Fig. 8.2 Polymer chain in the solution could be compared to a sunbather. In favourable
conditions (good solvent, T > T h ), it is extended and its radius of gyration (R)—being a measure of
mass distribution around the centre (or more trivially: a measure of space covered by a single
polymer chain) is proportional to N
m , the scaling exponent m (called also a Flory exponent) is a
dimension-dependent parameter: m = 3/(d + 2), where d is a so-called mass fractal dimension (for
a random chain in the 3-D system m = 3/5). In ideal (h) conditions, the polymer chain fulfills
criteria of the statistical random chain and its radius of gyration is defined by the random walk law:
R * N
1/2
. If the conditions are unfavourable (bad solvent, T < T h ), the polymer tries to occupy the
minimal volume and to reduce the contact with surrounding environment. In this state, the radius
of gyration is reciprocally proportional to d
Fig. 8.3 Phase diagram (temperature T vs. concentration c) for a chain of finite (a) and infinite
(b) length. The true h (tricritical) point occurs for the infinite (ideal) chain only if c reached 0.
Moreover, only for c = 0 swollen and collapsed states exist. For c 6 ¼ 0, semi-dilute solution exists.
The coexistence curve corresponds to states for which the osmotic pressure is zero (critical points
of the phase separation in polymer solution with given concentration). For the finite polymer chain,
a critical point for the polymer–solvent phase separation occurs. Furthermore, solution behaviour
is controlled by concentration fluctuations near the critical point. The h-like condition area is
extended to the finite range of temperature (blue horizontal dashed line marks the crossover to the
repulsive polymer solution) and concentration for high enough concentrations system crossovers
from diluted to semi-diluted (red-dotted line). [49] © IOP Publishing. Reproduced with
permission. All rights reserved
8 Vibrational Spectroscopy in Analysis of Stimuli-Responsive …
227
conditions (good solvent, T > T h ), it is extended and its radius of gyration (R)—being a measure of
mass distribution around the centre (or more trivially: a measure of space covered by a single
polymer chain) is proportional to N
m , the scaling exponent m (called also a Flory exponent) is a
dimension-dependent parameter: m = 3/(d + 2), where d is a so-called mass fractal dimension (for
a random chain in the 3-D system m = 3/5). In ideal (h) conditions, the polymer chain fulfills
criteria of the statistical random chain and its radius of gyration is defined by the random walk law:
R * N
1/2
. If the conditions are unfavourable (bad solvent, T < T h ), the polymer tries to occupy the
minimal volume and to reduce the contact with surrounding environment. In this state, the radius
of gyration is reciprocally proportional to d
Fig. 8.3 Phase diagram (temperature T vs. concentration c) for a chain of finite (a) and infinite
(b) length. The true h (tricritical) point occurs for the infinite (ideal) chain only if c reached 0.
Moreover, only for c = 0 swollen and collapsed states exist. For c 6 ¼ 0, semi-dilute solution exists.
The coexistence curve corresponds to states for which the osmotic pressure is zero (critical points
of the phase separation in polymer solution with given concentration). For the finite polymer chain,
a critical point for the polymer–solvent phase separation occurs. Furthermore, solution behaviour
is controlled by concentration fluctuations near the critical point. The h-like condition area is
extended to the finite range of temperature (blue horizontal dashed line marks the crossover to the
repulsive polymer solution) and concentration for high enough concentrations system crossovers
from diluted to semi-diluted (red-dotted line). [49] © IOP Publishing. Reproduced with
permission. All rights reserved
8 Vibrational Spectroscopy in Analysis of Stimuli-Responsive …
227