The paper is quite short and very readable (especially if you are just skimming and can skim over some of the details/jargon) but here [0] is a diagram (from the paper) that perhaps will help you understand what is going on.
[0] http://imgur.com/a/LNWUz
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To summarise, they prepared graphene oxide laminates using vacuum filtration, and then stored them at different relative humidities by changing the salt concentration of the storage liquid. The different relative humidities cause different layer spacing, which they measure with X-ray diffraction, and choose whichever layer spacing they want before adding the epoxy.
The relevant quote from the paper:
Thick (≈100 µm) GO laminates were prepared by vacuum filtration of aqueous GO solutions, as reported previously. The laminates were cut into rectangular strips (4 mm × 10 mm) and stored for one to two weeks at different relative humidities (RH), achieved using saturated salt solutions. The resulting interlayer spacing was measured by X-ray diffraction as
shown in Fig. 1e and varied from ≈ 6.4 to 9.8 Å with RH changing from zero to 100%. GO laminates soaked in liquid water showed d ≈ 13.7 ± 0.3 Å. All these values agree with previous reports, where the changes in d were attributed to successive incorporation of water molecules into various sites between GO sheets. Individual GO strips with desirable d were then encapsulated and stacked together using Stycast epoxy as shown in Figs. 1b,c to increase the available cross-section for filtration to 1 mm (see Methods and supplementary Fig. S1).
The stacked GO laminates, now embedded in the epoxy (Fig. 1c), are referred to as physically confined GO (PCGO) membranes because the epoxy mechanically restricts the laminate’s swelling upon exposure to RH or liquid water (Methods). The stacks were glued into a slot made in either metal or plastic plate (Fig. 1b). Two sides of these stacked PCGO membranes were then trimmed off to make sure that all the nanochannels are open (Fig. 1d) before carrying out permeation experiments, in which ions and water molecules permeates along the lamination direction as shown in Fig. 1a.