Final answer:
Alpha (α) and beta (β) glucose molecules cannot link together because their -OH groups are oriented differently on carbon #1, preventing proper alignment for stable glycosidic linkage formation.
Step-by-step explanation:
Alpha (α) and beta (β) molecules of glucose cannot link together because the orientation of their hydroxyl (-OH) groups on carbon #1, also known as the anomeric carbon, is different. In α-glucose, the -OH group is below the plane of the glucose ring, whereas in β-glucose, the -OH group is above the plane. This difference in configuration means that the molecules would not align properly to form a stable glycosidic linkage, which is why when α-glucose molecules polymerize, they create branched storage polysaccharides like glycogen and plant starches due to diverse α-glycoside linkages. On the other hand, the polymerization of β-glucose molecules results in the formation of rigid structural polysaccharides like cellulose because of their β-1,4 glycosidic linkages creating straight chains that stack well, leading to a more stable structure.