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Static and dynamic evanescent wave light scattering ... and dynamic evanescent wave light scattering studies of diblock copolymers adsorbed at the air/water interface Binhua Lin and

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  • Static and dynamic evanescent wave light scattering studies of diblock copolymers adsorbed at the air/water interface

    Binhua Lin and Stuart A. Rice Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 6063 7

    D. A. Weitz Exxon Research and Engineering Company, Annandale, New Jersey 08801

    (Received 15 June 1993; accepted 10 August 1993)

    We report the results of static and dynamic evanescent wave light scattering studies of a monolayer of a diblock copolymer, polystyrene-b-polymethyhnethacrylate ( PS-b-PMMA) with weight averaged molecular weights (M,) of 880 000:290 000 supported at the air/water inter- face. Our studies probe the interfacial structural and dynamic properties of the monolayer on a length scale which is a fraction of the wavelength of light. The static light scattering studies were carried out as a function of polymer surface coverage and temperature; we also report some preliminary data for the dependence of the static structure function on the relative molecular weights of the PS and PMMA blocks. The complementary dynamic light scattering studies were carried out only as a function of surface coverage. Our data suggest that, upon spreading in the air/water interface, PS-b-PMMA (880:290 K) copolymers form thin disklike aggregates con- taining about 240 molecules. These data are consistent with a model in which each such aggre- gate is a furry disk with a dense core consisting of a layer of collapsed PS blocks atop a thin layer of extended PMMA blocks on the water surface and a brushlike boundary of extended PMMA blocks. The data show that the furry disks diffuse freely when the surface coverage is small, but when the surface coverage is large, they are immobile. Our data also suggest that the furry disks can aggregate to form even larger islands of disks with an extension greater than 20 ,um. The static structure function of the assembly of furry disks is well described, over a wide range of surface coverage, by the structure factor of a two-dimensional hard disk fluid modu- lated by a two-dimensional hard disk form factor.


    The properties of polymers adsorbed at the liquid- vapor interface have been studied for many years, prima- rily with classical methods such as surface pressure-area- temperature measurements to define the equation of state of the monolayer, elhpsometric measurements to deter- mine the monolayer thickness,2 and quasielastic light scat- tering measurements to determine the viscoelastic charac- teristics of the monolayer.3 These methods give valuable information about the gross properties of the monolayer, but no information about the polymer molecule configura- tion or about the transverse (in the plane of the interface) and longitudinal (perpendicular to the plane of the inter- face) distributions of the polymer molecules in the mono- layer. Some information about the longitudinal density dis- tribution in a polymer monolayer has become available very recently from studies of x-ray4 and neutron reflectiv- ity5p6 as a function of angle of incidence, and from studies of fluorescence excited by evanescent wave x rays. There is also some information available about short range trans- verse order in a polymer monolayer obtained from grazing incidence x-ray diEraction.8 However, neither x-ray reflec- tivity nor grazing incidence x-ray diffraction are suitable for the determination of the configuration of the adsorbed polymer, e.g., its radii of gyration parallel to and perpen- dicular to the interface. A method which is suitable for the latter purpose has been proposed by Gao and Rice.9po

    Their method is based on measuring the in-plane and out- of-plane angular distributions of evanescent wave light scattered by the monolayer; the evanescent waves are gen- erated by the total reflection of light from the interface between the substrate and the monolayer. Because the wavelength of light and the polymer dimensions are com- mensurate, measurement of the angular distribution of the scattered evanescent waves allows the determination of a structure function that can be interpreted in terms of the characteristic size and shape of the adsorbed polymer.

    This paper reports an application of the Gao-Rice method to the study of block copolymers of styrene and methyl methacrylate adsorbed at the air/water interface. Specifically, we report the results of static light scattering studies of the m-plane configuration of the diblock co- polymer polystyrene-b-polymethylmethacrylate (PS-b- PMMA) with weight averaged molecular weights (44,) of 880 000:290 000. We complement these static light scatter- ing measurements with a study of the dynamic light scat- tering from this copolymer adsorbed on the surface of wa- ter; the results of the latter study confirm and extend the results obtained from the static structure functions deter- mined by evanescent wave scattering. Finally, we also re- port, briefly, the results of preliminary measurements of the static structure function of monolayers of PS-b-PMMA as a function of the relative molecular weights of the PS and PMMA blocks.

