Atkins & de Paula:
Atkins’ Physical Chemistry 9e
Chapter 18: Materials 1:
Macromolecules and Self-Assembly
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 polymer, a compound formed by linking together small molecules.
 naturally occurring polymers; Proteins, Nucleic acids, Cellulose, Rubber
 synthetic polymers; Nylon, Dacron, Lucite
 monomer, the small molecules linked together to form a polymer.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
STRUCTURE AND DYNAMICS
 configuration, the structural features that can be changed only by breaking chemical
bonds and forming new ones.
 conformation, the spatial arrangement of the different parts of a chain.
18.1 The different levels of structure
 primary structure, the sequence of small molecular residues making up a polymer.
 polypeptide, a macromolecule formed from amino acids .
 peptide link, the group –CONH–.
 sequencing, the determination of primary structure.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 degradation, a disruption of primary structure.
 secondary structure, the (often local) spatial arrangement of a chain.
 denaturation, the loss of secondary structure.
 tertiary structure, the overall three–dimensional structure of a macromolecule.
 quaternary structure, the manner where large molecules are formed by the aggregation
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 protein structure; intermolecular forces in a protein molecule.
ionic forces
hydrogen
bonds
dispersion
forces
dispersion
forces
dispersion
forces
ionic forces
dipole-dipole
forces
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.2 Random coils
 random coil, a conformation in which neighboring groups adopt random angles to each
other.
 freely jointed chain, the simplest model of a random coil, a conformation in which
any bond is free to make any angle with respect to the preceding one .
Freely jointed chain
Constrained chain
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.2 (a) Measures of size
 probability that ends of a long 1-D freely
jointed chain (N units of length l) are a
distance nl apart (n = NR-NL),
1/ 2
2
 2 
n / 2 N
P 
 e
 N 
(Further information 18.1(a) & Problem 18.20)
 probability that ends of a long 3-D freely
jointed chain lie in the range r to r+dr, f(r)dr
3
 a  2 a 2r 2
f ( r )  4  1 / 2  r e
,




a

2
2
Nl


(Further information 18.1(b))
3
1/ 2
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 contour length, Rc, the length of a macromolecule measured along its backbone: Rc = Nl.
 root mean square separation, Rrms, the square root of the mean value of R2: Rrms = N1/2l.
N 1
 R   R  R  
2
 r
N 1
rj 
i
i, j
N 
  
 r
i
N 1
2

 r
i
rj
i j
i
N

2
 ri   Nl
2
i
 radius of gyration, Rg, the radius of a thin hollow spherical shell of the same mass and
moment of inertia as the molecule: Rg = (N)1/2l. (Justification 18.1 & Problem 18.16)
N
I 
mr
i i
i0
N
2
 m  ri  m tot R    
 R 
2
2
g
m tot  ( N  1 ) m
i0
 Rg for 3-D random coil: Rg = (N/6)1/2l. (Problem 18.17)
2
g
1
N
r

N 1
i
i0
2
  Nl
2
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.2 (b) Conformational entropy
 conformational entropy, the statistical entropy
arising from the arrangement of bonds:
ΔS = –½kNln{(1 + v)1+v(1 – v)1–v}, with v = n/N,
when a coil of N bonds of length l is stretched or
compressed by nl. (Justification 18.2)
18.2 (c) Constrained chains
 constrained chains, Rrms & Rg should be multiplied by F= [(1-cosθ)/(1 + cosθ)]1/2
18.2 (d) Partly rigid coils
 persistence length, lp; when first monomer-monomer direction is sustained.
lp 
R rms
r1
R 
1 N 1
l
2l p

1/ 2 
 N l 
 1 
 l

l
 r
1
 ri 
i0
1/ 2
(Further information 18.1(c))
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.3 The mechanical properties of polymers
 elastic deformation, strain is proportional to the stress and is reversible.
 plastic deformation, strain is not proportional to the stress.
 yield point, turning point from elastic to plastic deformation.
 elastomer, a polymer with a long elastic range.
 perfect elastomer, an elastomer where the internal energy is independent of the extension.
 restoring force of a perfect elastomer extended or compressed by nl is F = (kT/2l) ln {(1 +
v)/(1 – v)}  nkT/Nl when v << 1 (with v = n/N). (Justification 18.3)
dU  TdS  F dx
 U 
 S 

 T
 F
 x T
 x T
For perfect elastomer,
x  nl

 F  
 U 
 S 

  0  F  T 

 x T
 x T
T  S 
T  S 
kT  1  v 
ln 

 

