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Chapter I Biophysics - States of Matter

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I – The three states of matter.
 A single body may exist in three different physical states: gaseous, liquid
and solid.
 The existence of these three states is due to the balance between
intermolecular forces and the molecular agitation which tends to separate
them from each other and to allocate them randomly.
 If the average energy of agitation is much higher, same order of magnitude,
or smaller than the average energy of interaction between molecules, the
body is a gas, liquid or solid respectively.
1- Molecular Agitation
 The idea of molecular agitation was suggested by the existence of Brownian
motion.
 If we look to an aqueous suspension of fine particles, pollen grains for
example, through the microscope we see that each particle moves tirelessly
in all directions. The movement is essentially irregular. The speed and range
of motion depend on the particle size (they are inversely proportional to it).
 This permanent agitation of the molecules, called thermal agitation is most
complex in the case of fluids (gas and liquid) because it combines
translation, rotation of the molecule around its center of gravity and
vibration of atoms within the molecule itself.
 In a gas, the distance traveled by a molecule as a result of thermal agitation,
before colliding with another, is very large compared to the molecular
volume.
 In a liquid, it is of same order of molecular dimensions.
 In a solid, the molecules can just oscillate with small amplitude.
2- Binding forces between molecules.
 Some properties of liquids, solids and gases depend on the existence of




molecular interaction forces.
For example, increasing the magnitude of these forces in a real gas explains
why it doesn’t strictly follow the laws of ideal gas under high pressure.
These forces do not lead to the formation of chemically stable compounds.
They only intervene on certain physical properties such as boiling, viscosity
or surface tension.
Finally, they all are of electrostatic nature.
According to the value of the binding energy (potential energy of
interaction), we differentiate:
- The forces of Van der Waals (< 8kJ/mol)
- The hydrogen bond (8 to 50 kJ/mol)
a- The forces of Van der Waals :
They consist of three aspects and their effects are cumulative:
- The interaction of Keesom which occurs between two neighboring polar
molecules.
 Due to their permanent dipole moment, when these two molecules are close
and in a positive direction, they attract each other by their ends of opposite
signs.
 Keesom proved that the binding potential energy has the following form:
2 1
4
Uk  
2
3 4 0  r 6 kT
Where r is the average distance (in meters) between two molecules, µ their dipole
moment (C.m), T the temperature in K and k the Boltzmann constant (k = 1.3805 1023 J.K-1).
From the formula any increase in temperature, promoting molecular agitation
decreases this kind of interaction.
- The interaction of Debye which occurs between a polar molecule and a
nonpolar one.
 The permanent dipole moment of the polar molecule, influencing the
electronic distribution of nonpolar molecule, induces its polarization. The
two dipoles can interact as previously.
 Debye proved that the binding potential energy has the following form:
1 2 2
UD  
4 0 r 6
Where α is the polarizability of the nonpolar molecule, µ its dipole moment.




- The interaction of London which occurs between two nonpolar
molecules.
The intermolecular binding energy is greater than the sum of the two
previous ones. Thus, there exists a third type of interaction.
At certain time, as a result of the continual movement of electrons around
the nucleus, the centers of masses of positive and negative charges may no
longer coincide, giving a polar structure to the molecule.
This instantaneous dipole is then able to induce a second dipole on
neighboring molecule and in the favorable cases to interact with it.
The binding potential energy is of the following form :
3 1 I 2
UL  
4 4 0 r 6
Where I is the instantaneous dipole moment.
b- Hydrogen bonds
 It is also an electrostatic interaction of dipole-dipole between:
- On one hand, hydrogen linked by a strong bond (covalent) to
another strongly electronegative atom. (F, O, N…)
- On the other hand, another electronegative atom.
 The energy is slightly higher than a bond of Van der Waals.
 Due to its high electronegativity, the oxygen atom attracts partially the
electrons of the bond. A partial positive charge appears on the hydrogen
atom that can attract a lone pair of another neighbor oxygen atom.
II-
The gaseous state.
 The gases are fluids which have no form or specific volume.
 Their molecules are in continuous fast motion.
Noting that their direction varies as a result of
intermolecular collisions and collisions with the container's
walls which limit them. These shocks are the source of the
pressure exerted by a gas on the walls.
Summary of macroscopic laws of gases
-Mariotte law : PV = RT. It only applies properly to gases approaching the
ideal gas (gas of low molecular weight, low pressure and high temperature)
if not, the real gases obey the law of Van der Waals.
a 

 P  2 V  b   RT
V 

a
 P
2
V
Internal pressure of a real gas or cohesion pressure
b is the covolume : The free volume v available for molecular motion is
less than the volume V occupied by gas. We call covolume the
difference b between V and v :
v = V - b.
-Law of Gay-Lussac : At constant volume PT-1 = cte
T 

P  P0 1 

273
.
15


-Law of Charles : At constant pressure VT-1 = cte
T 

V  V0 1 

273
.
15


-Law of Avogadro: At constant temperature and pressure, one mole of gas
occupies the same volume regardless of the gas. At normal temperature and
pressure (0°C et 1 Atm) this volume is 22.4 L.
-Law of Dalton: The pressure of a mixture of gases is equal to the sum of
partial pressures that the gases would exert if each separately occupied all
the available volume.
RT
Pi  ni
V
P   Pi
i
Mole fraction :
i 
ni
 ni
Pi   i P
-Law of Henry (gas solubility):
At equilibrium, the concentration C of a gas dissolved in a liquid is
proportional to the partial pressure « p » of the gas above the liquid:
C=kp
The constant k depends on the gas/liquid couple and varies with temperature.
III- The solid state
The solid state is a condensed state characterized by its rigidity.
1- The organization of solid.
ab-
Crystals (See Inorganic Chemistry course)
Glasses (See Inorganic Chemistry course)
c- Polymers

These are natural organic compounds (cellulose, starch rubbers,
proteins such as Keratin or collagen) or artificial (polyamides (nylon),
polyesters (tergal), polyvinyl, silicones).

