amphiphilic polymers) is often strongly limited compared to that of low molecular
weight compounds. To understand the nature of sensitivity to different stimuli in
polymer–solvent systems, the h conditions should be defined. In the simplest case
of a binary system containing a linear polymer and a low molecular weight solvent,
the h conditions relate to the temperature (T h ) and a type of a solvent in which the
polymer coil acts in the solution like an ideal chain i.e. can be considered as a
random walk. Such a situation arises if the following conditions are fulfilled:
(i) Gaussian statistics of polymer chains, (ii) ignorance of the segment–segment
correlation and (iii) ignorance of topological constraints. In reality, these conditions
are satisfied if the repulsions between polymer segments leading to polymer chain
expansion and contributing to energy U are balanced by the entropic contracting
force determining entropic part S of Helmholtz free energy F = U − TS. The
reduced Helmholtz free energy of mixing may be expressed according to the following formula:
F
k B T
¼
U p
M
ln U p þ U s ln U s þ vU s U p
ð8:1Þ
where k B is Boltzmann constant, M—average molar mass of polymer chain, while
U p and U s are molar fractions of polymer segments and solvent molecules,
respectively. The mixing parameter v represents the intermolecular interactions in
the system and determines the solvent quality:
v ¼
Z
2k B T
ð
Þ 2e sp À e ss À e pp
À
Á
ð8:2Þ
where Z is a coordination number (the number of the nearest neighbouring molecules), while e represents energies of intermolecular interactions between particular
elements (s and p indices correspond to solvent molecules and polymer segments,
respectively). If v = 0.5, a polymer–solvent system is in equilibrium in the given
temperature and pressure; for v > 0.5, the solvent is called a ‘poor solvent’ and the
polymer chain is susceptible to globular conformation (collapse); for v < 0.5, the
polymer chain is in the ‘good solvent’—well soluble and expanded—see Fig. 8.2.
The performed short analysis showed that the equilibrium in the polymer–solvent system may be perturbed by changes in temperature, addition of a co-solvent
or other components which impact polymer–polymer, solvent–solvent and polymer–solvent interactions. As a result, coil-to-globule transitions can be triggered. In
the ideal case of the infinite chain, the h temperature corresponds to the critical
solution temperature (the coil-to-globule transitions temperature)—see Fig. 8.3b.
In real systems, the length of a polymer chain is finite and the temperature–
concentration phase diagram looks like in Fig. 8.3a. Instead of h temperature, the
critical point occurs determining the upper critical solution temperature (UCST).
The systems exhibiting the lower critical solution temperature (LCST) are also
known, and from a practical point of view, they are even more important (they will
be presented in section Thermo-responsive systems—“non-ionisable” polymers).
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M. Kozanecki et al.
weight compounds. To understand the nature of sensitivity to different stimuli in
polymer–solvent systems, the h conditions should be defined. In the simplest case
of a binary system containing a linear polymer and a low molecular weight solvent,
the h conditions relate to the temperature (T h ) and a type of a solvent in which the
polymer coil acts in the solution like an ideal chain i.e. can be considered as a
random walk. Such a situation arises if the following conditions are fulfilled:
(i) Gaussian statistics of polymer chains, (ii) ignorance of the segment–segment
correlation and (iii) ignorance of topological constraints. In reality, these conditions
are satisfied if the repulsions between polymer segments leading to polymer chain
expansion and contributing to energy U are balanced by the entropic contracting
force determining entropic part S of Helmholtz free energy F = U − TS. The
reduced Helmholtz free energy of mixing may be expressed according to the following formula:
F
k B T
¼
U p
M
ln U p þ U s ln U s þ vU s U p
ð8:1Þ
where k B is Boltzmann constant, M—average molar mass of polymer chain, while
U p and U s are molar fractions of polymer segments and solvent molecules,
respectively. The mixing parameter v represents the intermolecular interactions in
the system and determines the solvent quality:
v ¼
Z
2k B T
ð
Þ 2e sp À e ss À e pp
À
Á
ð8:2Þ
where Z is a coordination number (the number of the nearest neighbouring molecules), while e represents energies of intermolecular interactions between particular
elements (s and p indices correspond to solvent molecules and polymer segments,
respectively). If v = 0.5, a polymer–solvent system is in equilibrium in the given
temperature and pressure; for v > 0.5, the solvent is called a ‘poor solvent’ and the
polymer chain is susceptible to globular conformation (collapse); for v < 0.5, the
polymer chain is in the ‘good solvent’—well soluble and expanded—see Fig. 8.2.
The performed short analysis showed that the equilibrium in the polymer–solvent system may be perturbed by changes in temperature, addition of a co-solvent
or other components which impact polymer–polymer, solvent–solvent and polymer–solvent interactions. As a result, coil-to-globule transitions can be triggered. In
the ideal case of the infinite chain, the h temperature corresponds to the critical
solution temperature (the coil-to-globule transitions temperature)—see Fig. 8.3b.
In real systems, the length of a polymer chain is finite and the temperature–
concentration phase diagram looks like in Fig. 8.3a. Instead of h temperature, the
critical point occurs determining the upper critical solution temperature (UCST).
The systems exhibiting the lower critical solution temperature (LCST) are also
known, and from a practical point of view, they are even more important (they will
be presented in section Thermo-responsive systems—“non-ionisable” polymers).
226
M. Kozanecki et al.