Equilibrium Swelling Behavior of Solid Supported Poly (ethylene

Langmuir 2000, 16, 3835-3845

3835

Equilibrium Swelling Behavior of Solid Supported Poly(ethylene glycol) Lipid Monolayers. Effects of Short Chain Lengths Gerald Mathe,† Christian Gege,‡ Klaus R. Neumaier,† Richard R. Schmidt,‡ and Erich Sackmann*,† Physik-Department der Technischen Universita¨ t Mu¨ nchen, Lehrstuhl E22, James-Franck-Strasse, 85748 Garching, Germany and Fakulta¨ t fu¨ r Chemie, Universita¨ t Konstanz, Fach M 726, 78457 Konstanz, Germany Received September 28, 1999. In Final Form: December 22, 1999 In this study phase transitions and thermodynamic properties of monolayers of short poly(ethylene glycol) chains (abbreviated as EG) covalently attached to lipids were determined by analyzing pressurearea isotherms at three different temperatures by using a film balance. The EG chain lengths were varied systematically between N ) 3 and N ) 15 repeating EG units. For the two longest EG chains (N ) 12 and N ) 15) a new synthesis is described. For short chains (N < 9) the monolayer phase transition is determined by the alkyl chain moiety of the headgroup, while for N g 9 the typical behavior of lipopolymers is observed. For the fluid-gel phase transition the entropy and the corresponding latent heat were determined for 3, 6, and 9 EG lipids. In the second part the lipids were transferred to hydrophilic silicon oxide substrates by the Langmuir-Blodgett technique and characterized by their equilibrium swelling behavior under controlled humidity by using ellipsometry. In agreement with the monolayer experiments, we find a “polymer brush”-like behavior already at chain lengths of N g 12 despite the fact that the “statistical” limit N . 1 is hardly fulfilled. For degrees of polymerization of N ) 3 and N ) 6 EG units, relative small swelling ratios F are observed due to a “rigid rod”-like behavior. Between N ) 6 and N ) 9 repeating units an intermediate swelling behavior is found.

1. Introduction During past years poly(ethylene glycol) covalently attached to lipids, so-called lipopolymers (in the following abbreviated as PEG lipids or EG lipids), received considerable attention because of their special physical and chemical properties that make them useful for a broad range of biomedical and technical applications. Pure PEG can be used to precipitate water-soluble proteins1 or to initiate cell-cell fusion. Furthermore, PEG is used as a coating of transplants because of its ability to suppress blood coagulation or protein adsorption.2 It is successfully used to passivate solid surfaces for biosensor applications in order to minimize nonspecific interactions.3 Technical applications include the use of PEG as a surface coating for contact lenses and as a lubricant. Lipid-coupled PEG was investigated extensively over the past few years.4,5 Needham et al.6 investigated liposome membranes with PEG head groups applying X-ray diffraction and micropipet techniques in combination with applied osmotic stress. In this work possible applications of PEG-lipid vesicles for drug delivery were demonstrated. The influence of the ethylene glycol chain length on several biophysical and chemical properties was * Corresponding author. E-mail: [email protected]. † Technischen Universita ¨ t Mu¨nchen. ‡ Universita ¨ t Konstanz. (1) Albertson, P. A. Partition of cell particles and macromolecules; John Wiley & Sons: New York, 1986. (2) Harris, J. M. Poly(ethylene glycol) Chemistry; Plenum Press: New York, 1992. (3) Sackmann, E. Science 1996, 271, 43-48. (4) Kenworthy, A. K.; Simon, S. A.; McIntosh, T. J. Biophys. J. 1995, 68 (5), 1903-1920. (5) Kenworthy, A. K.; Hristova, K.; Needham, D.; McIntosh, T. J. Biophys. J. 1995, 68 (5), 1921-1936. (6) Needham, D.; McIntosh, T. J.; Lasic, D. D. Biochim. Biophys. Acta 1992, 1108, 40-48.

already investigated in various works.7,8 In theoretical studies the ability of grafted EG polymer cushions to avoid nonspecific interaction of proteins with their ligands was shown: At a certain PEG chain length the polymers are able to exert repulsive forces on approaching proteins.2 In contrast, Meyuhas et al. demonstrated that under certain conditions PEG-containing vesicles show mutual attraction.9,10 However, only a few articles focus on quantitative studies of the thermodynamic and elastic properties of PEG lipids as a function of the chain length. Exceptions are the theoretical study of Szleifer et al.11 and the experiments by Hristova et al. and Rex et al.,12,13 where the phase behavior of bilayers built of lipopolymers and their mixtures with ordinary lipids was investigated. In the present work we were mainly concerned with short EG chains covalently attached to a lipid backbone in order to explore their possible use as a “spacer” of well-defined length and elasticity between the lipid backbone at one end and special bioactive ligands at the opposite end of the PEG chain, such as Lewis-X (LeX),14 sialyl-Lewis-X (sLeX)15 or other ganglioside-like receptor molecules. (7) Kuhl, T. L.; Majewski, J.; Wong, J. Y.; Steinberg, S.; Leckband, D. E.; Israelachvili, J. N.; Smith, G. S. Biophys. J. 1998, 75 (11), 23522362. (8) Kuhl, T. L.; Leckband, D. E.; Lasic, D. D.; Israelachvili, J. N. Biophys. J. 1994, 66 (5), 1479-1488. (9) Meyuhas, D.; Nir, S.; Lichtenberg, D. Biophys. J. 1996, 71 (11), 2602-2612. (10) Meyuhas, D.; Lichtenberg, D. Biophys. J. 1996, 71 (11), 26132622. (11) Szleifer, I.; Carignano, M. A. Tethered Polymer Layers; John Wiley & Sons: New York, 1996; Vol. 94, pp 165-260. (12) Hristova, K.; Needham, D. Macromolecules 1995, 28 (4), 9911002. (13) Rex, S.; Zuckermann, M. J.; Lafleur, M.; Silvius, J. R. Biophys. J. 1998, 75 (12), 2900-2914. (14) Geyer, A.; Gege, C.; Schmidt, R. R. Angew. Chem. Int. Ed. 1999, 38 (10), 1466-1468.

