference intensities. At longer times the intensity approaches slowly a constant value due to the water saturation within the layer. In Figure 9 the layer thicknesses normalized with respect to layer thickness h0 at dry atmosphere (called swelling ratio in the following) are plotted for the adsorbed dextran and hyaluronic acid layers versus time. The time evolution of swelling exhibits some similarities but also apparent differences for dextran and hyaluronic acid despite the fact that in a high-compressed state (F ≈ 1) hyaluronic acid should behave like a neutral polysaccharide with a swelling behavior similar to that of dextran,

Thin Adsorbed Polymer Films

as discussed above. For both polysaccharides a comparable thickness increase can be found up to ∼500 ms, whereas at a later stage the rate of the film expansion is different for the two polymer films: for hyaluronic acid the thickness increases very rapidly during the first 500 to 700 ms and reaches the equilibrium state after 2500-3500 ms. The slope of the curve that corresponds to the swelling velocity F˘ reaches a maximum value of 2.3 s-1 after 600 ms. For dextran the situation is remarkably different: the film shows slower swelling dynamics. The maximum slope of the curve, reached after 500 ms, has a value of 0.75 s-1, corresponding to an approximately threefold smaller swelling velocity than found for hyaluronic acid. The similarities of the swelling curves concerning the short time behavior may be due to a nonvanishing gradient in the glucose monomer density of the dextran layer that is located in the vicinity of the polymer surface and oriented perpendicular to it. This would implicate a locally increased mesh size of the polymer network, which leads to a faster water diffusion and therefore an enhanced swelling velocity. This is expected to hold especially at the beginning of the swelling process where the diffusing solvent molecules mainly probe the surface region of the polymer layer. A possible reason for this increased surface roughness of dextran may be found in the specific sterical properties of the monomer linkage that favors a more bulky structure,33 in contrast to hyaluronic acid, with which no comparable effects are known. The most striking difference appears in the region near the saturation limit. After about 5 s dextran exhibits a second relaxation time t2, leading to a slower creep-like swelling phenomenon that is not observed for hyaluronic acid. The meaning of t2 is not fully understood but our assumption of a glassy relaxation of dextran in the regime of medium swelling ratio leads to a consistent description of the observed behavior: in this regime the special sterical properties of dextran are expected to exhibit an influence on the swelling dynamics. The weak branching of the polymer in combination with a bulky structure of the polymer backbone leads to a state comparable with a gel or a glass. Therefore the penetrating water molecules should cause a decrease of the glass transition temperature Tg because of a breakdown of the physical linkages between the polymers. This happens usually on a much longer time scale, resulting in a second relaxation time t2. In this paper we restrict the discussion of t2 to this qualitative argument, being aware of the large number of parameters that are involved in microscopic theories for relaxation phenomena in glassy polymers.30 For the fast relaxation phenomena occurring at the beginning of swelling, the phenomenological model described in the theory section can be applied successfully to the swelling curves of both dextran and hyaluronic acid. The difference in chemical potential ∆µred, which represents the driving force for the polymer swelling, was measured independently for all relevant swelling ratios. As an example Figure 10 shows ∆µred(F) for hyaluronic acid. To apply eq 13 to our polymer systems we plotted the reduced swelling velocity F˘/∆µred(F), determined from the curves in Figures 9 and 10, versus the swelling ratio. The results and the fits of eq 13 to the reduced swelling velocity are shown in Figure 11 for both dextran (drawn curve) and hyaluronic acid (dashed curve). As the swelling approaches equilibrium, the reduced swelling velocity cannot be determined because ∆µred(F) approaches zero. Therefore only data up to F ) 1.8 are shown. However, in the region of low water content our model fits well to the experimental data for both polymers investigated. Whereas the reduced swelling velocity of hyaluronic acid increases

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Figure 10. Example for the difference in reduced chemical potential ∆µred ) ∆µ/RT plotted versus the equilibrium swelling ratio. ∆µred(F) represents the driving force for polymer swelling and can be measured independently for all relevant swelling ratios.

Figure 11. The reduced swelling velocity F˘/∆µred(F) of dextran (open rectangles) and hyaluronic acid (filled rectangles) corresponding to the swelling curves in Figure 9. The dashed and drawn curves are the fits of eq 13 to the data.

continuously up to about F ) 1.8, the swelling of dextran stops suddenly at F g 1.55. In this region our theoretical approach is no longer suited to the dextran data. Equation 13 contains in general three free parameters that can be fitted to the experimental data, namely the diffusion coefficient D1, the molecular parameter λ, and the exponent ν. D1 is the limit of the H2O diffusivity for F f ∞ and is equal to Deff, the self-diffusion constant of water. At room temperature D1 takes a value of 2.7 × 10-9 m2/s.38 This value was held constant during the fitting procedure and only the values of λ and the exponent ν were varied. However, we may point out that acceptable fits were only achieved if D1 did not deviate by more than ( 30% from the above D1. The above assumptions seem to represent our experimental situation reasonably well. By fitting our data we obtained λ ) 9.18 and ν ) 0.526 for hyaluronic acid and λ ) 10.3 and ν ) 0.479 for dextran. Interestingly, for both polymers a similar ν-value of about 0.5 is obtained. This exponent corresponds to a scaling (38) Hertz, H. G. Prog. Nucl. Magn. Reson. Spectrosc. 1967, 3, 159230.

