Confinement-induced order of tethered alkyl chains at the water Õ vapor interface

M. Fukuto, R. K. Heilmann, 1,* P. S. Pershan, 1 S. M. Yu, C. M. Soto, 3 and D. A. Tirrell Department of Physics and Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 0 Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003 Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 ~Received 9 November 2001; published 23 July 2002 !

The manner in which linear objects such as simple alkyl chains ͓u(CH 2 ) n u͔ and polymers order has been of interest for the past half century ͓1,2͔.Chain order affects the basic physical chemistry of lipids ͓3͔ and the function of biological membranes ͓4 -8͔.Properties of alkyl chains also influence phenomena such as friction and adhesion ͓9͔ and the phases of liquid crystals ͓10,11͔ and Langmuir monolayers ͑LM͒ ͓12,13͔.It is well known that in the absence of constraining effects, such as might arise from the tethering of one end of the chain ͓14,15͔ or competing effects within the internal structure of block copolymers ͓16͔, the local order of alkyl chains is relatively insensitive to the length of the chain ͓17͔.The tendency of alkyl chains to pack similarly in diverse systems is rather robust ͓13͔.
Details of chain packing, however, are affected by subtle differences in constraints on chain ends.For example, most LM on water spontaneously form two-dimensional ͑2D͒ crystalline phases with quasi-long-range positional order ͓12͔.In contrast, the positional order for monolayers of single-chain thiols on the surface of liquid Hg is only short range ͓18͔.This variation is attributed to differences in the strength of the chain-chain interaction relative to that between the subphase and the chain end.Similarly, selfassembled monolayers ͑SAM͒ of thiols on Au͑111͒ form single crystals with long-range order ͓19,20͔, while SAM of thiols on Ag͑111͒ ͓21͔ and siloxanes on SiO 2 ͓22͔ exhibit only short-range order.
Different phenomena are observed in the packing of polymer chains longer than some persistence length l p ͓2͔. Free polymers in good solvents can coil to form spheres with a radius of gyration R g ϳl p N 1/3 .By contrast, polymers tethered to substrates will not have sufficient room to pack as spheres if the mean distance between tethering sites is less than R g , resulting in partial unwinding of the chains to form polymer brushes ͑PB͒ ͓9͔.In most studies on PB, the ratio of tethering density to R g is controlled by varying the solvent, which in turn affects R g .There have been relatively few studies where tethering is to liquid surfaces, for which LM techniques can be used to obtain a direct measure of the effect of 2D compressive stress on chain packing.In the experiments by Factor et al. the packing density was varied by adding or removing molecules from a LM of diblock copolymers on the surface of various solvents ͓23͔.Prinz, Muller, and Maaloum carried out similar studies on polyelectrolyte brushes by physically compressing the LM ͓24͔.
We present an x-ray scattering study of the packing of constrained alkyl chains in which the tethering is to rods that form a LM.The chains are the free ends of the side chains ͓u(CH 2 ) 2 uCOOuCH 2 uC 6 H 4 uOu(CH 2 ) 15 CH 3 ͔ attached to the rigid cylindrical core of a helical polypeptide.The molecule poly͓␥-4-͑n-hexadecyloxy͒benzyl ␣,L-glutamate͔ ͑C16-O-PBLG͒ is a ''hairy rod'' in which hexadecyloxy chains ͑uOuC16; one chain per monomer͒ extend out from the ␣-helix PBLG core.C16-O-PBLG forms a LM on water in which the rods are oriented parallel to the surface and locally align parallel to neighboring rods within the LM plane.The hydrophobicity of alkyl chains causes them to segregate toward the film/vapor side of the LM, leaving PBLG cores near the water/film interface.We find that despite the highly complex structure of the molecule, the local packing of uOuC16 chains at high lateral pressures displays the herringbone ͑HB͒ order that is otherwise only known for densely packed alkyl chains.We show evidence that the HB order is first established in the 1D regions between aligned rods and grows laterally with compression.