Crystalline structure can be observed, but more often they are
organized in long chains more or less parallel and associated with each
other.

The mechanical properties of these solids (particularly their plasticity)
vary greatly with molecular structure.
d- The composite solid

Many solids found in nature or manufactured combine crystals,
glasses and polymers.

This is for example the case of cartilage composed of a glassy
substance (mucopolysaccharides of fundamental substance)
reinforced by polymer fibers (collagen).

The cartilage is therefore flexible and malleable. During the
growth, crystals of calcium phosphate impregnate the fundamental
substance. The cartilage becomes a bone stronger and stiffer.
2- Cohesive forces.
Whatever the structure of the solid is, their cohesion is ensured by the
interatomic or intermolecular forces according to their nature, we
differentiate:
 Atomic or covalent crystals (diamonds). All atoms are joined together by
strong covalent bonds.
 Ionic crystals; electrostatic forces.
 Metallic crystals; atoms are linked together with all the delocalized
electrons in the metal.
 Molecular crystals; force of Van Der Waals and hydrogen bonds.
 Cohesion of glasses and polymers is provided by covalent and Van Der
Waals bonds.
3- Electrical properties of crystals.
See Inorganic chemistry course (Insulator, conductor, semi-conductor….)
IV- Liquid state
The liquid state is considered to be the intermediate between gaseous
and solid states. It has properties in common with each of them: it’s a fluid
like gases (liquid also obeys the same equation of Van der Waals than its
vapor); it’s a condensed state like solids (intermolecular distances are very
small).
V-
The liquid crystalline state
We could manufacture ultrathin and flexible screens for computers and
televisions with a kind of material which seems to be neither solid nor
liquid.
Liquid crystals are substances that flow like viscous liquids, but whose
molecules are arranged almost like those of a crystal.
These substances are an intermediate state of the matter (mesophase state)
with the fluidity of a liquid and the molecular order of a solid.
The typical molecules of liquid crystals are long molecules in the form of
bars, an example is p-azoxyanisol :
H3C
O
N
O
N
O
CH3
 The bar shape allows the molecules to stack over each other like raw
spaghetti. They are parallel, and they can slide over each other in the
direction of their long axis.
 Because of this order, the liquid crystals are anisotropic. The properties of
anisotropic material depend on the direction in which the measurement is
made.
 The viscosity of liquid crystals is minimal in the parallel direction to that of
molecules. It takes less energy to their long molecules in the shape of bars
to slide over each other in the direction of axes, rather than rolling over each
other in the perpendicular direction.
 Isotropic material properties do not depend on the direction of
measurement. Ordinary liquids, for example, are isotropic: the viscosity is
the same in all directions.
 Liquid crystals become isotropic liquids when heated beyond a certain
temperature because their molecules will have enough energy to overcome
the attractive forces which restrict their movements.
There are three kinds of liquid crystals which differ in the
arrangement of their molecules:
 In a nematic phase (Greek word meaning thread),
molecules are placed next to each other, but they are
shifted like cars on a multi-line highway.
 In a smectic phase (Greek word meaning soapy, lamellar), the
molecules are lined up like soldiers on parade, and form layers.
 In a cholesteric phase (cholesterol is a Greek term meaning
solid bile), the molecules form nematic layers, but molecules of
two adjacent layers are oriented in different directions, so that
the arrangement of molecules in the liquid crystal is helical.
a)smectic liquid crystal, b) nematic liquid crystal,
c) Helical nematic liquid crystal (cholesteric)
We can also classify the liquid crystals according to their mode of
preparation:
 Thermotropic liquid crystals are obtained by melting a solid phase.
The liquid crystal phase exists in a temperature range between the
solid and liquid phase. p-azoxyanisol is a thermotropic liquid
crystal.
Thermotropic liquid crystals are very viscous and can be translucent
or opaque. They are used in watches, computer screens and
thermometers.
 Lyotropic liquid crystals result from the action of a solvent on a solid such
as: cleaning solutions, lipids (fat) and cell membranes.
These molecules like lauryl sulfate (C12H25OSO3- Na+ a detergent) are
composed of nonpolar long chains of hydrocarbons having a polar end.
OSO3- Na+
 Dilute solutions of detergents (or surfactant) tend to form layer on
the surface of water. The detergent molecules are aligned next to
each other at the surface of water with their polar heads in water and
their nonpolar tails in the air.
 At high concentrations, the detergents form micelles, small clusters
where the polar heads of the micelles link to water outside of the
micelle, and the hydrocarbon tails towards the interior of the micelle.
The hydrocarbon tails of the detergent molecules are
attracted by fat impurities and surround them by a
micellar structure.
The polar heads, at the outer surface of the micelle,
allow it to remain suspended in the water and
consequently gather fats.
Lipids which form cell membranes are structurally similar to
that of micelles. When mixed with water, they spontaneously
form very thin layers where the molecules are aligned in rows
and form a double layer. The polar heads are directed outwards,
on both sides of the double layer.
These sheets (double layer) form the protective membranes of
our cells.
 Electronic displays use the fact that the orientation of liquid crystal
molecules changes in the presence of an electric field.
 This reorientation causes a variation in their optical properties which make
them opaque or transparent, creating as well a drawing on the screen.
 The interest of cholesteric liquid crystals is that their helical structure
unfolds when the temperature varies slightly. As the torsion of their helical
structure affects their optical properties, these will vary with temperature;
this fact is used in liquid crystal's thermometers.
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