Water structure and science

(http://www1.lsbu.ac.uk/water/rheology.html)

There are two rheological properties of particular importance to hydrocolloid science. These are their gel and flow properties.

Viscosity

Viscoelasticity

Structural effects

Further rheological terminology

Viscosity is a property of fluids that indicates resistance
to flow. When a force is applied to a volume of material, then
a displacement (deformation) occurs. If two plates (area,
A), separated by fluid distance (separation height, H) apart,
are moved (at velocity V by a force, F) relative to each other,
Newton's law states that the **shear stress** (the force divided by area parallel to the force, F/A, Pa) is
proportional to the **shear strain rate** (V/H, s^{-1} ).
The proportionality constant is known as the (dynamic) **viscosity** (η, Pa ˣ s ).

The effect (**shear strain**)
is quantified by the displacement per unit height (D/H)
and the rate of this effect (**strain rate**)
is the velocity per unit height (V/H), where the height
is the distance to a relatively unaffected position. The
viscosity (η)
is the tendency of the fluid to resist flow and is defined
by:

Increasing the concentration of a dissolved or dispersed substance generally gives rise to increasing viscosity (that is, thickening), as does increasing the relative molecular mass (molecular weight) of a solute.

With Newtonian fluids (typically water and solutions containing only low molecular mass material) the viscosity is independent of shear strain rate and a plot of shear strain rate (for example, the rate of stirring) against shear stress (for example, force, per unit area stirred, required for stirring) is linear and passes through the origin.

At moderate concentrations above
a critical value (C*, [244]), hydrocolloid solutions exhibit non-Newtonian behavior where
their viscosity depends on the shear strain rate. It is shown typically
as opposite, where γ is the shear strain rate, η_{0} and η_{∞} are the viscosities at zero and infinite shear strain rate
respectively, and τ is a shear-dependent time constant that represents the reciprocal
of the shear strain rate required to halve the viscosity.

The exponent (m) gives the degree of thinning
(0 = no thinning, that is, Newtonian behavior; 1 = maximal
thinning; < 0 = shear thickening) and determines the slope
of the graph (that is, the slope is greater when m is
greater). The equation is one of a number of empirical relationships
that can be used. The viscosity depends on the cross-sectional
area in the direction of flow. At low flow rates, molecules
with preferred conformations that are long and thin have effectively
large cross-sections due to them tumbling in solution but
at high shear strain rate, the molecules align with the flow,
giving much smaller effective cross-sections and hence much
lower viscosities (see red line (a) above). More compact molecules are not so much affected
by their orientation relative to flow and, hence their viscosity
changes little with shear strain rate (see blue
line (b) above representing a solute with the same
molecular volume but more compact shape). The gradient of
the central linear part of the above log-log curve is equal
to minus the exponent (-m); 1-m is the behavior index (n)
also given by the exponent in the Ostwald relationship: shear
stress is proportional to the shear strain rate to the
power n (that is, shear stress = k γ^{n}).
A value for n of unity indicates Newtonian behavior, increasingly
non-Newtonian behavior results in a lowering in this behavior
index towards zero (for example, 0.25% xanthan solution has n = 0.4). [Back to Top ]

Many hydrocolloids are capable of forming gels of various strength dependent on their structure and concentration plus environmental factors such as ionic strength, pH and temperature. The combined viscosity and gel behavior (viscoelasticity) can be examined by determining the effect that an oscillating force has on the movement of the material.

With viscoelastic hydrocolloids, some of the deformation caused by shear stress is elastic (for example, the contortion of the chains into high energy conformations) and will return to zero when the force is removed. The remaining deformation (that is, the sliding displacement of the chains through the solvent) will not return to zero when the force is removed. Under a constant force the elastic displacement remains constant whereas the sliding displacement continues, so increasing.

If the force varies sinusoidally with time, then the viscous (sliding) energy is always positive and lost as heat whereas the changes in the elastic energy may be positive or negative and are recouped.

Under such conditions, the shear strain rate lags behind the changes in the causative force by a phase angle φ. φ is zero for an ideally elastic gel (all energy stored in the material) and 90° for an ideally viscous liquid (all energy dissipated as heat).

shear stress = shear strain ˣ sin(ωt + φ)

Solids respond with very short delays in the output response (φ very small) whereas liquids have greater delays. In real solutions, the shear stress wave may not keep the shape of the strain rate [2913].

It is convenient
to express the relationship between the shear stress, elastic
stress and viscous stress (resulting from changing stress)
in terms of a complex number (= i) where the
viscous stress is in-phase and the elastic stress is out-of-phase
and oppositely-directed.^{a}

**shear stress = viscous stress - i ˣ elastic stress
complex viscosity = viscosity - i ˣ elasticity**

**tan(φ)
= elasticity/viscosity**

The shear modulus (resulting from changing strain) is the ratio of the shear stress to the shear strain. It follows from the complex relationship similar to the above that:

**G* = G' + iG''**

where G* is the complex shear modulus, G' is the in-phase storage modulus and G'' is the out-of-phase
similarly-directed loss modulus; G* = √(G'^{2 } + G''^{2}).
The frequency where these parameters cross over corresponds
to a relaxation time (τ)
specific for the material.