10.1021/la991278b CCC: $19.00 © 2000 American Chemical Society Published on Web 03/08/2000

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Langmuir, Vol. 16, No. 8, 2000

From the theoretical point of view several attempts were made to describe the distinct static and dynamic properties of polymers adsorbed or end-grafted to a surface. De Gennes and Alexander16-19 derived simple scaling laws for adsorbed and end-grafted polymers. Depending on the mean density of grafting points on the surface, different regimes (like the “brush-like” and the “mushroom-like”) could be identified. In previous experimental work20 these regimes were successfully verified. However, the applicability of scaling arguments is expected to hold well only for good solvents. For PEG/water solutions this condition is only partially fulfilled due to a grade of hydrophilicity that is not completely comparable to that of polysaccharides such as dextran or hyaluronic acid where an astonishing high water uptake has been observed.21 Therefore, only certain regions of the predictions of the disjoining pressure-thickness relations can be fitted successfully, the remaining regions exhibiting more or less strong deviation from the theoretical prediction. A self-consistent-field (SCF) approach for grafted polymer brushes, developed by Milner et al.,22 overcomes this problem partially by proposing a polymer-solvent interaction close to the θ-point. The quality of this approach was demonstrated in the work of Elender,23 where the static swelling behavior of monolayers of PEG lipopolymers with monomer numbers of N ) 45 and N ) 110 was determined by ellipsometry under controlled relative humidity. In this work we show that both theoretical concepts, the scaling theory of de Gennes and the selfconsistent field approach of Milner et al., are able to fit our experimental data (obtained by point ellipsometry) for monolayers with N ) 12 segments surprisingly well, especially in the regime of lower disjoining pressure (∼107 Pa). Significant deviations from the theoretical predictions are, however, found for smaller degrees of polymerization (N < 9). 2. Materials and Methods 2.1. Substrates and Solvents. Thermally oxidized silicon wafers were a gift of Wacker Chemitronic (Burghausen, Germany). For all experiments freshly distilled ultrapure water (Millipore, Molsheim, France) was used. 2.2. Synthesis of the PEG Lipids. 2.2.1. Materials. Figure 1 gives an outline of the synthetic route to the compounds studied in this work. Procedures for preparation of 1-4 have already been reported:15 benzyl-protected triethylene glycol derivative 1 was synthesized in one step from commercially available triethylene glycol monochlorohydrin. The lipid 2 (N ) 3) was synthesized in high overall yield by the coupling of 1 (2.5 equiv) and 1,2-O-isoproylidene-sn-glycerol, followed by the removal of the isopropylidene group, dialkylation with hexadecyl bromide, and hydrogenation of the benzyl group. Repetitive coupling of 2 with the building block 1 (2.5 equiv) yielded the elongated lipids 3-6 after debenzylation. 2.2.2. Synthesis. Solvents were purified according to the standard procedures. Flash chromatography was performed on (15) Gege, C.; Vogel, J.; Bendas, G.; Rothe, U.; Schmidt, R. R. Chem. Eur. J. 2000, in press. (16) de Gennes, P. G. J. Phys. 1976, 37, 1445-1452. (17) Alexander, S. J. Phys. 1977, 38, 983-987. (18) de Gennes, P. G. Macromolecules 1980, 13, 1069-1075. (19) de Gennes, P. G. Adv. Colloid Interface Sci. 1987, 27, 189-209. (20) Baekmark, T. R.; Elender, G.; Lasic, D. D.; Sackmann, E. Langmuir 1995, 11 (10), 3975-3987. (21) Kjellander, R.; Florin, E. J. Chem. Soc., Faraday Trans. 1 1981, 77, 2053-2077. (22) Milner, S. T.; Witten, T. A.; Cates, M. E. Macromolecules 1988, 21, 2610-2619. (23) Elender, G. Pra¨paration und Charakterisierung ultradu¨nner, hydrophiler Polymerfilme an der Wasser-Luft-Grenzfla¨che und auf Festko¨rperoberfla¨chen. Dissertation, Institut fu¨r Kernphysik und Nukleare Festko¨rperphysik, Lehrstuhl fu¨r Biophysik E22, Technische Universita¨t Mu¨nchen, 1996.

Mathe et al.

Figure 1. Synthesis of ethylene glycol spacered 1,2-di-Ohexadecyl-sn-glycerol derivatives. J. T. Baker silica gel 60 (0.040-0.063 mm) at a pressure of 0.4 bar. Thin-layer chromatography (TLC) was performed on Merck silica gel plastic plates, 60F254; compounds were visualized by treatment with a solution of (NH4)6Mo7O24‚4H2O (20 g) and Ce(SO4)2 (0.4 g) in 10% sulfuric acid (400 mL) and heating at 150 °C. 1H NMR measurements were recorded at 22 °C on a Bruker AC250 Cryospec (using the deuterated solvent as internal standard). 3-O-(35-Benzyloxy-3,6,9,12,15,18,21,24,27,30,33-undecaoxapentatriacosyl)-1,2-di-O-hexadecyl-sn-glycerol (5a). To a solution of 1,2-di-O-hexadecyl-3-O-[26-hydroxy-3,6,9,12,15, 18,21,24-octaoxahexacosyl]-sn-glycerol 4 (457 mg, 488 µmol),15 8-benzyloxy-1-chloro-3,6-dioxaoctane 1 (190 mg, 734 µmol),15 and tetrabutylammonium iodide (10 mg, 27 µmol) in dry tetrahydrofuran (25 mL) was added sodium hydride (46 mg, 1.92 mmol). After stirring for 15 h under reflux, additional 1 (120 mg, 464 µmol) was added. After a further night under reflux the mixture was filtered and washed with tetrahydrofuran (150 mL). Evaporation of the solvent and flash chromatography (eluent: toluene/acetone 3:1) furnished the title compound (416 mg, 72%) as a white solid. TLC (toluene/acetone 2:1) Rf 0.39. 1H NMR (CDCl3, 250 MHz): δ 0.88 (t, 6H; 2 CH3), 1.25 (bs, 52H; 26 CH2), 1.51-1.57 (m, 4H; 2 OCH2CH2), 3.36-3.68 (m, 57H; 57 HCO), 4.57 (s, 2H; CH2Ph), 7.26-7.34 (m, 5H; C6H5). Anal. Found: C, 67.44; H, 10.55. Calcd for C66H126O15‚H2O (1177.7): C, 67.31; H, 10.70. 1,2-Di-O-hexadecyl-3-O-(35-hydroxy-3,6,9,12,15,18, 21,24,27,30,33-undecaoxapentatriacosyl)-sn-glycerol (5). Compound 5a (345 mg, 293 µmol) was dissolved in tetrahydrofuran (60 mL), and palladium on charcoal (40 mg, 10% Pd) was added. The mixture was stirred vigorously under a hydrogen atmosphere at normal pressure. After 16 h the catalyst was filtered off and washed with tetrahydrofuran. Evaporation of the solvent and flash chromatography (eluent: toluene/acetone 1:1 to 2:3) furnished the title compound (298 mg, 95%) as a white solid. TLC (toluene/acetone 2:3) Rf 0.51. 1H NMR (CDCl3, 250 MHz): δ 0.88 (t, 6H; 2 CH3), 1.25 (bs, 52H; 26 CH2), 1.51-1.57 (m, 4H; 2 OCH2CH2), 3.40-3.75 (m, 57H; 57 HCO). Anal. Found: C, 65.85; H, 11.31. Calcd for C59H120O15‚1/4H2O (1074.1): C, 65.98; H, 11.31. 3-O-(44-Benzyloxy-3,6,9,12,15,18,21,24,27,30,33,36,39,42tetradecaoxatetratetracosyl)-1,2-di-O-hexadecyl-sn-glycerol (6a). To a solution of 5 (152 mg, 142 µmol), 1 (55 mg, 213 µmol),15 and tetrabutylammonium iodide (10 mg, 27 µmol) in dry

