게시판 > 질답게시판 > 점도평균분자량에 관련해 질문드립니다.

스테파노 Stefano

14-08-04 15:31

(1) 고분자의 점도는 고유점도를 이용하여 구하는데 고분자를 용제에 녹여 점도를 측정했을 때 무한희석농도에서의 점도가 바로 고유점도(Intrinsic Viscosity)입니다. 수량평균, 질량평균, 등을 포함하여 점도평균 분자량은 이곳
http://nsdl.niscair.res.in/jspui/bitstream/123456789/406/2/Molecular%20weights%20of%20polymers.pdf 에 잘 설명되어 있습니다. 수식 번호만 고쳐서 인용하면 본 답글의 식(5, 원문의 수식 (28))를 이용하여 계산하면 됩니다.
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(Quote/)
General Expression for Viscosity Average Molecular Weight:

At infinite dilution (c → o), the polymer molecules in solution contribute to viscosity discretely without mutual interference. Solubilization of a polymer sample is preceded by a large amount of swelling if left undisturbed and the swelling degree is higher in a better solvent. Similarly, the intrinsic viscosity is also higher in a good solvent than in a poor solvent. What all these would mean is that in a better solvent, as the polymer chain molecules go into solution, a unit mass of the same expands more to give a higher hydrodynamic volume.

Let there be a heterogeneous (polydisperse) polymer in dilute solution of concentration c considered to behave ideally in that the individual molecules contribute to viscosity enhancement independently of one another. In that event, if ( ηsp ) i be the specific viscosity contribution due to the species of size i , then one may express the overall specific viscosity ηsp as
ηsp = Σ (ηsp )i ------------------------------(1)
Considering Mi and ci as the molecular weight and concentration of the species of size i and in view of the ideal specific viscosity component ( ηsp )i = KMi^ a * ci , it is further possible to write.

ηsp = K Σ (Mi^a * ci)------------------------(2)
and so,
( ηsp / c ) = [η] = ( K Σ Mi^a * ci ) / c -----(3)
where, c = Σ ci stands for overall concentration taking all polymer species into consideration. Further taking c = Σ ci = Σ Ni Mi , and considering the (Mark Houwink) equation (21), one may have :

[η] = K Σ Ni Mi^(1 + a)/Σ Ni Mi = K Mν^a -------------------(4)

such that,
Mν = {Σ Ni Mi^(1 + a)/Σ Ni Mi }^(1/a) -----------------------(5)

Clearly, one may see that for the limiting case when a = 1 , Mν = Mw
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(/Unquote)

인용한 부분을 간단히 요약하면 i 성분의 비점도 (Specificic Viscosity)는 ( ηsp)i = K Mi^ a 와 같이 나타낼 수 있는데 이를 각 i성분의 농도분율 ci 대해 가중평균하여 구한 값이 됩니다. K와 alpha(a)는 고유점도를 구하는데 사용하는 용제에 따른 상수입니다.

(1)~(5) 수식들 은 (5)식이 얻어지는 과정을 유도한 것이므로 결국 (5)식 만을 이용하면 점도평균 분자량을 구할 수 있습니다.

Let there be a heterogeneous (polydisperse) polymer in dilute solution of concentration c considered to behave ideally in that the individual molecules contribute to viscosity enhancement independently of one another. In that event, if ( ηsp ) i be the specific viscosity contribution due to the species of size i , then one may express the overall specific viscosity ηsp as 
            ηsp = Σ (ηsp )i ------------------------------(1) 
Considering Mi and ci as the molecular weight and concentration of the species of size i and in view of the ideal specific viscosity component ( ηsp )i = KMi^ a * ci , it is further possible to write.

ηsp = K Σ (Mi^a * ci)------------------------(2)   
and so, 
           ( ηsp / c ) = [η] = ( K Σ Mi^a * ci ) / c -----(3) 
where, c = Σ ci stands for overall concentration taking all polymer species into consideration. Further taking c = Σ ci = Σ Ni Mi , and considering the (Mark Houwink) equation (21), one may have :

[η] = K Σ Ni Mi^(1 + a)/Σ Ni Mi = K Mν^a -------------------(4)

such that, 
            Mν = {Σ Ni Mi^(1 + a)/Σ Ni Mi }^(1/a) -----------------------(5)
 
Clearly, one may see that for the limiting case when a = 1 , Mν = Mw 
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(/Unquote)

인용한 부분을 간단히 요약하면  i 성분의 비점도 (Specificic Viscosity)는  ( ηsp)i = K Mi^ a 와 같이 나타낼 수 있는데 이를 각 i성분의 농도분율  ci 대해 가중평균하여 구한 값이 됩니다.   K와  alpha(a)는 고유점도를 구하는데 사용하는 용제에 따른 상수입니다.

(1)~(5) 수식들 은 (5)식이 얻어지는 과정을 유도한 것이므로 결국 (5)식 만을 이용하면 점도평균 분자량을 구할 수 있습니다.