This answer is, unfortunately, wrong. Or at best, incomplete. And they say the best way to get the correct answer on the internet is to post an incorrect one. In fact, the fact that this (11-year-old) paper was published to HN last night has been irking me, and I have thrice started, then abandoned, a comment explaining why GO work in this field is mostly useless, and why peoples' hopes in "low cost desalination" are moonshine based on a misunderstanding of the relevant thermodynamics.

First, this article is 11 years old. This is extremely old news. To the best of my knowledge, most of the serious research on GO has fizzled out, except as a random "might as well be pencil shavings" additive to enhance the perceived novelty of bad research. A favorite of mine: "Will Any Crap We Put into Graphene Increase Its Electrocatalytic Effect?" (2020) (https://doi.org/10.1021/acsnano.9b00184). It seems as if the field has moved on to trying to better understand how existing crosslinked polyamide desalination membranes can be better optimized for neutral solute rejection (something that graphene doesn't, and likely won't ever, but very good at separating), as mentioned towards the end of this comment.

The helium parts of your explanation are correct. However, the sections pertaining to water and the explanation of the molecular interactions as a mechanistic model which explains the different behaviors of He and H2O in the paper are wrong. In fact, water does not have strong interactions with graphene or other fullerenes. For example carbon nanotubes, water permeation is modeled as being nearly frictionless.

Water does have strong interactions with itself, true. The permeation of penetrant through a membrane is usually rationalized in terms of its permeability, which can be thought of as the product of how much material is in the membrane phase (as opposed to the external solution -- gas or liquid) and how fast the penetrant moves through the material. He doesn't interact strongly with materials, so it doesn't sorb very strongly into materials. It is also very small and doesn't form transient bonds with other atoms, so it tends to diffuse very quickly as well. Water is very condensable and tends to form stronger interactions with atoms, so it tends to sorb more and diffuse less. You can think of He as a 1-lane 100 MPH highway through a material and water as a 200-foot-wide moving sidewalk, in terms of mass conveyed per time.

However, the tendency of water to form hydrogen-bonded networks is not, strictly speaking, why the membranes in this study behaved the way they did. The actual answer is incredibly simple. The water condenses into and swells the graphene oxide, so the material is physically separated apart and allows water (and anything that water can carry with it) to penetrate through.

These membranes are made out of graphene oxide (GO), not graphene (a different material). GO is (obviously) an oxidized form of graphene. In an ideal model, you can think of GO as a flake of graphene with a bunch of oxide groups around the edge (=O, -OH, -COOH, etc.). Water permeates GO rapidly because it interacts strongly with the terminal oxide groups on the edges of the GO flake and (again, this is the key part) swells the GO flakes apart from one another considerably. The flakes are physically further apart, which allows the water to freely permeate. This mechanism, by which a condensable gas or vapor condense to form a liquid-like phase in a porous solid is known as capillary condensation.

The fact that the flakes are physically spaced further apart also allows other gases to permeate as well. As discussed in the article, the GO membranes are no longer helium-leak-tight when the helium gas is humidified. He permeates the membrane in large part by sorbing into the water which has condensed between the GO flakes (this type of sorption is described by Henry's law) and diffusing as a dissolved gas through the water channels formed through the swollen GO material. In water, the d-spacing of GO (the space between the flakes) goes from 3-5 Å (good for molecular sieving) to 1-2 nm (will let food dye pass through).

This type of separation (which is not necessarily what the authors were trying to do, admittedly) has been mechanistically and mathematically described in the literature for at least 80 years (e.g., for packed plugs of amorphous carbon studied by Barrer). Also, note that the capillary condensation effect observed here is mostly a function of the properties of the penetrant components, not of the GO itself, outside of how strongly GO interacts with the penetrants.

People have spent a lot of time trying to chemically stitch GO flakes together so that they don’t swell as much, but they haven't had much success. Several years ago, a group cast a piece of dry GO in epoxy, and showed that the films being physically constrained by the epoxy can have ion-selective flow edge-on (the membranes in this study are top-down), but this is more of a proof of physical concept than a practical implementation. Reduced GO (GO that's reduced back into just graphene, but now with more defects where the oxide residues were removed) can be used for gas separations and don't swell, but are hard to make (reducing conditions are not good for materials) and not particularly beneficial over polymeric materials. Single-pore graphene is still researched, but I think the interest in it is severely misguided, because:

Even if researchers were to succeed in making a high-flux high-rejection GO or graphene-based membrane for desalination, these properties membranes don’t address the real issues in water treatment. Instead, they are a showy material that appeals to metrics and gets the university PR photographer in the lab, rather than industrial partners.

Some huge issues off the top of my head include: 1) RO membranes for desalination aren't actually that inefficient, the energy cost of desalination is a large, but not even the major, operating expense, and efficiency gains to be had by using high-flux low-friction materials are minor (if we had a thermodynamically ideal desalinator, it would only use 2-3x less energy than existing technology, and GO/CNT/MOFs, etc., are unlikely to provide 200-300% improvements in efficiency) 2) practical membranes needs to be more fouling resistant and easier to clean to maximize productivity and efficiency over their lifespan, 3) any efficiency gains made by high-flux materials aren't really that 3) ultra-high flux materials tend to foul faster even if they can be more easily cleaned, 4) there are fluid dynamic reasons why ultra-high flux membrane materials (i.e., >10x current desalination membranes) are useless (you can look up "concentration polarization"), and 5) there's a much more critically pressing need to improve the rejection of other neutral compounds like urea, pharmaceuticals, NDMA (and other chloramine disinfection byproducts), and boron. Graphene, graphene oxide, carbon nanotube, and MOF based membranes for desalination are almost invariably focused on high salt rejection and high flux, which it turns out isn't really that hard to do. Neutral organic and inorganic molecules, however, tend to pass straight most membranes, requiring post-treatment.

To make a computer analogy, graphene-based membranes in the real-world applications are like several terabytes of ECC RAM hooked up to Babbage’s computation engines. They don't address the real needs or bottlenecks of separation processes.

Some reading for the curious (you will need to figure out how to access). The last two were written mostly by environmental engineers, the first two by chemical engineers.

Evolving beyond the thermal age of separation processes: Membranes can lead the way (2004) - https://doi.org/10.1002/aic.10330

Seven chemical separations to change the world (2016) - https://doi.org/10.1038/532435a

The Critical Need for Increased Selectivity, Not Increased Water Permeability, for Desalination Membranes (2016) - https://doi.org/10.1021/acs.estlett.6b00050

Water Treatment: Are Membranes the Panacea? (2020) - https://doi.org/10.1146/annurev-chembioeng-111919-091940