    8308 J. Chem. Phys. 99 (lo), 15 November 1993 0021-9808/93/99(10)/8308/17/$6.00 @ 1993 American Institute of Physics

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  • The results of our experiments are striking. Contrary to common belief, we find, for the copolymer adsorbate studied, that there is no region of the surface pressure-area isotherm studied which corresponds to isolated molecules. Rather, the polymers self assemble into aggregates com- posed of many molecules, each with a diameter that is nearly independent of the surface concentration. Our data are consistent with a model in which each such aggregate is a furry disk with a dense core and a brush-like bound- ary; the former is determined by the PS portions of the molecules, and the latter by the PMMA portions of the molecules. This model envisages the dense core to consist of PS-b-PMMA molecules oriented so that the collapsed PS blocks are in the air, while the PMMA blocks are at the air/water interface. Those PMMA blocks attached to mol- ecules in the center of the disk, rather than its perimeter, spread in the water/air interface, but the geometry of the disk requires that these blocks lie almost entirely beneath the disk. In contrast, the PMMA blocks attached to mol- ecules on the perimeter of the disk are considerably ex- tended at the water/air interface, as in a polymer brush.


    Water I

    A preliminary version of the results of a small fraction of the work discussed in this paper has been reported pre- viously. This paper reports the results of an extended series of studies of monolayers of PS-b-PMMA (880:290 K) supported on water; it also provides a detailed descrip- tion of the experimental apparatus and methods used, along with an improved interpretation of the results of the experiments.

    FIG. 1. The geometric relationships between an incident electromagnetic plane wave with wave vector ki , an evanescent wave with wave vector k, and a scattered wave with wave vector k, at the air/water interface.

    light, then the component amplitudes of the electric field of the evanescent wave are

    lPAl=~$=J 2 cos 8i Jsin ei- n2 it4 C0S2 Bi+Sin2 ei- 2 (1)


    A. Principles of evanescent wave light scattering

    Since this paper reports the first application of the Gao-Rice method to a real system, we briefly review the principles of evanescent wave scattering.

    ,+& 2coseis~ei n4 cos2 Bi+ sin2 Bi - n (3)

    The geometric relation between an incident electro- magnetic plane wave, with wave vector ki, and an evanes- cent wave, with wave vector k,, at an interface between two nonabsorbing dielectric media is illustrated in Fig. 1. The xy plane is the interface between two semi-infinite nonabsorbing dielectric media, while the xz plane is the plane of incidence. Light is incident on the interface through the lower medium. The refractive index of the upper medium is n, and that of the lower medium is n2, where n, > n2. A straightforward application of electro- magnetic theory I2 shows that if the incident angle of the plane wave, 8, is greater than the critical angle 8,, [sin 8, = n = ( n2/nl)], the incident wave is totally reflected, and an evanescent wave is generated at the interface in the upper medium. The evanescent wave propagates along the interface in the incident plane, along the x axis; the ampli- tude of its electric field decays exponentially along the z axis.

    while the spatial dependence of the evanescent waves has the form


    where k, is given by

    27rnl sin ei km= A



    and d, is the penetration depth

    A d=

    2rrnt (sin2Bi-n2) * (6)

    Note that an evanescent wave does not have purely trans- verse character since the field component in the direction of propagation, 1 E, I, does not vanish. However, since lon- gitudinal oscillations of the electric field do not give rise to radiation, the longitudinal component can be omitted in our discussion of light scattered from an incident evanes- cent wave.

    The derivation of the field associated with an evanes- Since we have chosen to study polymers adsorbed at cent wave can be found in standard textbooks.12 In brief, if the water/air interface, medium 1 is water and medium 2 is All and A, are the amplitudes of the incident electric field air, leading to n=0.752 and 19~=sin-, n =48.9; the wave- parallel and perpendicular to the plane of incidence, re- length of the light in vacuum is 5145 A, while the polar- spectively, and il is the vacuum wavelength of the incident ization of the electric field is