It follows that,

**tan(δ)
= G''/G'**

where tan(δ) quantifies the balance between energy loss and storage.

As tan(45°) =1, a value for tan(δ) greater than unity indicates more "liquid" properties, whereas one lower than unity means more "solid" properties, regardless of the viscosity. [Back to Top ]

Linear and substantially linear
polymers behave in a qualitatively predictable way with respect
to the relationship of their viscosity to their structure and conformation.
In dilute solutions, this relationship depends effectively on the
volume "swept out" (that is, the hydrodynamic volume)
by the molecules as they tumble in the solution. At these low concentrations,
where there is effectively no interaction between molecules and
they are at their most extended, the viscosity may be little
different from that of water;
this small difference depending on the total spherical volume (itself
dependent on concentration and radius of gyration of the solute) taken up by the freely rotating molecules. The relationship
between viscosity with concentration is generally linear up to viscosity
values of about twice that of water. This dependency means that
more extended molecules increase the viscosity to greater extents
at low concentrations than more compact molecules of similar molecular
weight. Generally, less-flexible links between sequential monomers
in the polymeric chains give rise to more extended structures but
the linkage spacing, direction and charge density are all important
factors. The molecules most capable of an extended structure, due
the maximal linkage spacing and direction are -(14)-di-equatorially
linked between pyranose residues whereas those least capable
contain -(13)-diaxially linked pyranose
residues. Where residues are negatively charged, the repulsion between
similar charges increases molecular extension but this can be reduced
at higher ionic strength or below the pK_{a}'s of the anionic
groups and this reduction is particularly noticeable for polymers
with high molecular mass. The lack of much change in viscosity
of such molecules with ionic strength is indicative of an inflexible
rod-type conformation. It should be noted that although attaching
short sugar units as branch-points to linear polysaccharides does
increase their rigidity into an extended structure, this is at the
cost of greatly increased molecular mass.

The extended nature
of the molecules has an extreme effect on the molecular mass dependency
of the viscosity. This is as the hydrodynamic volumes (and hence viscosities)
of compact (highly flexible but poorly hydrated) molecules increase
approximately as the cube root of their molecular mass, whereas
those of more-extended well-hydrated molecules (such as alginate and xanthan gum) increase approximately
linearly with molecular mass. The relationship between the intrinsic
viscosity [η]
and the relative molecular mass (M_{w}) is given by [η]
= K M_{w}^{a}, the Mark-Houwink equation where
K and a are constants. Amylose, carboxymethylcellulose, arabinoxylans, and guar all have exponents (a) of about 0.7. Knowledge of these constants
allows the viscosity-averaged molecular mass to be calculated
from viscosity data.

The viscosity increases with concentration until the shape of the volume occupied by these molecules becomes elongated under stress causing some overlap between molecules and a consequent reduction in the overall molecular volume with the resultant effect of reducing the amount that viscosity increases with concentration (under stress).

At higher concentrations (above
a critical concentration C*), all the polymer molecules in
the solution effectively overlap, interpenetrate, and become
entangled (that is, their total hydrodynamic volume appears
greater than the solution volume) even without being stressed.
This changes the solution's behavior from mainly viscous to mainly
elastic with the viscosity (η_{0} at zero stress) being mainly governed by the mobility of the
polymer molecules. C* will depend on the shear strain rate
as, at high shear strain rate, the molecules take up a less
voluminous shape. At higher concentrations, the viscosity increases
up to about the fifth power of the concentration, and this
can cause apparently synergic behavior of hydrocolloid mixtures,
particularly if they cause phase separation with its inherent
concentration increases.

At high shear strain rate (and sufficient concentration), molecules may become more ordered and elastic. Shear flow (and its related stress) causes molecules to become stretched and compressed (at a right angle to stretch) resulting in isotropic solutions becoming anisotropic. After release from such conditions, the molecules relax back with time (the relaxation time). At low concentrations below the critical value (C*), the shear modulus of hydrocolloid solutions is mainly determined by the loss modulus at low frequencies (that is, G'' is relatively high for viscous materials). As G'' depends on the frequency but G' depends on the square of the frequency, G' becomes more important at higher frequencies. At higher concentrations in viscous solutions, G' is generally greater than G'' throughout a wide frequency range. This difference is very large for strong gels when the frequency has an almost negligible effect (that is, G' is high for elastic materials). Such gels often form above another critical concentration specific to the hydrocolloid, where junction zones occur so stabilizing intermolecular associations. [Back to Top ]

** Dilatancy** (**shear thickening**) shows an
increase in viscosity with shear stress and strain due to structural
enhancement. An example is uncooked cornstarch paste where shear stress squeezes the water from between the starch
granules allowing them to grind against each other. This property
is often used in sauces where, for example, tomato sauce flow
is prevented under small shear stress but then catastrophically
fails, producing too great a flow, under greater stress (shaking).
Another (and the strictly correct usage for the term) meaning for
dilatancy concerns the increase in the volume of suspensions of irregular
particles with shear due to the creation of small but empty cavities
between the particles as they scrape past each other.

