A four-component clay-polymer-salt-water system, consisting of n-butylammonium vermiculite, poly-(ethylene oxide) (PEO), n-butylammonium chloride, and heavy water was studied by wide-angle neutron diffraction. The one-dimensional nature of the system makes it ideal for model studies of colloids. Previous results had shown that if the size of the polymer, given as the end-to-end distance, is larger than the spacing between the clay platelets the polymer chains bridge between the platelets and draw them together. In order to further investigate the bridging mechanism we have studied the structure of the polymer chains using H/D isotope substitution of the polymer. The volume fractions of clay r and PEO nu were r=0.05 and nu=0.04, respectively, and the salt concentration c was 0.1 M. The results indicate that a significant part of the polymer chains are directly bound to the clay surfaces, and that the remaining (at least 50%) polymer segments have a Gaussian-like distribution in the middle between the clay layers. Previous studies of the corresponding three-component system without added polymer had shown the surface to be covered with two layers of water molecules. The new results show that the ethylene oxide segments displace water molecules immediately adjacent to the clay surfaces, bonding directly to them by physical adsorption. Due to the polymer induced reduction of the interlayer spacing it is likely that each polymer chain is adsorbed on both clay surfaces. The findings are consistent with our newly proposed model for polymer bridging flocculation.