The thermodynamic properties of the masson polymerization models of liquid silicates
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has b e e n r e a l i z e d for s o m e t i m e that explanation of the t h e r m o d y n a m i c p r o p e r t i e s of b a s i c s i l i c a t e m e l t s r e q u i r e s p o s t u l a t i o n of the o c c u r r e n c e of a size r a n g e of s i l i c a t e a n i o n g r o u p s in t h e s e m e l t s , ~ i . e . , that the e a r l i e r s u p p o s i t i o n that b a s i c s i l i c a t e m e l t s contain only SiO~" and O 2- a n i o n s in s t o i c h i o m e t r i c p r o p o r t i o n is i n c o m p a t i b l e with o b s e r v e d t h e r m o d y n a m i c b e h a v i o r . F u r t h e r d e v e l o p m e n t of slag t h e o r y beyond this point thus awaited i d e n t i f i c a t i o n of the s i l i c a t e ion types p r e s e n t , q u a n t i f i c a t i o n of the size r a n g e and d i s t r i b u tion of these ions and d e t e r m i n a t i o n of the f a c t o r s which c o n t r o l the a n i o n i c e q u i l i b r i u m . Although s e v e r a l a p p r o a c h e s have b e e n made t o w a r d s solution of this p r o b l e m , 2'3 it is only r e c e n t l y that specific m o d e l s of s i l i c a t e anion p o l y m e r i z a t i o n have been developed. T h e s e a r e the M a s s o n p o l y m e r i z a t i o n m o d e l s of liquid s i l i c a t e s . 4 - a It is the p u r p o s e of the p r e s e n t c o m m u n i cation to e x a m i n e the t h e r m o d y n a m i c p r o p e r t i e s of these models. Whiteway, Smith, and M a s s o n 4 showed that the mole f r a c t i o n of x - m e r s , N x , in the e q u i l i b r i u m c o n f i g u r a tion r e s u l t i n g f r o m p o l y c o n d e n s a t i o n of f - f u n c t i o n a l m e r u n i t s is
Nx = ( f x --2--x+ 1)Ix!
Application of this equation to b i n a r y s i l i c a t e m e t t s g i v e s two m o d e l s of s i l i c a t e anion p o l y m e r i z a t i o n ; a l i n e a r chain model 5'6 and a m u l t i c o n f i g u r a t i o n model. 7,s The f o r m e r is obtained by c o n s i d e r i n g the SiO~- ion to be a b i f u n c t i o n a l m e r unit, such that only l i n e a r chain s i l i c a t e p o l y i o n s can f o r m . In this model the e q u i l i b r i u m d i s t r i b u t i o n of s i l i c a t e ions is given as 5 _
N.ro'x'-'3x+l c-,2(x+I)NSix+ l O 3x+4 2(x+2)-
[21 w h e r e k is the e q u i l i b r i u m constant for the r e a c t i o n o, , ' ~ ( x + l ) - - S : ~2(x+2)- O 2SiO~- + ~lx~3X+l ~X+1~3x+4 +
[3]
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D. R. GASKELLis Associate Professor, School of Metallurgy and Materials Science and Laboratory for Research on the Structure of Matter, University of Pennsylvania,Philadelphia, Pa. 19104 Manuscript submitted February 14, 1972. METALLURGICALTRANSACTIONS
k --
No2" 1 - N O ~-
ot 1 -a
[4]
w h e r e a i s the extent of the p o l y m e r i z a t i o n r e a c t i o n and is given as the f r a c t i o n of s i n g l y - b o n d e d oxygens, (O-), p r e s e n t in the c o m p l e t e l y d e p o l y m e r i z e d m e l t , which have p o l y m e r i z e d to f o r m d o u b l y , b o n d e d oxygens,
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