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Swelling-Related Processes in Hydrogels

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Hydrogel Sensors and Actuators

Part of the book series: Springer Series on Chemical Sensors and Biosensors ((SSSENSORS,volume 6))

Abstract

The swelling equilibrium of gels can be explained by the Flory-Rehner theory. The FR theory calculates the difference of the chemical potential of a solvent inside a gel to the surrounding pure solvent as a sum of the mixing and the elastic part. The first is based on the Flory–Huggins theory, the second on the rubber elasticity theory (Sect. 1). An important role for gels with volume phase transition plays the Flory–Huggins interaction parameter and its dependencies on temperature and concentration. In a system with specific interactions between the solvent and the network, additional contributions to the chemical potential have to be taken into consideration. The application of hydrogels is based on changes of the gel properties, mostly the dramatic change of their swollen volume, in response to specific environmental stimuli. The velocity of changes of the degree of swelling is of outstanding importance. The kinetics of swelling and shrinking is determined by different diffusion processes (Sect. 2). The cooperative motion of the net chains is characterized by a cooperative diffusion coefficient D coop . The time dependence of the degree of swelling for gels of different geometries is followed and D coop calculated. Processes happening at the volume phase transition were discussed. Section 3 introduces then the fundamental concepts of the spectroscopic characterization of hydrogels. The focus of Sect. 3.1 is a practical hands-on advice that everyday practitioners of infrared and Raman spectroscopy will find useful. The reader will be introduced to spectroscopic methods and to sample preparation techniques. More advanced techniques like imaging spectroscopy and chemometric data analysis are discussed. Section 3.2 discusses the NMR imaging technique as an important method to visualize swelling-related processes in hydrogels.

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Notes

  1. 1.

    It was observed, that a gel swollen to equilibrium in the liquid solvent shrinks as soon as it is transferred to the vapour phase of the same solvent. This phenomenon is known as the “paradox of Schroeder” (Freundlich 1932). For a theory of swelling with solvents in various phases, see (Borchard & Steinbrecht 1991).

  2. 2.

    Also, the swelling can be measured as the equilibrium water fraction EWF, defined as the wet weight fraction of swollen gel:

    EWF = [(weight of swollen gel) – (weight of dry gel)]/[weight of swollen gel]; \( {\rm \varphi_2}\, = \,{{\left( {1 - EWF} \right)\,{\rho_1}} \mathord{\left/{\vphantom {{\left( {1 - EWF} \right)\,{\rho_1}} {\left[ {{\rho_1}\, + \,EWF\,\left( {{\rho_2}\, - \,{\rho_1}} \right)} \right]}}} \right.} {\left[ {{\rho_1}\, + \,EWF\,\left( {{\rho_2}\, - \,{\rho_1}} \right)} \right]}}\, \)

  3. 3.

    Other values for Δs and Δh were given in (Shibayama et al. 1994a):

    Δs = −2.8 10−23 J/K; Δh = –6.5 10−21 J

  4. 4.

    Changes in the Gibbs (G) and the Helmholtz (\( F\, = \,f(T,V,{n_1},\,{n_2}\,) \)) free energies are assumed to be equivalent since the product pΔV is small at low pressures.

  5. 5.

    The cycle rank ξ, or number of independent circuits, characterizes the network with greater generality, regardless of the nature of its imperfection. ξ is the minimum number of scissions required to reduce the network to a spanning tree.

  6. 6.

    Uniaxial means: λx = λ; λ y = λ z = λ −1/2 ; λ = x/x 0 with x 0 the un-deformed and x the deformed length, respectively.

  7. 7.

    The mole number of net chains is n c = N c/NL = m/M c, where m is the mass of the network. The density of the network is ρ2 = m/V o.

  8. 8.

    It is possible to use the volume of the polymer in the state of preparing the network as a reference. The deformation of the network by swelling is then measured as the ratio of the swollen volume to the volume at preparation, see Chapter 1. This quantity is called as swelling ratio.

  9. 9.

    The memory term describes the changes of the network chain conformation in a solution at a concentration of the reacting system to the conformation in a dry state (reference state).