Behavior of PEG Lipid Monolayers

Langmuir, Vol. 16, No. 8, 2000 3837

tetrahydrofuran (15 mL) was added sodium hydride (14 mg, 0.58 mmol). After stirring for 15 h under reflux, additional 1 (55 mg, 213 µmol) was added. After a further night under reflux the mixture was filtered and washed with tetrahydrofuran (150 mL). Evaporation of the solvent and flash chromatography (eluent: toluene/acetone 3:2 to 1:1) furnished the title compound (121 mg, 65%) as a white solid. TLC (toluene/acetone 1:1) Rf 0.55. 1H NMR (CDCl3, 250 MHz): δ 0.88 (t, 6H; 2 CH3), 1.25 (bs, 52H; 26 CH2), 1.51-1.57 (m, 4H; 2 OCH2CH2), 3.38-3.69 (m, 69H; 69 HCO), 4.57 (s, 2H; CH2Ph), 7.26-7.35 (m, 5H; C6H5). Anal. Found: C, 66.18; H, 10.63. Calcd for C72H138O18‚H2O (1309.9): C, 66.02; H, 10.77. 1,2-Di-O-hexadecyl-3-O-(44-hydroxy-3,6,9,12,15,18,21, 24,27,30,33,36,39,42-tetradecaoxatetratetracosyl)-snglycerol (6). Compound 6a (103 mg, 78.6 µmol) was dissolved in tetrahydrofuran (20 mL), and palladium on charcoal (10 mg, 10% Pd) was added. The mixture was stirred vigorously under a hydrogen atmosphere at normal pressure. After 16 h the catalyst was filtered off and washed with tetrahydrofuran. Evaporation of the solvent and flash chromatography (eluent: CHCl3/methanol 50:1 to 25:1) furnished the title compound (82 mg, 86%) as a white solid. TLC (CHCl3/methanol 15:1) Rf 0.49. 1H NMR (CDCl3, 250 MHz): δ 0.88 (t, 6H; 2 CH3), 1.25 (bs, 52H; 26 CH2), 1.511.57 (m, 4H; 2 OCH2CH2), 3.40-3.71 (m, 69H; 69 HCO). Anal. Found: C, 64.48; H, 11.07. Calcd for C65H132O18‚1/2H2O (1210.8): C, 64.43; H, 10.97. 2.3. Technical Setup and Data Evaluation. 2.3.1. Film Balance Experiments. Langmuir isotherms were determined with a film balance designed in our laboratory. A conventional Wilhelmy system was used for lateral pressure measurement. The whole trough was temperature-controlled with a commercially available heating/cooling system. Typical errors in temperature measurement were in the range of (0.5 °C. 2.3.2. Static Swelling Measurements. Measurements of the equilibrium thickness of lipopolymer monolayers transferred onto hydrophilic thermally oxidized silicon wafers as a function of the relative humidity of the air were performed with a conventional ellipsometer which was attached to a film balance (Plasmos GmbH Prozesstechnik, Mu¨nchen, Germany) equipped with a humidity chamber allowing control of the relative humidity between 4% and 98% (cf. Figure 2). Dry EG lipids were dissolved in chloroform and spread on the film balance attached to the ellipsometer while a vertically mounted Si/SiO2 substrate stays dipped into the subphase. After compressing the monolayer to a well-defined pressure value (25 and 30 mN/m in this work), the substrate was pulled out of the subphase with a velocity of ∼0.1 mm/s (Langmuir-Blodgett transfer). The so prepared supported lipid monolayer was then investigated by ellipsometry at constant wavelength (λ ) 632.8 nm) and fixed angle of incidence (70°). In principle the adsorbed monolayer consists of two layers: the PEG layer and the layer of the alkyl chains. Unfortunately it is for practical reasons impossible to distinguish optically between these two ultrathin layers. Therefore only the thickness of the whole monolayer was measured. To get the thickness of the PEG layer, values for the thickness of the alkyl chain layer (∼1.8 nm) and for the dedicated refractive index (n ) 1.50) had to be assumed. Values of the thickness of the PEG layers were 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 ratios of the complex incident and evanescent electric fields; Rp ) Ep,evan/Ep,incid and Rs ) Es,evan/ Es,incid. The thickness of the PEG layer was determined by a first measurement in the fully nonhydrated state (i.e., at humidities below ∼30%). To do this, a refractive index of n ) 1.47 of dry PEG was used.23 The thickness was then evaluated by computerassisted analysis of Rp/Rs in terms of the Fresnel equations of reflection and transmission for light of both s- and p-polarization.24 (24) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and polarized light; North-Holland: Amsterdam, 1977.

