Acidic nature of boric acid when its concentration high Following statement was given for boric acid $(\ce{H3BO3}):$


  At low concentrations $(\leq\pu{0.02 M})$ essentially $\ce{B(OH)3}$ and $\ce{B(OH)4-}$ are present, but at higher concentration the acidity increases and pH studies are consistent with the formation of polymeric species such as $$\ce{B(OH)3 &lt;=&gt; H+ + [B3O3(OH)4]- + H2O}$$


Please explain the meaning of the italicised statement i.e. pH studies are consistent with the formation of polymeric species?
In the equation $\ce{H2O + H3BO3 -&gt; H+ + B(OH)4-}$, one negative charge on the anion is shared among 4 electronegative oxygens. Yes, one positive charge on the proton is also shared with some water molecules, so the orthoborate ion probably shares some negative charge with some waters, but let's keep it simple.

Boric acid is known to complex with sugars to generate higher acidity. If boric acid complexes with itself, as in $$\ce{3 H3BO3 -&gt; H+ + [B3O3(OH)4]- + 2 H2O}$$, the one negative charge on the anion can be considered to be distributed among 7 electronegative oxygens, or maybe still distributed mostly on the OH groups, but since they will be separated more, the stability of the ion will be greater, and the tendency to lose a proton will be greater: greater acidity. The electronegativity of boron is less than that of hydrogen (2.02 vs 2.2, electronegativity, Wikipedia), so when the atoms in the ions are counted, the first ionization equation has one hydrogen and one boron as the metallic atoms getting the positive charge, while the second equation has one hydrogen and 3 borons donating electrons - more sharing of the positive charge here, tho the hydrogen still gets the positive charge.

But this structure may be only a suggestion. Well-known polyborate anions include the triborate(1-), tetraborate(2-) and pentaborate(1-) anions. The condensation reaction for the formation of tetraborate(2-) is as follows Wikipedia

$$\ce{2 B(OH)3 + 2 [B(OH)4]− ⇌ [B4O5(OH)4]2- + 5 H2O}$$

The italicized text mentions an observation of pH that is consistent with the complexation of boric acid with itself. It doesn't prove the existence of the triborate ion only, and perhaps is only a way to keep the text shorter without ignoring complexation completely. Then along comes a student who looks into the sentence and sees that something was omitted or not explained thoroughly. (Keep asking questions!)