According to the chemical formula $\ce{H−(O−CH2−CH2)_n−OH}$ of polyethylene glycol, or PEG, I assume that this organic compound has a long chain structure when it is dry and in powder form. (This is also what guys in the chemistry field say.)

But when PEG is dissolved in water, would it form some structure like a cluster or would it remain a long chain? Can we somehow calculate the diameter of a dissolved PEG molecule when $n$ is given? Or the dissolved PEG molecules band randomly so there are no calculations for an average diameter statistically at all?

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    $\begingroup$ Polymer molecules form individual "random coils" in solution. The end-to-end distance of the molecule and thereby also its coiled "diameter" (radius of gyration) scales linearly with molecular weight. The absolute numbers depend of course on the stiffness of the molecule, kind of solvent, solute-solvent interaction, and temperature. $\endgroup$ – Karl Jul 6 '20 at 19:30

PEG is the term usually reserved for shorter chains, while PEO is used to refer to longer chain molecules. When polyethylene glycols are dissolved in water, they increase the viscosity of the solution. While it might be easy to model short-chain polymers in dilute solution as some kind of folded chain approaching a spherical volume, as the chains get longer and the solution becomes more concentrated (>1%), there is significant entanglement.

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The picture above is for a long-chain polyacrylate, which can be adjusted to be very hydrophilic by adding alkali to generate anions all along the chain. The images show various shapes in water: some fairly tight, some looser (spread out), some spread out but very much entangled. At some point in increasing chain length or increasing concentration, it becomes difficult to project the image of a single molecule of PEO into useful predictions of solution properties. Measurements of dilute or shorter chain molecules would include viscosity; as the solution becomes more concentrated or the chain longer, the property includes some elasticity, so we have viscoelasticity, and at very high chain lengths, we have pituosity (more commonly known as stringiness or ropiness). A video shows this effect dramatically: https://www.neatorama.com/2017/10/09/Fun-with-Polyethylene-Glycol/.

Since PEGs and PEOs are so soluble and compatible with water, the first molecules to be added just fill all the volume of water; you could calculate how long a PEO molecule would be if completely stretched out. Stirring can extend the molecule, showing effects due to viscoelasticity and pituosity.

  • $\begingroup$ Your last paragraph is blatantly wrong. $\endgroup$ – Karl Jul 6 '20 at 19:18
  • $\begingroup$ The probability for an ethylene or oxymethylene chain with N > 25 or so to exist in all-trans conformation at room temperature is, for any practical purpose, zero. If you pull at its end groups, it will rip long before you can stretch it to its contour lenght. $\endgroup$ – Karl Jul 6 '20 at 19:42
  • $\begingroup$ @Karl: Experimentally, if you allow a moderately concentrated solution of PEOs to stand, it seems fairly isotropic. If, however, you stir it, a weak structure will form in the liquid, which is evidenced by viscoelasticity, that is, when stirring is suddenly stopped, the liquid continues to flow: BACKWARD. A backwards flow of 45 degrees is easy to obtain. While only an idealist would consider that a polymer chain could be stretched out completely, I think that one molecule in a liter wouldn't necessarily bunch up - and if it did, I could stir the solution a bit and s t r e t c h it out a lot. $\endgroup$ – James Gaidis Jul 7 '20 at 15:03
  • $\begingroup$ You will be able to detect the prolate deformation of the polymer coil in a shear flow, for example by light scattering, and by the effect of its mechanical relaxation, but you are nowhere near stretching the coil out. Not least because the viscosity drops remarkably, and you cannot stir very fast before the flow becomes turbulent. Last but not least, what you describe proves that the polymer forms a compact, spherical coil. (The latter only by the fact that the solution becomes isotropic again after stirring). $\endgroup$ – Karl Jul 7 '20 at 18:12
  • $\begingroup$ Btw. the contour length of a 1000 kg/mol PEO is in the range of ten microns. $\endgroup$ – Karl Jul 7 '20 at 18:31

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