Figure 2. Schematic description of the experimental setup used for the swelling experiments of solid supported lipid monolayers. The commercial rotating analyzer ellipsometer is combined with a humidity chamber and a conventional film balance. The humidity inside the chamber can be 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 is adjustable between 4% and 98%. The film lift is used for transferring a lipid monolayer on vertically mounted substrates. 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 4% and 98%. The humidity control device and the hygrometer used were described by Elender et al.25 Between two subsequent equilibrium thickness measurements, the film was allowed to equilibrate for at least 10 min. For the thickness evaluation of the swollen PEG film containing increasing amounts of water, the refractive index was calculated by applying the Garnett equation26,27 which relates the refractive index nF of a homogeneous solution to the volume fraction Φ of the solute:

x

nF ) nM

1+

(

2

n0

3Φ + 2nM2

n02 - nM2

)

(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 PEG layer thickness d by Φ ) d0/d, where d0 is the film thickness measured at very low relative humidity (≈4%). As described by Elender et al.,23,28 the film thickness can be calculated self-consistently by starting from the refractive index of the dry layer and by application of Garnett’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 the film thickness d: p ) -∂G/∂d;29 G is the free energy of the film which is a function of the thickness d and the water volume fraction within the film. (25) Elender, G.; Sackmann, E. J. Phys. II Fr. 1994, 4 (3), 455-479. (26) Garnett, J. C. M. Philos. Trans., A 1904, 203, 385-420. (27) Garnett, J. C. M. Philos. Trans., A 1906, 205, 237-288. (28) Elender, G.; Ku¨hner, M.; Sackmann, E. Biosens. Bioelectron. 1996, 11 (6/7), 565-577. (29) Landau, L. D.; Lifschitz, E. M. Lehrbuch der theoretischen Physik, Band V, Statistische Physik Teil 1; Berlin, Akademie-Verlag: 1987.

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Mathe et al.

The disjoining pressure can be expressed by use of van’t Hoffs law:29

Dmushroom ≈ aN3/5

( )

The interaction energy of the polymers, compressed to a thickness D < Dmushroom, can be written as

P)-

RT ln(X) Vm

(3)

where Vm is the molar volume of water, T is the temperature, R is the molar gas constant, and X is the relative humidity inside the chamber: X is equal to the ratio of actual 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. Combining the determined film thickness as a function of the relative humidity and disjoining pressure finally yields the disjoining pressure-thickness relations.

3. Theoretical Concepts 3.1. General. For understanding of the measured swelling curves, two different physical concepts can be considered. The first (also from the historical point of view) is the scaling theory by Alexander and de Gennes;16-19 the second concept is based on a mean field approach.22 In contrast to the experimental situation where mirror symmetry with respect to the sample surface is not given, both theoretical concepts assume a planar symmetric situation, with the polymers confined between two parallel plates. Nevertheless, all the equations discussed in the following section can be applied to the experimental data by taking into account that all the theoretically predicted expressions have to be multiplied by a factor of the order of unity. 3.2. Scaling Concepts. For terminally fixed polymers a general expression for the free energy F of a surfacegrafted polymer was given by de Gennes, Alexander, and Daoud:16,17,30

F ≈ kTN

() a D

5/3

-δ

( ) ( ) ( )( )

Na Na3 5/4 +δ + D σD D 2 ξ -1/3 -1 N + kT ln σ (4) kT a a

N is the number of monomer segments with length a, D is the thickness of the polymer layer, δ is the surface adsorption energy per monomer in units of kT, σ is the mean area per polymer, and ξ is the blob diameter in a polymer melt.18 Inside a blob single polymer chains do not interact with neighboring polymers and therefore behave like ideal chains. The first term describes the energy needed to confine a polymer molecule, assumed to behave as a self-avoiding chain in a surface layer of thickness D. The second term stands for the adsorption energy of a chain on the surface, and the third term stands for the repulsion between single polymer chains, which is important in the regime of overlapping chains. The fourth term is necessary to describe elongated chains occurring in the so-called “brush” regime at high grafting densities. The last term represents the translational entropy of the polymers. Due to the solid support of the lipopolymers and our assumption that the alkyl chains are completely immobilized on the surface of the substrate, it can be neglected in our case. On the basis of the general expression (4) several characteristic regimes can be determined: At grafting distances dp comparable to the Flory radius RF ≈ aN3/5 (“mushroom” regime), the equilibrium thickness D is also comparable to the Flory radius, giving (30) Daoud, M.; de Gennes, P. G. J. Phys. 1977, 38, 85-93.

Vmushroom ≈ -

(5)

(

)

3 kT Dmushroom 5d 2 D p

5/3

(6)

and the pressure caused by the compressed polymers reads as

Pmushroom ≈

kT(Dmushroom)5/3 1 D d2

8/3

()

p

(7)

In the regime of grafting distances dp < RF, the polymers begin to elongate their contour perpendicular to the grafting surface. This leads to a “brush”-like conformation of the polymers, consisting of linear chains of “blobs” with diameter ξ. The equilibrium thickness Dbrush can then be written as Dbrush ≈ aNAp-1/3, Ap-1 :) dp-2. The interaction energy of the polymers, compressed to a thickness D < Dbrush, can be written as

Vbrush ≈

[( )

4 Dbrush kT Dbrush 3 5 D dp

5/4

( )]

4 D 7 Dbrush

+

7/4

(8)

and the resulting pressure takes the form

Pbrush ≈

[( ) ( ) ]

kT Dbrush D dp3

9/4

-

D

3/4

(9)

Dbrush

3.3. Self-Consistent-Field Theory for Polymer Brushes. The basis of the SCF approach are terminally fixed linear chains exhibiting a high grafting density and therefore sufficient high polymer densities. In contrast to the scaling approach, for the SCF theory the quality of the solvent should not be too good, as it is approximately the case for the PEG/water mixtures investigated in this work. Milner et al.22 found a parabolic density profile for scf given the monomers with a equilibrium thickness Dbrush by

