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Surface and Interface Chemistry

Rheology
Valentim M. B. Nunes
Engineering Unit of IPT
2014
Rheology: Study of deformation and flow of matter
Rheo = Deformation
Logia = Science or Study
The rheological studies allow to characterize colloid systems,
namely colloidal dispersions and emulsions. The technological
importance of rheology is manifest in areas such as rubbers,
paints, textiles, pulp, etc.
The rheological behavior depends on :
 Viscosity of the dispersant phase
 Concentration of particles
 Particle size and shape
 Molecular interactions
Importance of the rheological studies (examples)
Production of paint: the paint should be easy to spread and do
not seeping through the walls.
Cosmetics and hygiene: how a cream spreads or the time it took
to flow from a recipient.
Stability of emulsions or
suspensions.
Viscosity: the viscosity of a liquid measures the resistance offered
to flow. A liquid is Newtonian when the tangential force per unit
area between two parallel planes of fluid is proportional to the
velocity gradient.
  D
Viscosity coefficient.
Methods of measurement
Capillary method (Ostwald, Ubbelohde)
  k t
1 1t1

 2  2t 2
Rotational method (Couette viscometer)
Particularly useful for non-Newtonian fluids.
 
k

 - angular velocity of the
outer cylinder.
 - angular deflection of
the inner cylinder.
Viscosity of dilute solutions and colloidal dispersions
Concepts:
0 - viscosity of pure solvent or dispersant phase
 - viscosity of the dispersion
/ 0 - relative viscosity


i    1 - increment of the relative viscosity
 0 
i /c - reduced viscosity
Spherical particles, hydrodynamic calculation:
Einstein:
  0 1  k 
 - volume fraction
k =2.5
   0 1  2.5 

 1  2.5
0
i  2.5
Solvation and asymmetry: the term  must also include the solvent
which kinetically acts as part of the particles. The asymmetry of
particles also has a great effect on viscosity.
Intrinsic viscosity
   lim
C 0
i
C
The Intrinsic viscosity has inverse concentration units.
Determination of relative molecular weight of polymers from
measurements of viscosity.
Viscosity measurements cannot be used to distinguish between
particles of different sizes but with the same format and degree
of solvation. However, if the format (configuration) or solvation
factor change with the size of the particle, then viscosity can be
used to determine the size of the particles.
The intrinsic viscosity of a polymer solution is proportional to
the molar mass. If the orientations of the macromolecular chain
are random:
   kM
0.5
r
Linear polymers in solution are more than oriented at random,
and the relationship is (Mark and Houwink):
   kMr

 - depends on the configuration.
The following viscosities were measured for solutions of cellulose
acetate in acetone, with concentration of 0.5 g/100 cm3:
10-3 Mr
/10-4 Pa.s
85
5.45
138
6.51
204
7.73
302
9.40
The viscosity of acetone at this temperature is 3.2×10-4 Pa.s
Derive an expression from these data that permits the routine
determination of the relative molar mass of samples of cellulose
acetate. What additional information from this expression?
Shaw, Introduction to Colloid and Surface Chemistry, 4th ed., ButterworthHeinemann, Oxford, 1991
log i / c  log k   log M r
log Mr
4.93
-0.85
log i/c
5.14
-0.69
log viscosidade
-0,3
5.31
-0.55
   1.6 10
y = 0,7998x - 4,7946
R2 = 1
-0,6
5.48
-0.41
5
0.8
r
3
M m kg
1
The average configuration of
polymers is between random
and extended.
-0,9
4,8
5
5,2
log Mr
5,4
5,6
The viscosity of a range of solutions of polystyrene in toluene
were measured at 25 °C:
c/g.L-1
 /10-4 kg.m-1.s-1
0
5.58
2
6.15
4
6
6.74 7.35
8
7.98
10
8.64
Calculate the intrinsic viscosity and estimate the molar mass of
polymer knowing that in the Mark-Houwink equation,
k = 3.8×10-5 L.g-1 and  = 0.63
Atkins, Physical Chemistry, Oxford University Press, Oxford, 2006
c/g.L-1
2
5.11
100(/0 -1)/c
4
5.20
8
5.38
10
5.49
   0.0504L.g 1
5,6
viscosidade intrinseca
6
5.28
5,4
   
M  
 k 
1/ 
y = 0,0011x 2 + 0,0341x + 5,04
R2 = 0,9993
5,2
5
0
5
10
c (g/L)
15
 90 103 g .mol 1
Newtonian and non-Newtonian behavior
In some fluids, viscosity depends on the applied tension or the
time of they application. For these fluids, viscosity is no more a
constant for becoming a property dependent on the conditions
under which the fluid is deformed or under tension. In this case,
the viscosity of the fluid is called apparent viscosity
Fluids
Newtonian
Non Newtonian
Non- Newtonian behavior (independent of time)
Dilatant behavior: when the apparent viscosity increases with the
application of a force (corn starch in water).
viscosity
tension
Pseudo plastic behavior: when the apparent viscosity decreases
with the application of a force (creams, ointments, etc.)
Velocity gradient
1. Dilatant; 2. Newtonian; 3. Pseudo plastic
Viscoplasticity or Bingham Fluids
tension
Fluids characterized by the existence of a value of tension that
must be exceeded so that the material presents a viscous flow. It is
necessary that the force exceeds this limit for seepage occurs
(tomato sauce, etc.)
Velocity gradient
Thixotropy and Antithixotropy (time- dependent)
Certain materials present change of viscosity when the applied
voltage is maintained for a certain time.
Thixotropy: when the viscosity decreases with time of application
of force and retrieves the initial state after prolonged rest (paints,
oils, yogurt, etc.)
Antithixotropy or Rheopexy: when the viscosity increases with
time.
World’s Longest Running Laboratory Experiment – The Pitch Drop
Experiment
Pitch – derivative of tar. At room
temperature feels solid and can be
shattered with a blow of a hammer.
This experiment shows that in fact at
room temperature pitch is a fluid!
http://www.physics.uq.edu.au/physics_museum/pitchdrop.shtml