How does existence of alpha and beta form of glucose prove that it exists as a cyclic structure

Question

My book says that

Glucose is found to exist in two different crystalline forms which are named as $\alpha$ and $\beta$.

Next it says that

This behaviour could not be explained by the open chain structure for glucose.

I am not able figure out how does existence of two crystalline forms prove that glucose exists as a cyclic structure? Are there no noncyclic compounds which exist in more than once crystalline forms?

And why can't it be explained by the open chain structure?

I think I am missing something, but what?

Thanks!

Edit:

If we take the example of glycine, it exists in two different crystalline forms, but doesn't have a cyclic structure like that of glucose. So why does existence of two crystalline forms for glucose seen as a supporting evidence of its ring form?

Answer 1

According to Wikipedia:

Glucose is usually present in solid form as a monohydrate with a closed pyran ring (dextrose hydrate). In aqueous solution, on the other hand, it is an open-chain to a small extent and is present predominantly as α- or β-pyranose, which partially mutually merge by mutarotation.

Glucose predominantly occurs in nature in the form of the D‐enantiomer, which is generally believed to exist in three crystalline forms: $\alpha$‐D‐glucose monohydrate (Figure 1A)(Ref.2), anhydrous $\alpha$‐D‐glucose (Figure 1B)(Ref.2), and anhydrous $\beta$‐D‐glucose (Figure 1C)(Ref.1,3). Both anhydrous $\alpha$‐D‐ and $\beta$‐D‐glucose crystals are orthorhombic while $\alpha$‐D‐glucose monohydrate crystals are monoclinic (see Fig. 1A-C). However, a fourth form, which is metastable in solution phase at $\pu{38\!-\! 50 ^{\circ}C}$ and thought to be a hydrated form of $\beta$‐D‐glucose, has been reported as well (Ref.1,4).

The crystal structure of $\beta$-D-glucose published in 1960 (Ref.5) clearly showed the exsistence of pyranose ring system. As in the inserted box in Figure 1 state that, in aqueous solutions, 99% of D‐glucose exists as a mixture of the $\alpha$- and $\beta$-forms (approximately 62%  $\beta$ and 38% $\alpha$ when equilibrated at $\pu{31 ^{\circ}C}$ (Ref.1). Recent NMR study using fully $\ce{^13C}$ labelled glucose (Ref.6) clearly showed $\alpha/\beta$ ratio of $37/63$, which is almost identical to this literature value (Figure 2):

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References:

1. F. W. Schenck, "Glucose and Glucose-Containing Syrups," In Ullmann's Encyclopedia of Industrial Chemistry: Ullmann's Food and Feed, Vol. 2; B; Elvers, Ed.; Wiley‐VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2017, pp. 781-802, doi 10.1002/14356007.a12_457.pub2.
2. W. B. Newkirk, “Manufacture and Uses of Refined Dextrose,” Ind. Eng. Chem. 1924, 16(11), 1173-1175, doi 10.1021/ie50179a028.
3. G. R. Dean, “Optical-Crystallographic Properties of $\beta$-D-Glucose,” Anal. Chem. 1973, 45(14), 2440–2441, doi 10.1021/ac60336a005.
4. G. R. Dean, “An unstable crystalline phase in the D-glucose-water system,” Carbohydr. Res. 1974, 34(2), 315–322, doi 10.1016/S0008-6215(00)82906-7.
5. W. G. Ferrier, “The crystal structure of $\beta$-D-glucose,” Acta Cryst. 1960, 13, 678-679, doi 10.1107/S0365110X60001588.
6. T. Richter, S. Berger, “A NMR method to determine the anomeric specificity of glucose phosphorylation,” Bioorg. Med. Chem. 2013, 21(10), 2710–2714, doi 10.1016/j.bmc.2013.03.008.

Answer 2

The open chain is floppy. The relative stereochemistry between two centers is fixed and unchanging.

But the existence of geometric isomers implies additional structure imposed on the molecule. In this case, in 6-member ring, one can have axial or equatorial substitution which are distinct. The relative stereochemistry is the same but the relative substitution patterns are now different.

Take a look at the following structure (source).

In the $\alpha$-form, the hydroxyl group at C-1 is axial, and in the $\beta$-form, it is equatorial. However, this change does not affect anything else in the molecule of glucose, so the relative positions of substituents becomes different.

The tricky part is that this doesn't necessarily imply a cyclic structure, but a cyclic structure is probably the easiest way to impose structure on the molecule that will rationalize two forms. (And I am hard pressed at the moment to actually come up with an alternative.)