Dscf brush ≈

( ) 12 π2

1/3

(σw)1/3N

(10)

where σ ) Ap-1 ) dp-2 is the grafting density, w the “excluded volume”, and N the degree of polymerization. scf the expression for Compressed to a thickness D < Dbrush the interaction energy per unit area reads

Vscf brush ≈

()

[

( ) ( )]

Dscf 1 D π2 brush 2/3 + N(σw) 12 2D 2 Dscf brush

2

-

1 D 10 Dscf brush

5

(11)

and the resulting pressure is given by

Pscf brush ≈

()

π2 1 N(σw)2/3 scf 12 D

brush

[ ( ) scf 1 Dbrush 2 D

2

+

D Dscf brush

-

( )]

1 D 4 2 Dscf brush (12)

All the analytical formulas described in this section can be in principle applied to the experimental data, only


taking into account that all the theoretically predicted expressions have to be multiplied by a factor of order 1. 4. Results and Discussion The samples were investigated by two experimental approaches: Langmuir film balance studies of monolayers at the air-water interface at three different temperatures and point ellipsometry of monolayers on solid supports3 at room temperature under controlled humidity. 4.1. Langmuir Isotherms. PEG functionalized lipids with different EG chain lengths (3, 6, 9, 12, and 15 EG units) were dissolved in ultrapure chloroform at a concentration of 2 × 10-3 mol/L and spread on a waterfilled and temperature-controlled film balance. Then pressure-area isotherms were measured at 10, 20, and 30 °C both during compression and expansion to avoid misinterpretation of the data due to hysteresis effects. The Langmuir isotherms of the N ) 3 lipid are mainly dominated by the C16 chains due to the shortness and thus rod-like nature of the head group. The head group thus seems to act as a prolongation of the alkyl chains (Figure 3a). The position of the main transition pressure pK is marked by arrows. At T > 20 °C one observes a transition of the monolayer from an expanded fluid phase to a condensed phase at a transition pressure pK which increases with temperature. At 10 °C the expanded fluid phase does not exhibit a clearly defined fluid phase. It thus corresponds to a condensation from an expanded gaslike state (or two-dimensional vapor state) to a condensed (solid-like) state which is well-known from studies of ordinary phospholipid monolayers.31 For N ) 6 lipids a qualitatively similar shape of the curves is observed (Figure 3b). The isotherms exhibit a single plateau regime, with the transition pressures increasing with temperature. The transition pressure is systematically higher than for the lipid with N ) 3: even at 10 °C a plateau with an astonishing high onset pressure (p ∼ 10.5 mN/m) is found. This shows that the steric interaction between neighboring lipid molecules caused by the repulsion of the head groups of the lipid is already visible. However, the qualitative shape of the phase coexistence region is again mainly dominated by the alkyl chains and not by typical “polymer” effects of the head groups, as found for longer head groups. Increasing the EG spacer length to values N g 9 results in both qualitative and quantitative different phase behavior (Figures 3c-e). The rather flat plateau regime, clearly visible for all PEG lipids with N < 9 at all applied temperatures, becomes more and more broadened, and a pronounced shoulder appears near the transition to the condensed phase, indicated by an arrow in the isotherm for N ) 9 (Figure 3c). The slope increases very strongly at the transition to the solid state. The shoulder found at N ) 9 becomes an additional transition for head groups with N ) 12. The onset pressure pK increases with increasing chain length and temperature. The increased slope of the plateau at the transition pressure pK can be attributed to the growing influence of the grafted polymers on the phase behavior. These changes can be seen by comparing the isotherms for the N ) 6 and the N ) 12 lipids. In the latter case the transition can be divided in an alkyl chain dominated regime, where only a little influence of the PEG headgroups on the isotherms is observed, and a regime dominated by the steric and entropic repulsion of polymers, as discussed by Baekmark et al. and Elender et al.20,23 In the case of an increasing (31) Albrecht, O.; Gruler, H.; Sackmann, E. J. Phys. 1978, 39, 301313.

Langmuir, Vol. 16, No. 8, 2000 3839

size of the PEG head group, the fluid-gel transition of the alkyl chains for a given temperature is shifted to higher transition pressures. The increased pK with N is thus a consequence of the decrease in hydrocarbon chain packing density, suggesting that the PEG head group repulsion controls the state of the alkyl chains. Despite the fact that the chain lengths investigated here are very short, the Langmuir isotherms for N g 9 exhibit, at least qualitatively, a phase behavior which is typical for lipopolymers. We thus conclude that for the N ) 12 and N ) 15 lipids at 10 °C even the often discussed “mushroom-brush” transition20 is indicated as a small plateau at pressures of p ) 24.0 mN/m (molecular area 0.55 nm2) and p ) 28.5 mN/m (0.53 nm2) as can be seen in Figure 3d,e. The astonishing, “polymer-like” behavior of such rather short PEG head groups can be also observed in the swelling behavior of supported monolayer, as it will be discussed in the following section. Using the Clausius-Clapeyron equation

dpK q s ) ) dT T(A2 - A1) A2 - A1

(13)

important thermodynamic quantities such as the molar latent heat q and the molar transition entropy s :) q/T can be determined from the variation of the transition pressure with the absolute temperature T, dpK/dT. Only estimates of the above parameters are provided: the difference between the molar areas of the lipid monolayer at the onset and end point of the condensation transition, A2 - A1, is not well-defined (Figure 4a). However, only lipids with polymer chain lengths of N ) 3, 6, and 9 exhibit a clearly detectable plateau regime, necessary for the successful application of the Clausius-Clapeyron equation. For EG chain lengths N ) 12 and N ) 15 no plateau regime is observable. Figure 4b shows the entropy s of the fluid-gel phase transition as a function of temperature for lipids functionalized with 3, 6, and 9 EG units, and in Figure 4c the corresponding molar latent heat q is plotted for the same molecules. In Figure 4b,c the following general tendency can be observed: for N ) 3, q and s change barely with temperature and values of q ≈ 32 kJ/mol and s ≈ 115 J/mol‚K are found. Both the absolute values of q and s vary with chain length. This can be explained qualitatively in terms of the growing contribution of the PEG head groups on the entropy and the heat of transition. Due to the increase of packing density at the transition of the hydrocarbon chains, the covalently coupled PEG chains are forced into a more “brush-like” conformation. This “stretching” of the chains to a more elongated configuration leads to a reduction of the possible chain conformations and therefore to a significant change in entropy and latent heat at the transition. The rapidly growing number of chain configurations with chain length and the monotonically increasing entropic elasticity of the chains with growing temperature can explain the increase in q, at least for temperatures smaller than 30 °C. For N ) 3, q and s are dominated by contribution of hydrocarbon chains, whereas at N ) 6 and 9 half the contribution to s and q comes from PEG head groups. It is also noticeable that the strong decrease of s and q with temperature for N ) 9 indicates that a critical point is reached.31 This can be understood in terms of the well-known van der Waals gas: near the critical point the fluid-gas coexistence line can be described by a parabola whose vertex coincides with the critical point. This means that at increasing temperature the area difference used in the Clausius-

