248 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



20-25 for trivalent ions, (b) The above treatment assumes that ions are 

 point charges and takes no account of ionic radii. It is probable that the 

 greater the ionic size, the smaller will be the required value of D. There 

 are no means for estimating the magnitude of this correction but it is pro- 

 bably small, (c) Most treatments assume a minimum value for D of around 

 3 at very small distances. This is based on the dielectric constants of solids 

 at low temperatures (ice, 3.1; dodecane, 2.2; hydrogen sulfide, 3; hydrogen 

 chloride, 3.1; octadecanol, 3; monopalmitin, 2.4; isobutyl chloride, 2.8; 

 etc.), these values being related to the electronic polarizabilities since the 

 molecules are rigidly fixed and orientation polarization does not occur. How- 

 ever, the validity of this assumption may be questioned. When ions are 

 in contact (that is, with no water molecules between them), the presence 

 of water dipoles oriented around the ions outside the area of contact will 

 reduce the interaction; however, if the ionic groups are bonded to mole- 

 cules it may be that water is excluded from direct interaction with the ions 

 and this reduction does not occur. The problem of hydration will be con- 

 sidered in more detail in the next section. 



Variation of Potential Energy with Distance in Ion-Ion Interactions 



Since the dielectric constant varies with interionic distance, the po- 

 tential energy of two ions will no longer be inversely proportional to the 

 distance as in a vacuum. Combining Eqs. 6-5 and 6-74 we have: 



(p = 332 — r-n ^r^ kcal/mole (6-75) 



a(6a — 7) 



Figure 6-13 is an energy-distance diagram for the interaction of two uni- 

 valent ions, assuming a reasonable repulsion constant. The effect of the 

 water on the interaction is given by the change from curve B to curve A; 

 the equilibrium potential energy is decreased markedly and the equilibrium 

 distance is increased by almost 0.5 A. The energy involved in displacement 

 of bound water was ignored in the calculation of these curves. 



Dielectric Constant for Different Types of Interaction 



It is probable that the estimations of D given above apply to any type 

 of interaction involving an ion, including ion-dipole and ion-induced dipole. 

 The dielectric constant does not enter into the dispersion energy because 

 the oscillating fields are both small and of such a high frequency that no 

 effect on the solvent molecules would be expected. A problem, however, 

 arises in dipole-dipole interactions. The electrical field around a dipole 

 is not negligible. A dipole of moment // = 1.5 possesses a mean electrical 

 field strength in a vacuum of 22 X 10^ volts/cm at 3 A, 9.8 X 10^ volts/cm at 