 

l  n T
Nl   v  T
2l  1  v 
  S   12 kN ln{( 1  v )
1 v
(1  v )
1 v
}, where v  n / N
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 melting temperature, Tm, the temperature at which
a polymer melts.
 glass transition temperature, Tg, the temperature at
which a polymer undergoes a transition from a state
of high chain mobility to one of low chain mobility.
18.4 The electrical properties of polymers
 conducting polymer, a polymer with extensive conjugation and thereby conducts electricity.
 polaron, a partially localized cation radical in a polymeric solid.
 bipolaron, a di-cation version of a polaron.
 soliton, two separate cations that move independently in a polymeric solid.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.5 The structures of biological macromolecules
18.5(a) Proteins
 Corey–Pauling rules, a set of rules that account for the secondary structures of proteins.
1. C, O, N, and H lie in a relatively rigid plane.
2. N, O, and H of a H-bond lie in a straight line.
3. All NH and CO groups are engaged in H-bonding.
restricted rotation
 α-helix, a helical conformation formed by hydrogen bonding between peptide links.
 β-sheet, a planar conformation formed by hydrogen bonding between peptide links .
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 geometry of polypeptide, specified by φ and ψ
 Ramachandran plot, a contour diagram of the conformational energy in which one axis
represents φ and the other represents ψ.
nonchiral glycine
Right-handed α-helix (poly-L-glycine)
all φ = 570 and all ψ = -470
chiral L-alanine
Ramachandran plot
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 anti-parallel β-sheet, a β-sheet in which φ = –139o, ψ = 113 o, and the N–H–O atoms
of the hydrogen bonds form a straight line; very common in proteins.
 parallel β-sheet, a β-sheet in which φ = –119, ψ = 113 and the N–H–O atoms of
the hydrogen bonds are not perfectly aligned.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
The stability of proteins
 denaturation, the loss of their natural conformation.
 cooperative process, a process which becomes more probable the further it proceeds.
 melting temp., Tm, where the fraction of unfolded protein is 0.5.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.5 The structures of biological macromolecules
18.5(b) Nucleic acids
 polyelectrolyte, a macromolecule with many different charged sites and an overall charge.
 base stacking, the organization of the planar π systems of bases by dispersion forces
between them.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
tRNA
Chapter 18: Materials 1: Macromolecules and Self-Assembly
Aggregation & Self-Assembly
 Self–assembly, the spontaneous formation of complex structures of molecules or
macromolecules held together by molecular interactions.
18.6 Colloids
18.6(a) Classification and preparation
 colloid (disperse phase), a dispersion of small particles of one material in another.
 sol, a dispersion of a solid in a liquid or of a solid in a solid.
 aerosol, a dispersion of a liquid in a gas .
 emulsion, a dispersion of a liquid in another liquid.
 lyophilic, solvent attracting.
 lyophobic, solvent repelling.
 hydrophilic, water attracting.
 hydrophobic, water repelling.
 gel, a semirigid mass of a lyophilic sol in which all the dispersion medium has penetrated
into the sol particles..
 surfactant, a surface–active agent.
 electrodialysis, dialysis in the presence of an electric field.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.6(c) The electrical double layer
 radius of shear, the radius of the sphere that captures a rigid layer of charge around a
colloidal particle.
 zeta potential (electrokinetic potential), ζ, the electric potential at the radius of shear
relative to its value in the distant, bulk medium .
 electrical double layer, the inner shell of charge and the outer ionic atmosphere around a
colloidal particle.
 DVLO theory, a thery of the stability of lyophobic dispersions; balance between repulsive
interaction between the charges of the electrical double layers and the attractive vdW
interactions between the molecules in the particles.
Aa 
2
V repulsion 
V repulsion 
2
e
 s / rD
,
R
1
Aa 
2
V attraction  
B
s
2
ln( 1  e
  RT
where rD  
2

 2  F Ib
 s / rD
),



1/ 2
,
when a  rD
when rD  a
a: particle radius, A & B: constant, R: separation of
centers, s: R-2a, rD: thickness of double layer, I: ionic
strength, ρ: mass density, bΘ: 1 mol kg-1
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 flocculation, the reversible aggregation of colloidal particles at high ionic strength.
 coagulation, the irreversible aggregation of colloidal particles.
 Schultze–Hardy rule: hydrophobic colloids are flocculated most efficiently by ions of
opposite charge type and high charge number.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.7 Micelles and biological membranes
18.7(a) Micelles formation
 micelle, colloid–sized clusters of molecules.
 critical micelle concentration (CMC), the concentration above which micelles form .
 Krafft temperature, the temperature above which micelles form.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 surfactant parameter, Ns = V/Al (V: volume of hydrophobic tail, A: area of hydrophilic
head group, l: maximum length of tail)
 liposome, a vesicle with an inward pointing inner surface of molecules surrounded by an
outward pointing outer layer.
 lyotropic mesomorph, an orderly arrangement of micelles; a liquid crystalline phase.
 reverse micelles, form in nonpolar solvent
Chapter 18: Materials 1: Macromolecules and Self-Assembly
Impact on nanotechnology
 Self-Assembly of Mesoscopic Metal-Polymer Amphiphiles
S. Park et al., Science 2004, 303, 348.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.7(b) Bilayers, vesicles, and membranes
 fluid mosaic model, a model of a cell membrane in which the proteins are mobile but have
diffusion coefficients much smaller than those of the lipids.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.7(c) Self-assembled monolayers
 monolayer, a single layer of molecules on a surface.
 Langmuir–Blodgett film, a monolayer that has been transferred to a solid support.
 self-assembled monolayer (SAM), an ordered molecular aggregate that form a monolayer
of material on a surface.
Chapter 18: Materials 1: Macromolecules and Self-Assembly
DETERMINATION OF SIZE AND SHAPE
18.8 Mean molar masses
 monodisperse, a sample with a single, definite molar mass such as proteins.
 polydisperse, a sample with a wide range of molar masses such as synthetic polymers.
 number-average molar mass,
1
M 
 N M  M 
N
n
i
i
i
 viscosity-average molar mass, the average molar mass obtained from viscosity
measurements.
 weight-average molar mass, the average molar mass obtained from light-scattering
experiments:
NM
1
M 
M 
m M      M 