  10. 10.

    The ratio of the characteristic relaxation time to the characteristic diffusion time is the so-called Deborah number (De). The smaller De is, the more fluidic the material appears.

  11. 11.

    A solution of 20 wt-% polymer in water was irradiated with a dose of 80 kGy.

  12. 12.

    A gel consists of polymer chains, cross-links and solvent. The polymer chains undergo Brownian motion while the cross-links remain at the same position. Light scattered from gels therefore has a dynamic and a static contribution. The scattering by chain segments resulting in an exponential decay of the scattering field is called homodyne scattering. Contrary, cross-links behave as local oscillators and do not produce any decay of the scattering field. This non-decaying component heterodynes with the decaying part and is called heterodyne scattering.

  13. 13.

    For an ergodic system the long-time average is equal to the ensemble average – the average with respect to the configuration of the systems (average over all possible positions and shapes).

  14. 14.

    Contrast means a difference in NMR signals which enables us to identify and to observe a defined species in an ensemble of other species.

Abbreviations

AMTIR-1:

Ge33As12Se55 glass

ANN:

Artificial neural network

ATR:

Attenuated total reflectance

BaF2 :

Barium fluoride glass

CA:

Cluster analysis

CaF2 :

Calcium fluoride glass

CCD:

Charge-coupled device

CH3OD:

Per-deuterated methanol

D2O:

Deuterium oxide (heavy water)

DC:

Direct current

DLS:

Dynamic light scattering

EWF:

Equilibrium water fraction

FA:

Factor analysis

FESEM:

Field emission scanning electron microscopy

FPA:

Focal plane array

FT-IR:

Fourier transform infrared spectroscopy

GAR:

Grazing angle reflectance

Ge:

Germanium

IR:

Infrared

KBr:

Potassium bromide

LDA:

Linear discriminant analysis

MBAAm:

N, N’-methylene bisacrylamide

NMR:

Nuclear magnetic resonance

PAAc:

Poly(acrylic acid)

PCA:

Principal components analysis

PEG:

Poly(ethylene glycol)

PLS:

Partial least squares

PNIPAAm:

Poly(N-isopropyl acrylamide)

PVA:

Poly(vinyl alcohol)

PVME:

Poly(vinyl methyl ether)

PVP:

Poly(vinyl pyrrolidone)

RET:

Rubber elasticity theory

NMR:

Nuclear magnetic resonance

Si:

Silicon

UV:

Ultraviolet

Vis:

Visible

ZnS:

Zinc sulfide

ZnSe:

Zinc selenide

A :

Area

A0 :

Structure factor (RET)

a1 :

Correction term

B:

Volume factor (RET)

B 0 :

Static magnetic field power

B1 :

Intercept

c :

Concentration

c* :

Overlap concentration

d :

Diameter of gel cylinder

D :

Diffusion coefficient

D coop :

Cooperative diffusion coefficient

d p :

Depth of penetration

E :

Young's modulus

f :

Functionality of junction points

f :

Friction coefficient

f:

Force

F :

Free energy (intensive, with index)

G :

Gradient of magnetic field

G :

Free enthalpy (intensive, with index)

G :

Shear modulus

g (1)(t):

Electric field correlation function

g (2)(t):

Intensity correlation function

H :

Enthalpy

I F :

Scattering intensity for thermal fluctuations

k :

Cylinder diameter; disc thickness

K :

Bulk modulus

K(λ):

Hindrance of fluctuation (constraint function)

kB :

Boltzmann constant (1.381×10−23 J K−1)

m :

Mass

M :

Molecular weight

M c :

Molecular weight of network chain

n :

Number of moles

n :

Refractive index

n S :

Refractive index of the sample

nC :

Refractive index of the ATR crystal

N :

Number of molecules or particles

N 0 :

Number of monomers

NL :

Avogadro number (6.022×1023 mol−1)

p :

Pressure

q :

Scattering vector

q 2/3 :

Memory-term

Q :

Degree of swelling

Q m :

Mass degree of swelling

Q v :