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thickness of less than 1 nm. In Figure 12 (bottom) we plotted the height profiles along the cross--section indicated by the white rectangle in Figure 12 (top) for relative humidities of 28%, 80%, and 93%, corresponding to disjoining pressures of 1.8 × 108, 3.1 × 107, and 1.0 × 107 Pa. The corresponding swelling ratios F ) h/h0 determined from the average layer thicknesses of the bar region are 1.0, 1.5, and 2.3. It is clearly seen that the swelling ratio for a humidity of 80% agrees well with the static swelling behavior obtained for laterally homogeneous films (as shown in Figure 5, bottom). In contrast, the swelling ratio at the highest humidity of 93% is much smaller because a value of ∼2.7 is expected from the study of the homogeneous films. A closer examination of the thickness profiles shows that the rims of the bar are smeared out and the effect increases with increasing relative humidity, that is, with growing swelling ratios F. By a quantitative evaluation of the material deposited at both rims of the bar during the swelling process it can be seen that the predominant part of the material (∼90%) that is lacking inside the bar can be found within the first 15 µm measured laterally from each rim of the bar. A very simple explanation for this phenomenon is the osmotic pressure inside the polymer network, which not only causes the adsorbed film to expand in z-direction but also to expand laterally in the absence of fixed boundary conditions. The lack of cross-links between the polymers in the spin-coated films allows viscous flow of the polymer solution in the lateral direction. Figure 12. (top) Three-dimensional reconstruction of a hyaluronic acid layer, laterally structured by photolithography, at relative humidity of 28%. The width of the bars is 20 µm and the side length of the holes is 42 µm. The thickness difference is about 7 nm. (bottom) Height profiles along the cross-section marked by the white rectangle in (top) for relative humidities of 28, 80, and 93%. The corresponding swelling ratios F ) h/h0 determined from the average layer thicknesses in the plateau region are 1.0, 1.47, and 2.3.

law ξ ∼ Φ-1/2 for the variation of the mesh size with the polymer volume ratio, which is predicted by several theories9,31 and which was also observed experimentally by diffusion measurements in hyaluronic acid.15,16 As mentioned above, λ can be interpreted in terms of the ratio of the effective solvent molecule diameter to the mesh size in the highly condensed limit: F ) 1. For water molecules (exhibiting a diameter of ∼1.7 Å) this interpretation leads to a mesh size of about 0.2 Å. This very small value for the mesh size (which is equal to the molecular separation distance) is explainable when the externally applied extreme high pressure of about 5 × 108 Pa in the dry state (humidity ∼4%) is taken into account, forcing the polymer network to a highly compressed state, similar to that of glass. Moreover, the relative free volume caused by the mentioned mesh size can be estimated to about 4-7%, a typical order of magnitude expected for systems in a glassy state. 4.3. Local Swelling of Structured Polymer Films. The microellipsometric methods introduced here to investigate equilibrium states and kinetics of swelling polymer layers are not restricted to laterally homogeneous films but offer also the possibility of studying local swelling behavior of structured polymer films. As an example we monitored the static swelling behavior of a photolithographically patterned hyaluronic acid layer that was prepared as described in section 2.2. In Figure 12 (top) a three-dimensional reconstruction of the hyaluronic acid layer is shown. The initial dry thickness of the polymercovered bars is about 7.5 nm and within the square domains the hyaluronic acid layer is removed to a dry

5. Conclusion In this work we presented a method to study the statics and dynamics of swelling of two biologically relevant polysaccharides, hyaluronic acid and dextran. Although both polysaccharides exhibit similar behavior at low water content, remarkable differences in the swelling behavior occur at high degrees of hydration. In particular, a considerably larger swelling ratio was found for hyaluronic acid compared to dextran. It seems that the special structural and chemical properties of both polysaccharides such as charging or branching are not relevant in the high-pressure regime but dominate the swelling behavior immediately after leaving the region of hard-core repulsion. The forces operating within the thin hydrophilic polysaccharide films at high relative humidities are assumed to result from the rearrangement of water molecules, leading to exponentially decaying hydration forces. This assumption is verified by our finding that the internal pressures and decay lengths obtained by our fitting procedure agree well with values obtained by other studies of hydration forces.8,34 In contrast to earlier investigations of several authors about hydration forces,8,34 we could observe the crossover from hard-core repulsion to hydration forces in the highly condensed limit. Concerning the dynamic swelling behavior we successfully applied a simple diffusion model of de Gennes and the GMS approach to describe the swelling kinetics of condensed polymer films. We obtained values less than 1 Å for the effective mesh size ξ0 in the dry limit and we find a power law of ξ ∼ Φ-1/2 during film expansion. Finally we presented first results about the local swelling behavior of structured polymer films studied by imaging microellipsometry. Only equilibrium measurements are shown for this case but local dynamic swelling studies can be well investigated with our experimental setup. In summary, our experimental setup offers the possibility of investigating many aspects of the swelling

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behavior of thin polymer films. However, a complete quantitative description of the phenomena in terms of microscopic theoretical models was found to be difficult. For further investigations, more experimental data and also more detailed theoretical considerations are necessary to give a fully quantitative explanation of the experimental results.

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Acknowledgment. We are grateful to the Wacker Chemitronic GmbH (Burghausen, Germany) for providing thermally oxidized silicon wafers as a gift. This work was supported by the Deutsche Forschungsgemeinschaft (DFG Gz. SA 246/27-1) and the Fond der Chemischen Industrie. LA990658U