SPECTRA OF CRYSTALLINE AND COLLOIDAL PIGMENTS 



1823 



where Eo is the energy of an isolated molecule, and AE^, the change in 

 energy caused by an infinite cubic lattice with a lattice constant Ro and a 

 virtual dipole n in each lattice point. 



For a monomolecular layer traversed by light perpendicular to its plane, 

 the phase difference is zero for all molecules in the plane, and the inter- 

 action energy is therefore a rapidly converging function of the radius of 

 the monolayer. For a circular, isotropic array of dipoles, ^vith a radius 

 R, the interaction energy in the excited state is: 



(37C.2) 



AE„ = 



Rl \ r) 



The saturation energy oXR = oo is: 



(37C.2A) 



AE = 



TTfJ. 



VRl 



The value of A£'„ is equal to V4 of that of A£'„ given in (37C.1) for an 

 infinite cubic crystal with the same lattice constant. 



The dipole moments of the transitions can be estimated from the in- 

 tensity of absorption {i. e., the total area under the absorption band), 

 and the lattice constant, from x-ray diffraction studies. Using these 

 data, Jacobs obtained table 37C.IIIA for the crystals whose structure is 

 known or can be surmised (no such surmise is as yet possible for chlorophyll, 

 cf. chapter 37B, section 5). The table shows that the "limiting" shifts, 

 found in three-dimensional crystals of the two chlorophyllides and their 

 pheophorbides, are close to the theoretical estimates. 



Table 37C.IIIA 



The experimentally observed dependence of the band shift on crystal 

 size, illustrated in fig. 37C.16, indicates rapid rise to saturation at 72 <C 

 100 m^u, as expected theoretically for a two-dimensional system, and not 

 the sigmoid shape predicted for a three-dimensional lattice. It follows 