**Dynamic viscosity** is the commonly used form of viscosity, often abbreviated to just **viscosity **

The units are either the** **SI units of pascal seconds (Pa ˣ s) or the poise (P = 0.1 Pa ˣ s).

**Eutectic point **is the lowest possible melting point (equilibrium freezing point) that a mixture of solutes may have. No other mixed composition of the same materials will have a lower melting point. Thin films of fluid may remain below the eutectic point in microcrystalline ice due to surface effects [1010].

**Fluidity** is the reciprocal of the
viscosity (= 1/η).

The **glass
transition temperature** (T_{g}) is the temperature at which the molecular relaxation time reaches 100 s, and the viscosity of the system becomes 10^{12} Pa ˣ s. It is a time-temperature kinetic transition rather than a thermodynamic transition and different methods of cooling produce slightly different glass transition temperatures. Usually, there are discontinuities in physical, mechanical, electrical, thermal, and other properties of the material. Therefore, the
value of T_{g} depends somewhat on the method
of its determination; the glass transition (unlike true thermodynamic phase
changes) occurring over a range of a few Kelvin. In the
diagram, the supersaturated solution is unstable with
respect to the solution and the crystalline solid. Further discussion
of this topic may be found in a review of water and solids
mobility in foods [720].

**Intrinsic viscosity** ([η])
is the limit of the reduced viscosity extrapolated
to zero concentration. As with the reduced viscosity, it has units of reciprocal concentration, for example, mL g^{-1}.

**Kinematic viscosity** is the dynamic viscosity divided by the density
of the liquid (= η/ρ).
The units are either the** **SI units of meter squared per second (m^{2} ˣ s^{-1})
or the stoke (St).

**Poise** (P) is
a unit of dynamic viscosity (dyne ˣ s ˣ cm^{-2}). The SI unit of viscosity is Pa s (pascal second = N ˣ s ˣ m^{-2} =
10 poise).

**Pseudoplastic**
materials instantaneously decrease in viscosity with an increase in
shear strain rate (for example, flow) and are therefore easier
to pump and mix. They are **shear-thinning**. This
is often a consequence of high molecular mass molecules being
untangled and oriented by the flow. Generally, this behavior increases
with concentration.

**Radius
of gyration** (R_{g})_{ }is defined
as

where n is the number of entities in the chain, and r_{i} is the radius of each from the center of mass (also defined
using the distance between all pairs of entities ).

Typically for a linear polysaccharide (M_{w} 10^{6}), this would be approximately 6 nm if spherically
packed

(),
940 nm if as an extended stiff rod (),
and 17 nm ()
if as a random coil. Its relationship to the effective radius the
tumbling molecule represents to a flowing liquid (hydrodynamic radius,
R_{h}) depends upon the flexibility and density of the structure;
R_{g}/R_{h} generally being about 1.6 but
lower for branched and globular structures and gels.

**Reduced viscosity** (η_{red})
is the specific viscosity divided by the concentration. It has units
of reciprocal concentration, for example, mL g^{-1}. It
is related to the intrinsic viscosity [η]
by the Huggins-Kramer equation: η_{red} = [η] + k_{1}[η]^{2}c, where c is the concentration.

**Relative viscosity** (η_{rel})
is the ratio of the dynamic viscosity of
the solution to that of the pure solvent (η_{rel} = η/η_{0} where η is the dynamic viscosity of the solution, and η_{0} is the dynamic viscosity of the solvent). As it is a ratio,
it is dimensionless having no units. It is related to the intrinsic viscosity [η]
by the Huggins-Kramer equation:

ln(η_{rel})/c = [η] + k_{2}[η]^{2}c where c is the concentration.

**Shear stress** is the force divided by area parallel to the force, F/A. The SI unit is the pascal, Pa.

**Specific viscosity** (η_{sp})
is one less than the relative viscosity (η_{sp} =_{ }η_{rel} -1; η_{sp} = (η - η_{0})/η_{0} where η is the dynamic viscosity of the solution and η_{0} is the dynamic viscosity of the solvent). As with the relative
viscosity, it has no units.

**Stoke** (St) is
a unit of kinematic viscosity (cm^{2} ˣ s^{-1}). The SI unit
of kinematic viscosity is m^{2} ˣ s^{-1} ( =
10000 stoke).

**Thermogelling** materials gel above a temperature; usually reversible.

**Thixotropic** liquids
exhibit a time-dependent response to shear strain rate over a longer
period than that associated with changes in the shear strain rate.
They may liquefy on being shaken and then solidify (or not) when
this has stopped.

^{a} See a similar
treatment of dielectric [Back]

(c) Martin Chaplin 10 January, 2019

(printed 16 February 2019)