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Figure 3. (a) p-A isotherms of the N ) 3 lipid at 10, 20, and 30 °C. For T ) 20 °C and T ) 30 °C coexistence plateaus at 3 and 7 mN/m due to the increased thermal motion of the EG groups and the alkyl chains can be observed. (b) p-A isotherms of the N ) 6 lipid at 10, 20, and 30 °C. The onset of the plateau regime at pressures of 10, 15, and 20 mN/m depending on the temperature indicates the increasing influence of the EG units on the phase behavior. (c) p-A isotherms of the N ) 9 lipid at 10, 20, and 30 °C. The observed behavior is similar to that of part b. The high onset of the plateau regime is nearly fully dominated by the EG units; the influence of the lipid backbone becomes more and more negligible. The indication of the main transition of the lipid is marked by an arrow (“shoulder”). (d) p-A isotherms of the N ) 12 lipid at 10, 20, and 30 °C. The observed behavior is similar to that of part c. The isotherm for T ) 10 °C shows a plateau-like region at a pressure of 24 mN/m due to the main transition of the lipid. (e) p-A isotherms of the N ) 15 lipid at 10, 20, and 30 °C. The observed behavior is similar to that of part d.

Clapeyron equation is rapidly vanishing. To ensure a finite value for dpK/dT, the transition entropy and therefore also the latent heat must tend to zero.31 4.2. Evaluation of Swelling Behavior by Measurements of Disjoining Pressure. Swelling curves were

taken for all discussed PEG lipids as described previously.32 The lipids were transferred at a temperature of (32) Albersdo¨rfer, A.; Elender, G.; Mathe, G.; Neumaier, K. R.; Paduschek, P. Appl. Phys. Lett. 1998, 72 (23), 2930-2932.


Figure 4. (a) Derivative dp/dT as a function of EG chain length for T ) 10, 20, and 30 °C. All curves (except for T ) 30 °C, where no value for N ) 9 is available) exhibit a significant increase of dp/dT between N ) 6 and N ) 9. (b) Molar transition entropy as a function of T for lipids with N ) 3, 6, and 9 EG units. Discussion: see text. (c) Molar latent heat of the phase transition as a function of T for lipids with N ) 3, 6, and 9 EG units. Discussion: see text.

20 °C to the solid substrates at a relative high lateral pressure of 30 mN/m (and, in the case of N ) 9, also at 25 mN/m), corresponding to grafting densities between 2.86 nm-2 (for the lipid with N ) 3 at 30 mN/m) and 1.25 nm-2 (for the lipid with N ) 9 at 25 mN/m). The relative humidity was varied between 30% and about 98%,

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corresponding to a change of the disjoining pressures between 1.69 × 109 and 2.83 × 106 Pa. It is important to note that the grafting densities studied correspond to the region of the condensed state of the pressure-area isotherms. For the N ) 9 lipid a measurement also was performed at 25 mN/m which corresponds to a packing density of 1.82 nm-2. At p > pK the alkyl chains orient nearly perpendicular to the surface and the covalently coupled PEG chains are in a rather strongly compressed state, similar to the “brush” regime.20 Although it would be also interesting to study the swelling properties of supported PEG lipids systematically as a function of transfer pressure (and therefore of grafting density), such experiments could not be performed since all swelling experiments made at pressures below the plateau regime yielded only poorly interpretable ellipsometric data. This is attributed to the orientational disorder (random tilt) of both the PEG chains and the alkyl chains at the surface, especially at lower grafting densities. An exception is the monolayer N ) 9 transferred at the lower pressure (25 mN/m) which corresponds to the onset of the condensation transition. Figure 5a shows all measured swelling curves. The disjoining pressure is plotted against the absolute thickness of the swollen PEG layer. In Figure 5b the thicknesses were normalized by the thickness of the PEG layer in the “dry” state, which corresponds to a humidity of about 30%. The results are presented as a log-log plot to expose possible power law dependencies of the disjoining pressure vs thickness relations. Figure 5b allows the comparison of the distinct swelling behavior shown by the different PEG lipids. For N ) 3 the swelling curve exhibits a straight line at high pressures (6 × 107-2 × 108 Pa) while the slope decreases continuously at disjoining pressures around 107 Pa. The maximum swelling ratio F ≡ d/d0 is reached at a pressure of ∼6 × 106 Pa and assumes a value F ≈ 1.4. The disjoining pressure vs F plot shows a break at 6 × 107 Pa. The very short PEG head group does not play the major role and the thickness change of the EG trimer during swelling is mainly determined by the hydrocarbon chains. The increase in thickness with increasing water vapor pressure is due to the decreased tilt with increasing water content. The reason for this behavior may be found in our assumption that the short EG trimers are randomly tilted at the humidity of ∼30% during Langmuir-Blodgett transfer due to the high corresponding disjoining pressure. Due to the limited flexibility of the combined PEG-alkyl chains, this random disorientation is partially transferred to the lipid backbone leading also to some tilt. At decreasing disjoining pressure, however, the PEG trimers become more and more able to orient themselves perpendicular to the substrate surface, leading also to a decreased tilt of the alkyl chains of the lipid backbones. At p > 107 Pa for N ) 6 a behavior similar to that at N ) 3 can be observed; again an abrupt change in slope can be seen at 4 × 107 Pa. In the pressure region below, however, the curve exhibits a slightly higher swelling ratio as a function of disjoining pressure, but ends at a comparable swelling ration of ∼1.4. For chain lengths N g 9 the swelling behavior changes drastically. A power law behavior is observed over an extended range of water vapor pressure. The slope of the curves (i.e., the exponent of the power law p ∝ Fn ) (d/d0)n) decreases systematically with chain length, indicating an increasing ability for water uptake. Besides this qualitative analysis of the measured data, it is also interesting and of fundamental importance to analyze the results in terms of the theoretical models to

