160 



J. D. BERNAL 



A co-ordination number of two leads to an unbranched linear association. If 

 the two co-ordinating are nearly at i8o° the result is a nearly straight line 

 polymer of indefinite length ; if the angle is smaller it is a ring or close helix. 

 Angles of 90° or less will produce fourfold or triple aggregations without much 

 waste space, as for instance in the 33,000 mol. wt unit in zinc insuUn. The 

 helix will be the most probable form for larger angles owing to the stabilizing 

 effect of secondary interactions between successive coils. This seems to be the 

 explanation for the arrangement of the protein shell in the rod-like viruses such 

 as tobacco mosaic virus, though we cannot be sure yet whether in this case there 

 is one closely packed helix or an aggregation of several sUghtly coiled heUces. 



The simplest form of three co-ordinated pattern is that of a hexagonal plane 

 net. This, however, imless stabilized, is hkely to curl into a cylinder or spiral 

 roll. At any rate no indisputable example of it has been analysed though it may 

 account for the protein part of cellular or intracellular membranes. Another 

 product of three co-ordination is the closed basket of cubic, often of isoctahedral, 

 symmetry (532) which has been revealed as the shell of the globular viruses — 



(b) 



Types of aggregate formed by 4 co-ordination when angle a between 

 vectors joining neighbours is : 



(a) — less than 90° leading to closed octahedron; (b) — equal to 90^ leading to an 



indefinite plane square net; (c) — greater than 90° leading to a three-dimensional 



extended (diamond) structure. 



tomato bushy stunt and turnip yellow [5, 6]. Higher co-ordinations lead to 

 clump-like aggregates or to indefinitely extending crystals. The former occur if 

 the points of attachments are concentrated on one side of the particles. For 

 instance, four attachments in the form of a pyramid would lead to a closed group 

 of six in the form of an octahedron, while four in the form of a tetrahedron 

 would lead to an indefinite arrangement of the type of a diamond crystal (Fig. 4). 

 If we consider the further aggregations, not of quasi-spherical particles, but 

 of the kinds of structures which, as shown above, can be derived from them, 

 there are further possibihties of complexity. In essence, however, these reduce 

 to two: the packing of elongated particles, which may include twining; and the 

 piling of platy ones, which may include rolling up. The simplest arrangement of 

 straight or quasi-straight elongated particles is hexagonal packing (Fig. 5, a and 

 b). This will result in two kinds of structures according as to whether the elon- 

 gated particles can be arranged with all their ends in parallel shells, nearly 

 normal to their general direction, or not. In the latter case, which is the only 

 one for particles of unequal length, a long aggregate with characteristic grain 



