Polymer Physics

respectively. Therefore, the complex viscosity is

jj^ ¼ð^02 þ^002 Þ^1 =^2 (6.47)

Under high shear rates, the viscosity exhibits the empirical Cox-Merx rule
(Cox and Merz 1958 )as

jj^ ðoÞ ðg^0 Þ (6.48)

This empirical rule is practically useful, which allows an estimation of viscosity
in the practical processing with high shear rates, by using the high-frequency
rheometric study in the laboratory. The high shear rates of processing are quite
difficult to be realized directly in the laboratory.

6.3 Glass Transition and Fluid Transition

6.3.1 Glass Transition Phenomena

Glass transition widely exists in various condensed materials, such as the network
glass SiO 2 þNa 2 O formed by silicon oxide and sodium oxide, linear and branched
polymers like polystyrene, zinc chloride ZnCl 2 , the mixture KNO 3 þCa(NO 3 ) 2
with potassium nitrate and calcium nitrate, HCl aqueous solution, metal aluminum,
2-methyl pentane, colloidal clusters due to volume exclusion or attractions, liquid
crystal rigid-rod molecules in orientational order or disorder, etc. Almost all the
materials can perform glass transition if the cooling rates are large enough to
suppress the crystallization.
The glass state is readily accessible for polymers by the following two reasons.

1. High content of irregular chain sequences suppresses the melting point mono-
   tonically down to the glass transition temperature, like atactic polystyrene (aPS)
   and atactic poly(methyl methacrylate) (PMMA). Therefore, no matter how large
   the cooling rate is, one always gets the glass state of the polymer. Such kind of
   polymers are called non-crystalline polymers;


2. The rigid-chain polymers crystallize very slowly. Therefore, they are very able
   to vitrify into the glass state, like polycarbonate (PC) and PET.
   In the semi-crystalline polymer solid, most of polymers trespass the crystalline
   interfaces, and a restriction occurs to the mobility of non-crystalline part of
   polymers near the crystalline-amorphous interfaces. The restricted portion of
   polymers displays glass transition at the temperature higher than those non-
   crystalline free polymers. Wunderlich named this non-crystalline part of polymer
   near the crystalline surfaces as therigid amorphous polymer(Wunderlich 2003 ).
   Treating semi-crystalline polymers as formed by three parts (flexible amorphous far

6.3 Glass Transition and Fluid Transition 109