Chapter 32, Polymer Solutions Video Solutions, Molecular Driving Forces

Problem 1

Concentrations: mole fractions $x$ versus volume fractions $\phi .$ Consider a solution of polymers $P$ and small molecules $s$, with $\phi_{s}=\phi_{P}=0.5$. The polymer chain length is $N=1000$.
What are the mole fractions $x_{s}$ and $x_{p}$ ?

Kratika Bhadauria

Numerade Educator

01:23

Problem 2

Excluded volume in protein folding.
(a) Use the Flory-Huggins theory to estimate the number $v_{1}(c)$ of conformations of a polymer chain that are confined to be maximally compact, $M=N$. Simplify the expression by using Stirling's approximation.
(b) If the number of conformations of the unfolded chain is $v_{1}(u)=M(z-1)^{N-1}$ (since $M \gg N$ ), then compute the entropy of folding,
$$
\Delta S_{\text {fold }}=k \ln \left[\frac{v_{1}(c)}{v_{1}(u)}\right] .
$$

Dennis Howard

Numerade Educator

01:54

Problem 3

Flory-Huggins mixing free energy. A polymer $A$ with chain length $N_{A}=1000$ is mixed with a small molecule $B$. The volume fractions are $\phi_{A}=0.3$ and $\phi_{B}=$ $0.7$, and $\chi_{A B}=0.1$. The temperature is $300 \mathrm{~K}$. Using the Flory-Huggins theory,
(a) Compute $\Delta S_{\operatorname{mix}} / M k$.
(b) Compute $\Delta U_{\mathrm{mix}} / M k T$.
(c) Compute $\Delta F_{\mathrm{mix}} / M$.

Manik Pulyani

Numerade Educator

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Problem 4

The critical point of a Flory-Huggins solution. For the mixing of a polymer $A\left(N_{A}=10^{4}\right)$ with a small molecule $B$ ( $N_{B}=1$ ), compute the critical volume fraction $\phi_{c}$ and the critical exchange parameter $\chi_{c}$.

Victor Salazar

Numerade Educator

00:11

Problem 5

Volume fractions versus mole fractions. For what class of model mixing process are volume fractions identical to mole fractions?

Shoukat Ali

Other Schools

00:24

Problem 6

Solvent chain lengths affect partition coefficients. What is the maximum effect of the solvent chain length on the partition coefficient according to the Flory-Huggins model?

Amy Jiang

Numerade Educator

05:48

Problem 7

The colligative properties of polymers. Show how a small-molecule diluent can reduce the freezing point of a polymer solution.

Ronald Prasad

Numerade Educator