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extract numerical data, for instance the diameters of the “mushroom” or “brush” states of the grafted polymers. However, the problem arises that all analytical approaches, as summarized in section 3, assume very large degrees of polymerization N enabling the application of basic statistical mechanical principles. In our case, where N varies between 3 and 15, this condition is only poorly fulfilled. In principle, an alternative approach is provided by a number of numerical techniques, ranging from ab initio molecular dynamics simulation (assuming certain potentials for inter- and intramolecular interactions) to Monte Carlo calculations,13,33 where the average chain conformation with minimal free energy is determined. However,

these numerical techniques require sophisticated algorithms and much computing time to yield precise results. This is a consequence of the complex interplay between elastic and entropic forces between the monomers in the same chain and the steric interactions between neighboring grafted chains.11,34 We therefore decided to fit only the analytical approaches described in section 3, being aware of the fact that the basic condition N . 1 is not or only badly fulfilled. For the two longest PEG chains N ) 15 and N ) 12 (Figure 6a,b) the static swelling behavior can be explained with the models discussed in the theory section. The measured data can be reasonably well described in terms of the two discussed “brush” theories mentioned above except in the region of low humidity where significant deviations from the theoretical predictions are observed. In the disjoining pressure region between 5 × 107 and 1.8 × 108 Pa a power law like behavior can be observed, similar to the results of Elender et al.23 It is worth noting that no significant difference between the quality of the fits for the lipids with N ) 12 and the lipids with macromolecular head groups (N ) 45 and N ) 110) could be observed.23 In Figure 6c the swelling curves for the case N ) 9 deposited at two different transfer pressures (25 and 30 mN/m) are compared with the theoretical predictions. It is noticeable that already the relative short chain with N ) 9 exhibits a “polymer”-like behavior at swelling ratios bigger than 1.8. Comparison of the curves taken at 25 and 30 mN/m shows an astonishing weak dependence on the grafting density: The swelling curve is only slightly higher scf , for lower grafting densities. The fit parameters Dbrush st st Dbrush, Dmushroom exhibit similar tendency: at the lower grafting density (dF = 9 Å) they are 29, 25, and 23 Å, respectively, whereas for denser lateral packings (dF = 7.4 Å), values of 25, 22, and 26 Å are obtained. It is evident that both “brush” models fit to the experimental data over a wider range of swelling ratios than the “mushroom” model. In Figure 6d the experimental data for N ) 6 and the corresponding to theoretical fit curves are shown. Similar to the case N ) 3 (see Figure 6e), only the region of very small swelling ratios F can be approximately fitted by the different theoretical curves. At higher humidities both the SCF approach and the scaling theory for brushes fail again completely. The observable saturation (at swelling ratios > 1.25, see Figure 5b) occurs at a lower disjoining pressure than theoretically predicted. These subtle effects are not fully understood and are not considered in the existing theories. However, the fitted characteristic scf st ≈ 12.7 Å and Dbrush ≈ 12.1 Å obtained parameters Dbrush by the two scaling approaches correspond quite well with the measured thickness of the PEG layer at lower disjoining pressures, i.e., in the fully swollen state. The “mushroom” model fails again completely. Figure 6e shows the measured data for N ) 3 together with the fits of the different theoretical models. It is obvious that the fit of scaling approach for “mushrooms” (small dashes) completely fails, giving a wrong value for the slope. For “brushes” the scaling approach fits to the data reasonably well at smaller swelling ratios (Figure 6e) but fails at higher values of F where too small values for the disjoining pressure are predicted (cf. big dashes). The SCF approach for “brushes” describes the experimental curve

(33) Laradji, M.; Guo, H.; Zuckermann, M. J. Phys. Rev. E 1994, 49 (4), 3199-3206.

(34) Israelachvili, J. N. Intermolecular and surface forces; London, Academic Press: 1992.

Figure 5. (a) Absolute value of the disjoining pressure as a function of the thickness of the EG layer for different EG chain lengths N. The disjoining pressure is calculated by using the formula P ) -1.4 × 108 ln(X) N/m2, where X stands for the relative humidity. The thickness of the PEG layer confined between solid substrate and alkyl chains was determined by point ellipsometry using the empirical Garnett relation between relative water content of the polymer and refractive index of the polymer-water mixture. (b) Absolute value of the disjoining pressure as a function of the relative EG layer thickness, i.e. the absolute thickness normalized to the thickness of the layer in the completely dried state. The legend shows the length of the EG chain, the transfer pressure, and the corresponding molecular area.


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Figure 6. (a) Measured data for the N ) 15 (a) and N ) 12 (b) lipid at 30 mN/m transfer pressure and application of the theoretical models presented in section 3. Solid lines, SCF model for “brushes”; big dashes, scaling approach for “brushes”; small dashes, scaling approach for “mushrooms”. In general, a more polymer-like behavior can be observed in the region of low disjoining pressure. Especially the measured data for N ) 15 can be fitted reasonably well by the “brush” models of the SCF and scaling approach. However, the “steeper” regime at higher disjoining pressure cannot be explained in terms of the discussed polymer theories. (c) Measured data for the N ) 9 lipid at 25 mN/m, i.e., slightly below the plateau-like region (open triangles), and at 30 mN/m, i.e., above the coexistence region. Both the SCF model for “brushes” and the scaling approach for “brushes” fit to the data even at lower disjoining pressure reasonably well but not at higher pressures, where a different regime seems to appear (see text). In general, no big influence of the transfer pressure on the swelling behavior can be observed despite the significantly different grafting density. (d) Experimentally determined swelling curve (squares) for the N ) 6 lipid at a transfer pressure of 30 mN/m. Both the SCF “brush” model and the scaling approach for “brushes” exhibit some similarities with the measured data in the high-pressure regime. The st “mushroom” model clearly fails, giving a too high value for Dmushroom . (e) Experimentally determined swelling curve (squares) for the N ) 3 lipid at 30 mN/m. Similar to the N ) 6 lipid, both SCF “brush” model and the scaling approach for “brushes” exhibit some similarities with the measured data in the high-pressure regime. The “mushroom” model clearly fails, giving a too high value st for Dmushroom .