Volume degree of swelling

R:

Gas constant (8.314 J K−1 mol−1)

r :

Radius

r:

Rocking vibration

R h :

Hydrodynamic radius

S :

Entropy (intensive)

s:

Scissoring vibration

T :

Tempereture

t :

Delay time

t:

Twisting vibration

T 1 :

Relaxation time

T 2 :

Relaxation time

T c :

Critical temperature

T g :

Glass transition temperature

t lag :

Time-lag

u:

Displacement

\( \overline {V_i} \) :

Partial molar volume of component i

V i :

Molar volume of component i

x,y,z:

Space coordinate

X P :

Fraction of dynamically scattered light

\( \langle \rangle \) :

Time average

\( {\left\langle I \right\rangle_{t,P}} \) :

Total time-averaged scattering intensity at a constant sample position

α:

angle of incidence

γ :

Gyro-magnetic ratio

Γ:

First cummulant

δ :

Deformation vibration

δ(u):

Displacement

Δ:

Total change

Δx:

Spatial resolution

Δω :

Width of resonance line

ηs :

Viscosity of solvent

Θ :

Theta condition

θ :

Scattering angle

λ:

Extension ratio relative to isotropic state of reference

λ0 :

Wavelength of the incident light

μ:

Poisson´s ratio

μ i :

Chemical potential of component i

μJ :

Number of junction points

ν :

Stretching vibration

ν :

Wavenumber

ν as :

Antisymmetrical stretching vibration

ν s :

Symmetrical stretching vibration

νc :

Cross-linking density (mol network chains / volume)

ξ:

Cycle rank

ξ:

Screening length

π:

Osmotic pressure, swelling pressure

σ:

Stress, force per area of un-deformed sample

τ :

Relaxation time

ϕA :

Volume fraction swelling agent

ϕ:

Volume fraction

χ:

Huggins interaction parameter

ω :

Resonance frequency of the signal

ω:

Wagging vibration

0:

Reference state

1:

Solvent

2:

Polymer

c :

Cross-linked

cr :

Critical

d :

Dry, unswollen

dry :

Dry state

el :

Elastic

exp :

Measured quantity

lo :

Longitudinal

m :

Medium intensity of the vibration mode

m :

Mixing

net :

Network

P :

Sample position

Q :

Swollen state

s :

Swollen

tr :

Transversal

u :

Uncross-linked

v :

Strong intensity of the vibration mode

VPT:

Volume phase transition temperature

vs :

Very strong intensity of the vibration mode

w :

Weak intensity of the vibration mode

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Acknowledgments

The author thanks M. Knörgen (Martin-Luther-Universität Halle) for the fruitful cooperation on application of NMR imaging on smart hydrogels, and R. Reichelt (Westfälische Universität Münster) for the FESEM micrograph.

Author information

Authors and Affiliations

  1. Department of Chemistry and Food Chemistry, Physical Chemistry of Polymers, TU Dresden, 01062, Dresden, Germany

    K.-F. Arndt & F. Krahl

  2. Leibniz Institute of Polymer Research Dresden, Hohe Straße 6, 01069, Dresden, Germany

    S. Richter

  3. Medical Faculty Carl Gustav Carus, Clinical Sensoring and Monitoring, TU Dresden, 01307, Dresden, Germany

    G. Steiner

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  1. K.-F. Arndt
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  4. G. Steiner
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Correspondence to K.-F. Arndt .

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Editors and Affiliations

  1. Fak. Elektrotechnik, TU Dresden, Helmholtzstr. 18, Dresden, 01069, Germany

    Gerald Gerlach

  2. Inst. Physikalische Chemie und, TU Dresden, Bergstr. 66 B, Dresden, 01069, Germany

    Karl-Friedrich Arndt

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Arndt, KF., Krahl, F., Richter, S., Steiner, G. (2009). Swelling-Related Processes in Hydrogels. In: Gerlach, G., Arndt, KF. (eds) Hydrogel Sensors and Actuators. Springer Series on Chemical Sensors and Biosensors, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75645-3_3

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