The Langmuir trough was described previously ͓26͔.A LM was spread on pure water at a specific area A Ͼ40 Å 2 /monomer from a chloroform solution.Surface pressure ⌸ was monitored by a Wilhelmy plate.X-ray measurements were made on the Harvard/BNL liquid spectrometer ͓26͔ at Beamline X22B of the National Synchrotron Light *Present address: Space Nanotechnology Laboratory, Center for Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139.Source (ϭ1.55 Å).For x rays striking the film at angle ␣ to the surface and scattered at angles ␤ to the surface and 2 to the plane of incidence, the wave-vector transfer q has the surface-normal component q z ϭ(2/)͓sin(␣)ϩsin(␤)͔ and the in-plane component q xy ϭ(2/)͓cos 2 (␣)ϩcos 2 (␤) Ϫ2 cos(␣)cos(␤)cos(2)͔ 1/2 .Angular acceptance of the NaI scintillation detector was controlled by two sets of crossed slits, one closer to the sample cell and the other immediately before the detector.For reflectivity ͑XR͒, the fraction R of the incident intensity detected at ␤ϭ␣ and 2ϭ0 ͑or q xy ϭ0͒ is measured as a function of q z ϭ(4/)sin(␣).The data reported here is the difference between the signal at 2ϭ0 and the background measured at 2 offsets of Ϯ0.25°.For q z /q c у4 -5, where q c ϭ(4/)sin(␣ c ) ͑ϭ0.0218 Å Ϫ1 or ␣ c ϭ0.154°for water͒ is the critical wave vector for total reflection, XR is described by the formula ͓27͔ where R F represents the Fresnel reflectivity of an ideally flat and sharp interface between the subphase (ϭ ϱ ) and the vapor (ϭ0).The average electron density profile ͗(z)͘ along the surface normal can be extracted by constructing a model and fitting the calculated R/R F to the data.For grazing incidence diffraction ͑GID͒, the incident angle was fixed at ␣ϭ0.12°(Ͻ␣ c ) and intensities scattered away from the incidence plane were measured as a function of q xy with a typical in-plane FWHM ͑full width at half maximum͒ resolution of ␦q xy ϳ0.026 Å Ϫ1 and an out-of-plane detector acceptance of ⌬q z ϭ0.11 Å Ϫ1 .
Measured ⌸-A isotherms and XR results are summarized in Fig. 1.A typical GID scan at low q xy is shown in Fig. 2͑a͒, and the extracted interhelix d spacing between aligned ␣ helices are plotted in Fig. 2͑b͒.The ratio A/L 1 ͓solid lines in Fig. 2͑b͔͒ represents the d spacing expected of close-packed horizontally oriented rods.For comparison, Figs. 1 and 2͑b͒ include the results for the LM of ␣-helical PBLG ͓28͔, which lacks the uOuC16 group and collapses at ⌸ 1 ϳ9 dyn/cm.The profiles ͗(z)͘ for the PBLG LM on water ͓dashed curves in Fig. 1͑d͔͒ can be described by a one-box model with Gaussian roughnesses and are consistent with a single surface layer whose thickness l PBLG is comparable to the diameter D PBLG ϳ13 Å of PBLG.The observed lateral d spacing ͓diamonds in Fig. 2͑b͔͒ is also comparable to D PBLG and follows the expected dϭA/L 1 behavior for ⌸Ͻ⌸ 1 .From this we conclude that the PBLG rods are oriented along the surface and align parallel to their neighbors with an area A PBLG ϭL 1 D PBLG ϭ19.5 Å 2 /monomer.
Similarly, the rods in the C16-O-PBLG LM lie horizontally and align locally.The effect of the uOuC16 side chains is to induce a nonuniform profile ͗(z)͘ across the water/C16-O-PBLG/vapor interface that requires a two-box model ͓solid lines in Fig. 1͑d͔͒.According to analyses to be described elsewhere ͓29͔, the profile parameters core , chain , l core , and l chain , defined by the extremum points in ͗(z)͘ and d͗(z)͘/dz, are consistent with segregation of the LM into a lower sublayer dominated by the PBLG core and an upper sublayer occupied by uOuC16 chains ͓Fig. in ordered phases of alkyl chains ͓12,30͔.Given the hydrophobicity of the side chains this extra spacing most certainly arises from chains that are tethered on the water side of the helix backbone and extend toward the vapor.This is supported by the fact that core is slightly lower than the maximum in the PBLG profile ͓Fig.1͑d͔͒.
High-q xy GID results summarized in Fig. 3 illustrate chain ordering effects.The positions of peaks ͑11͒ and ͑02͒ observed at high ⌸ ͑տ5 dyn/cm͒ are consistent with the HB arrangement of alkyl chains, with an orthorhombic unit cell ͑two chains/cell͒ of dimensions a 1 ϫa 2 ϭ5.0ϫ7.5 Å in the plane perpendicular to chain axes ͓12,13,17,31͔.The model illustrated in Fig. 4 for the development of the HB order is based on the following observations.First, the packing order of uO-C16 chains is a local effect in that the magnitude of the chain tilt relative to the surface normal is not uniform over the surface.Figure 3͑b͒-3͑c͒ show that at fixed ⌸, the ͑11͒ peak shifts with q z along an arc qϭ͓q xy 2 ϩq z 2 ͔ 1/2 ϳ1.5 Å Ϫ1 , while the ͑02͒ is only visible at q z ϳ0.This signifies tilts of HB-packed chains toward NN ͑i.e., toward ͓10͔͒ with a distribution in tilt angles that vary from ϭ0°͑untilted͒ to տ30°, even at high ⌸.In view of the tethering of the uOuC16 chains the lack of a unique tilt angle is not surprising.
