Page 109 - Carrahers_Polymer_Chemistry,_Eighth_Edition

72 Carraher’s Polymer Chemistry

where τ is the measure of the decrease of the incident-beam intensity per unit length (l) of a given
solution and is called the turbidity of the solution.
The intensity of scattered light or turbidity (τ) is proportional to the square of the difference
between the index of refraction (n) of the polymer solution and of the solvent (n ), to the molecu-
o
lar weight of the polymer (M ) and to the inverse fourth power of the wavelength of light used (λ).
w
Thus,
Hc = 1 ( 12Bc Cc + ⋅⋅⋅ )
+
+
2
τ MP (3.14)
W θ
where the expression for the constant H and for τ is as follows:
 2 
2 
 32π   n 0  dn     i 
2
H =      dc    and τ = K n 2  90  (3.15)
  3    λ 4 N   i 
0
   

where n = index of refraction of the solvent, n = index of refraction of the solution, c = polymer con-
0
centration, the viral constants B, C, and so on are related to the interaction of the solvent, P is the
θ
particle-scattering factor, and N is Avogadro’s number. The expression dn/dc is the specifi c refrac-
tive increment and is determined by taking the slope of the refractive index readings as a function
of polymer concentration.
In the determination of M , the intensity of scattered light is measured at different concentra-
w
tions and at different angles (θ). The incident light sends out a scattering envelope that has four
o
equal quadrants (Figure 3.14(a)) for small particles. The ratio of scattering at 45 compared with
that for 135 is called the dissymmetry factor or dissymmetry ratio Z. The reduced dissymme-
o
try factor Z is the intercept of the plot of Z as a function of concentration extrapolated to zero
0
concentration.
For polymer solutions containing polymers of moderate to low molecular weight, P is 1 giving
θ
Equation 3.16. At low-polymer concentrations Equation 3.16 reduces to Equation 3.17 an equation
for a straight line (y = b + mx) where the “c”-containing terms beyond the 2Bc term are small:
Hc = 1 ( 12Bc Cc + ⋅⋅⋅ ) (3.16)
+
+
2
τ
M w
90° 90°
135°
45° 135° 45°

Incident light Incident light
0° 0°

Scattering particle
(a) (b)

FIGURE 3.14 Light-scattering envelopes. Distance for the scattering particle to the boundaries of the enve-
lope represents an equal magnitude of scattered light as a function of angle for a small-scattering particle (a)
and a large-scattering particle (b).

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