m
M 
NM
2
i
mi  N iM i / N A
W
i
i
i
2
i
W
i
i
i
i
 Z-average molar mass, the average molar mass obtained from sedimentation
measurements:
NM
3
i
M
Z

i

N iM i
M 
3
i
2

M 
2
Example 18.1
i
 heterogeneity index,
MW
Mn
M 
2

M 
2
Typical synthetic materials = 4
Monodisperse synthetic polymer < 1.1
commercial polyethene = 30
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.9 The techniques
18.9(a) Mass spectrometry M n , M W
 matrix–assisted laser desorption/ionization (MALDI), a laser-based technique for
ionization of macromolecules.
 electrospray ionization, another technique for ionization of macromolecules.
 MALDI-TOF mass spectrometry, a technique for the determination of molar masses of
macromolecules that combines MALDI and time-of-flight mass spectrometry.
trans-3-indoleacrylic acid (matrix)
+
NaCl, silver trifluoroacetate
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.9(b) Laser light scattering M W , R g
 Rayleigh scattering, the scattering of light by particles with diameters much smaller than
the wavelength of the incident radiation.
sin 
2
I ( ,  , r )  R ( ) I 0 
Rayleigh
ratio , R ( ) 
I ( ,  , r )
I0
2 n r
2
R ( )  Kc p M W , K 
N A
4
2

r
2
2
sin 
2
dn r
dc p
16  R g sin
2
structure
r
factor , P ( )  1  p ( ) with p ( ) 
2
3
2
2 1
2

Chapter 18: Materials 1: Macromolecules and Self-Assembly
1
R ( )
1
R ( )
1
R ( )


1
KP ( ) c p M W
1
Kc p M W

1
Kc p M W

1

Kc p M W 1  p ( ) 
p ( )
R ( )
 a
(1  x )
sin
p ( )
Kc p M W
2 1
2

R ( )

p ( )
R ( ) / P ( )
p ( ) P ( )

R ( )
16  R g
2
a 
1
3

1
1  x
   
R ( )
p ( )( 1  p ( ))
R ( )
1

Kc p M W
p ( )  p ( )
2

R ( )

1 
p ( )  
1
Kc p M W

p ( )
Kc p M W
p ( )
R ( )
2
2
Rg
MW
Example 18.3
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.9(c) Sedimentation M n , M W
 sedimentation, the settling of particles to the foot of a column of solution.
 ultracentrifugation, a sedimentation technique in which particles move under the
influence of a centrifugal field.
effective mass , m eff  bm , b  1   v s (  : solution density , v s : partial specific volume of solute )
 drift speed, a constant speed through a medium when the driving and retarding forces are
balanced.
2
2
s  dr / dt , sf  m eff r   s 
2
m eff r 
f

bmr 
f
( f : frictional coefficien t )
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 sedimentation constant
S 
s
r
2

bM
n
bM
Stokes ' relation , f  6  a 
       S 
fN A
n
6 a  N A
( a : radius ,  : vis cos ity of solvent )
dr
 r S
2
dt
S  Mn
ln
r
  St
2
r0
Example 18.4
 sedimentation equilibria, the equilibrium distribution of particles in a gravitational or
centrifugal field.
MW 
2 RT
( r2  r1 ) b 
2
2
2
ln
c2
c1
( Justificat ion 18 . 5 )
Chapter 18: Materials 1: Macromolecules and Self-Assembly
18.9(d) Viscosity M V
 intrinsic viscosity, the coefficient [η] in η = η0(1+ [η]c + ).
 Ostwald viscometer, a device for measuring viscosity from the time taken for a solution to
flow through a capillary and compared with a standard sample..
 rotating rheometer, a device for measuring viscosity that consists of rotating concentric
cylinders.

o

t

t0
Ostwald viscometer

0
rotating rheometer
Chapter 18: Materials 1: Macromolecules and Self-Assembly
 Mark–Kuhn–Houwink–Sakurada equation for the intrinsic viscosity in terms of the
a
molar mass.
[ ]  K M V
[ ]  lim (
c 0
 0
c 0
)  lim (
Example 18.5
[ ]  M V
c 0
 / 0  1
c
)