The question doesn't involve the application of any physical principles to the design or manufacture of any real-world product, nor does it involve any consideration for practical utility*, costs, material availability, or existing technologies. Additionally, the creation of nano-scale hook and loop fasteners is a profoundly stupid idea, as adhesion via intermolecular, electrostatic, and/or magnetic interaction is infinitely easier (and presumably less costly) to achieve at this scale than mechanical adhesion**, so if this were intended as an engineering question it wouldn't be a very good one. It would make very little sense for me to ask the question except out of pure, academic curiosity.
The linked meta post regarding the distinction between physics and engineering questions explicitly states that questions inspired by engineering considerations may be considered on-topic. In particular, questions regarding physical limits of man-made systems (e.g. telescopes, computers, wires) are considered relevant. My question concerns the [estimation of the] theoretical lower limit of the diameter of the fibers/wires used in the construction of hook and loop fasteners. I believe that this should be considered an engineering-inspired question, rather than an engineering question, in the same manner as the listed examples.
Considered at the level of a single hook and loop, the question is quite nearly "what is the smallest possible diameter for a spring?" The reason I didn't ask that question is that 1) I already know the answer (either "smaller than we can resolve" or "define spring") and 2) that isn't what I'm concerned with. The entire reason for asking the question is that I don't have a neat form-fitting model for the seemingly simple system under consideration, and I want to make an educated guess. It's a physical Fermi problem which I find particularly interesting for its occupation of the unknown (to me) space between "quantum" and "classical."
Now I can understand if the writing is misleading, so I will try to clarify the things that look the most engineery or otherwise non-physicsy to me:
- I included some details regarding the hypothetical (and potentially impossible) construction of atomic-scale fasteners using graphene, and maybe this made it seem that I was genuinely proposing the creation of such a "product." This was not my intention, the point was to illustrate a scale at which I am confident that hook and loop fasteners can't work, and to give some justification for my thinking. I named graphene as a material because carbon compounds are exceptionally well-studied, and it would be the easy to find any information I might need for an estimate of, say, the rate of formation of chemical bonds between the strips. I could have assumed sheets of an arbitrary two-dimensional material instead, but that would make the problem harder than it already is. The whole point of the introduction was to establish that there is probably some limit to the size of hook and loop fasteners, so attempting to account for every possible version of the atomic setup would only make sense if I thought it would produce a positive result.
Of course, I could be entirely wrong. Maybe interactions between atom-thick hooks and loops are predominantly mechanical; but that's why I'm asking the question.
Likewise, I bring up that certain biological structures can become tangled. The point of this was to indicate that classical effects (e.g. stiffness, friction, other stress/strain type stuff) persist at the μm scale.
I later mentioned biological activity as a source of deterioration. This second reference to biology is unrelated to the first, and was not meant to indicate something to be accounted for in the problem, rather to illustrate that macroscopic hook and loop fasteners are not immune to chemical, thermodynamic, etc. effects and to provide an example of such an effect - as well as to illustrate why such effects can generally be neglected in the macroscopic case. I wanted to distinguish mechanical failure from failure due to chemical decomposition, because the latter becomes increasingly significant at smaller scales. The point I was trying to make is that while deteriation through means other than mechanical failure does occur even in the macroscopic case, it is less significant. To still count as "hook and loop fasteners" the same relation should hold at the microscopic scale - we need the hooks and loops to remain intact for at least as long at takes to undergo structural failure. If molecular interactions overtake mechanical ones before structural failure, then the system shouldn't be considered an example of hook and loop fasteners.
This is probably the least clear of my points, and I can see how it might be counterintuitive. At the macroscopic scale, we don't usually think about chemical interaction at all, we just assume that everything is made out of pure geometry, and immune to thermodynamics. But at the microscopic scale, chemical interactions are often more significant than mechanical ones. In order to count as a hook and loop fastener, interaction between the hook and loop needs to be primarily mechanical and the structures need to remain stable long enough for this interaction to occur multiple times.
- I suppose that the use of the academic "we" and the specific naming of Velcro (a registered trademark of the of Velcro IP Holdings LLC) could make it seem that I am representing Velcro or some other company. This is certainly not the case, I used the term "velcro" (note the lack of capitalization) colloquially in place of "hook and loop fastener" because 1) it is a commonly understood name for the mechanical system in question and is more likely to be recognized by the casual reader than the technically correct "hook and loop fastener" 2) it is shorter and less tedious than "hook and loop fastener" 3) it carries the denotation of a surface with many individual hooks and loops, whereas "hook and loop fastener" is ambiguous and could refer to a single hook-loop pair. Similarly, my use of "we" was meant in the usual sense to refer to the speaker/writer (myself) and the listener/reader following the convention of scientific and mathematical literature when posing hypotheticals, definitions, or conventions, as in "we adopt the $(+,-,-,-)$ sign convention."
The additional use of "Atomic Velcro (TM)" was intended to be humorous and does not, to my knowledge, refer to any existing, planned, or proposed product or trademark of Velcro or any other company. As stated previously, the creation of literal atomic scale hook and loop fasteners is wildly impractical, if not wholly impossible, and, more significantly, entirely pointless given the existence of much better alternatives.
If the use of the term "velcro" is in violation of any site rule and/or negatively impacts the clarity of the question, I am happy to change it.
Aside from these issues, I'm not sure how the question could be misinterpreted. Is there some other reason that the question is off-topic? Is there anything I can do to improve it?
*Beyond "the structure in question must remain physically stable for long enough that its classification as 'hook and loop fastener' makes sense". If we regard this as an engineering concern, rather than a definition, then the retention of elasticity in a spring is likewise an engineering concern and should neither motivate nor be included in the discussion of mass-spring systems. That is to say, we should regard the long-term retention of elasticity - operationalized analogously to my question as "not undergoing degradation through non-mechanical means in less time than is required for structural failure (permanent deformation and/or loss of elasticity through mechanical means)" or equivalently as "doesn't turn to dust after a single cycle" - as an engineering concern. (Taken to its logical conclusion, the continued consideration of "springiness" as a physical property, rather than engineering concern, then either makes anything capable of deformation (for example, a steel chair) a "spring," or leaves the term "spring" undefined. Or it renders our categorization of things as "of concern primarily to physics" and "of concern primarily to engineering" arbitrary.)
**In fact some of the world's most brilliant engineers have recently proposed an innovative design for a new kind of adhesive surface which operates on precisely these principles. They're calling it "adhesive tape." While it's still experimental, it could become commercially by the early 1920s.