Second, the correlations of the HB order are anisotropic with respect to the alignment of PBLG cores.This can be seen from the fact that the ͑02͒ peak is noticeably narrower than the ͑11͒ peak ͓Fig.3͑a͔͒.Defining hk ϵ2/͓⌬q xy (hk) Ϫ␦q xy ͔ with ⌬q xy (hk) representing the FWHM of the ͑hk͒ peak, we estimate the lateral correlation length 01 along the ͓01͔ axis ͑i.e., perpendicular to the tilt direction͒ to be 01 ϭ 02 տ100 Å, which is roughly of the same order of magnitude as the lengths L of typical C16-O-PBLG rods.At high ⌸, the projection of 11 onto the ͓10͔ axis ͑i.e., 10 ϭ 11 a 2 /͓a 1 2 ϩa 2 2 ͔ 1/2 ϭ0.83 11 ͒ reaches 10,max ϭ11-14 Å for PD 325 (⌸տ25 dyn/cm) and 10,max ϭ17-21 Å for MD76 (⌸տ15 dyn/cm), which are comparable to the observed interhelix d spacing, i.e., 10,max ϳd.From this we infer that the local ͓01͔ axis runs parallel to the aligned PBLG cores, as shown in Fig. 4͑a͒.
Third, the presence of a weak ͑02͒ peak and the near absence of the ͑11͒ peak for ⌸Շ5 dyn/cm indicate that although uOuC16 chains are mostly disordered at low ⌸, a small fraction of them form a locally HB-packed structure.As shown in Fig. 2͑b͒, the PBLG cores align locally without external pressure, implying strong mutual attraction.It follows that even at ⌸ϭ0, the chains between aligned cores, which extend out to the vapor from below, are confined onedimensionally under a high local compressive stress.It would thus seem that the chain order appearing at low ⌸ ͓i.e., the ͑02͒ peak͔ is a consequence of the 1D confinement between aligned PBLG cores.Moreover, the growth of the ͑11͒ peak with increasing ⌸ can be interpreted as enhancement of the HB order along the ͓10͔ axis perpendicular to the cores with decreasing interhelix d spacing.On compression the unconfined chains sitting directly above the cores are brought into the HB structure.The conclusion that the HB order is first established along the helix backbone and then grows with increasing ⌸ is the most important message of this study.Figure 4͑b͒ illustrates an idealized model of the initial HB structure.Two rows of uOuC16 chains form a zigzag pattern in the confined region, where each row is contributed by one of the two neighboring C16-O-PBLG.The positions of chains along each row are periodic with repeat distance a 2 and are related to those of the other row by a vector (a 1 /2,a 2 /2) in the plane normal to the chain axes.It is not possible to fit more than two rows within the gap ⌬dϳ5 Å between aligned PBLG cores.As indicated in the figure, there is probably a distribution in the vertical tethering position of uOuC16 chains within a given ordered domain, and for those domains that are tilted, the direction is transverse to the rod axis.Given a 2 ϭ7.5 Åϭ5L 1 , the model implies that on average, every segment of five monomers in each rod would contribute one chain to the zigzag structure on one side of the core and another to the other side ͓32͔.If this is true, the area taken up by a five-monomer segment should be approximately A 5 ϳ5A PBLG ϩ2A HB , where A HB ϭa 1 a 2 /2ϭ18.8Å 2 /chain for the HB packing.Taking A PBLG ϳ19.5 Å 2 /monomer for the core at low ⌸ ͓Fig.1͑a͔͒, the model predicts the area/monomer for C16-O-PBLG to be A 5 /5ϳ27.0Å 2 /monomer, which agrees well with Aϭd ϫL 1 ϳ28 Å 2 /monomer at ⌸ϭ0 ͓Fig.2͑b͔͒.As for the unconfined chains above the core ͑roughly three per fivemonomer segment͒, the average area of 5 3 A PBLG ϳ32.5 Å 2 /chain available to each at low ⌸ is more than enough room for these chains to be disordered.In summary, the system studied here is qualitatively different from any other system of alkyl chains studied to date in that 2D order grows out epitaxially from the 1D order of the confined chains.It should also be noted that according to the generalized phase diagram of fatty acid monolayers, the ordered phase formed by C16 acid at room temperature should have hexagonal symmetry and lower density than the HB-packed phases L 2 Љ ͑tilted to NN͒ and CS ͑untilted͒, which would only occur below ϳϪ20 °C ͓12͔.The difference here is probably caused by confinement-induced reduction in the chain entropy.This is interesting because one should expect subtle changes in the properties of tethered chains as the chain length increases towards the polymer regime.For example, Kraack, Deutsch, and Sirota recently studied the effect of chain length variation on the degree of undercooling of n alkanes ͓33͔.We hope to continue the studies reported here with side chains of increasing length.