PHYSICAL CHEMISTRY OF ENAMEL DISSOLUTION 253 



If the strength of the buffer decreases ( i.e., the dissociation constant 

 decreases), the rate should increase, reach a maximum, and then 

 decrease. For most practical cases, the first term as well as the [H+] 

 in the denominator of the second term can be ignored since they 

 are small, and then : 



f^ = A,Ifl[ra] (6) 



For these expressions, all other variables are assumed to be con- 

 stant, such as the cation and organic polymer concentration of the 

 decalcification medium. To incoi"porate these other variables into 

 the function requires additional terms which must be added to or 

 multiplied by the existing terms. The preceding equation, however, 

 is the fundamental expression of the rate of incipient carious lesion 

 formation. 



Calcium suppresses the rate, and this inhibition can be expressed 

 by including a term, k[Ca]'\ in the immediately preceding equation. 

 The value of the exponent n is determined from the slope of the 

 logarithmic plot (Fig. 31, n = ¥4) of the rate versus calcium concen- 

 tration. It has not yet been determined how best to incorporate this 

 additional term to augment the fundamental expression for rate of 

 formation of incipient carious lesion. 



Phase Identification by Equilibrium Solubility Studies 



The mechanism of rate inhibition by calcium is complicated but 

 is almost certainly not a reversal of the reaction to re-form hydroxy- 

 apatite (i.e., common ion effect) (Gray, 1962). One reason for this 

 conclusion is that phase diagram data (Van Wazer, 1958) indicate 

 that dicalcium phosphate, not hydroxyapatite, will be the existing 

 phase under the conditions present during enamel dissolution. An- 

 other supporting fact is that many, if not all, cations forming in- 

 soluble phosphate salts have a similar repressing effect (although 

 to widely different degrees ) , leading to the conclusion that inhibition 

 is a generalized effect of cations. To a much more limited extent, 

 similar effects can be expected and are found for anions, particularly 

 those which form insoluble calcium salts. 