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5. Conclusion

scf st st Figure 7. Scaling parameters Dbrush , Dbrush , and Dmushroom determined by fitting eqs 7, 9, and 12 to the experimentally determined curves as a function of EG spacer length N. scf st Especially for Dbrush and Dbrush a monotonic increase can be observed.

over the largest distance but fails again at high swelling ratios. Therefore, no interpretation of the parameters scf st st Dbrush , Dbrush , and Dmushroom are given. However, we want to point out that, despite the successful formal application of the described theoretical polymer models (especially for the longer chains N ) 9, 12, and 15), the concrete quantitative value of the scf st st , Dbrush , and Dmushroom take determined parameters Dbrush their specific meaning only in the corresponding regimes, st takes an interpretwhich simply means that Dmushroom able value only if the polymer is in a “mushroom”-like scf st or Dbrush only make conformation and values for Dbrush sense for “brush”-like chain conformations. It is evident from the way of preparation of the solid-supported lipid monolayers (high transfer pressure, short PEG head groups) that the EG oligomers have a more “brush”-like st were only character. Therefore, the values for Dmushroom taken into account to complete the analysis of the disjoining pressure-thickness relations. scf , Figure 7 shows molecular size parameters Dbrush st and Dmushroom obtained by our analysis of the theoretical disjoining pressure vs thickness plots as a scf st (N) and Dbrush (N) a function of chain length. For Dbrush monotonic increase with the chain length N is observed. scf st Dbrush (N) lies systematically above Dbrush (N), but the qualitative shape is quite similar. It is worth noting that the slopes of both plots exhibit a break between N ) 6 and N ) 9 and the slope is smaller above N ) 9. This may indicate a transition from a “rigid-rod”-like behavior of the EG chains to a more “polymer”-like behavior, but this st (N) interpretation remains rather tentative. For Dmushroom scf st a shape similar to that of Dbrush(N) and Dbrush(N) can be observed. An exception is the value for N ) 12, where an st (N) was found, astonishing small value for Dmushroom which cannot be explained rigorously in terms of the theories of grafted polymers used in this work. However, as noted above, the mushroom model is in general only a bad approximation for the lipids with small degrees of scf (N) and polymerization. Therefore, the parameters Dbrush st Dbrush(N) reflect the experimentally observed swelling behavior more appropriately. st Dbrush ,

In this work lipids with poly(ethylene glycol) headgroups of different lengths N ) 3, 6, 9, 12, and 15 were studied by two different experimental techniques. The phase transitions were studied by the film balance technique, and the increase of thickness of solid-supported lipid monolayers at increasing humidity was measured by ellipsometry. The Langmuir isotherms demonstrate clearly the systematic change of the thermodynamic behavior with increasing chain length. For small N (3, ..., 6) a phase behavior typical for lipids with fully saturated alkyl chains and small head groups was measured. The phase diagram exhibits a broad transition from fluid expanded to the condensed (gel-like) state. Typical for phospholipids,31 the plateau pressure increases systematically with temperature corresponding to an exothermic phase transition determined by the alkyl chains. For longer PEG head groups (N ) 9, ..., 15) the phase behavior becomes more and more dominated by interacting chains of the head groups resulting first in an increase of the transition pressure. On the other hand, a shoulder arises near the condensed state. For the shorter PEG lipids (N ) 3, ..., 9), where phase coexistence regions could be identified, the molar transition entropy s and the corresponding molar latent heat q were determined by applying the well-known Clausius-Clapeyron equation.29 The values are similar to those of ordinary phospholipids. Using the results from film balance experiments as a basis, especially for the determination of the important grafting density for single polymer chains, we could first demonstrate the possibility to determine absolute values of the water disjoining pressure inside the PEG layer. We secondly showed that it is possible to apply scaling approaches developed for the theoretical description of surface grafted polymer “mushrooms” and “brushes” and to interpret our results in terms of the self-consistentfield theory for polymer “brushes” despite the fact that the conditions (N . 1) for the applicability of the theories are only badly fulfilled. For short chain length (N ) 3, ..., 6) all applied theories fail in particular in the limit of low disjoining pressure at least if one neglects additional contributions like “finite size” effects. The latter are expected to be particularly important due to the rod-like structure of the head group. With growing chain length (N > 6) the theoretical approaches are becoming more and more subtle to fit to the measured data within a broader range of swelling ratios. This reflects the growing influence of the randomness of the conformations of the polymer chains between substrate and alkyl chains. Finally, at N g 15 no qualitative difference from previous results observed on the PEG lipids with long PEG chain randomness20 was detectable. The present study was motivated by the potential application of PEG lipids with oligomeric ethylene glycol head groups as carrier for the coupling of biological functional oligosaccharides such as blood group antigens. Varying the number of EG units (and therefore the length and flexibility of the “spacer”) can provide some information on the effect of the conformation and size of this spacer on the protein-ligand interaction. While for very short spacer length the orientation of the coupled ligands is nearly fully dominated by the orientation of the lipid “backbone” due to a small elasticity of the short chain, for longer “spacers” a significantly higher flexibility in connection with a more and more random orientation of the ligand should be observed, creating the possibility for the ligand to probe also deeper recognition sites of an interacting protein. From this point of view it is interesting


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to study the mechanical and thermodynamic properties of PEG functionalized lipids with a systematically varying number of EG repeating units, especially to optimize the spacer length for different protein-ligand systems.

thermally oxidized silicon wafers as a gift. This work was supported by the Deutsche Forschungsgemeinschaft (DFG Gz. SA 246/27-1) and the Fonds der Chemischen Industrie.

Acknowledgment. We are grateful to Wacker Chemitronic GmbH (Burghausen, Germany) for providing

LA991278B

Equilibrium Swelling Behavior of Solid Supported Poly (ethylene

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