nanoscale physics and modelingmaeresearch.ucsd.edu/~arya/lecture1.pdf · 2010-01-10 · nanoscale...
TRANSCRIPT
1
Nanoscale Physics and Modeling
Lectures: Tue and Thu, 5:00-6:20pm HSS 1138
Instructor: Gaurav Arya, Assistant Professor of
Nanoengineering [[email protected]]
URL: http://maeresearch.ucsd.edu/arya/MAE207.html
Office hours: 5pm Friday, #2304 Atkinson Hall
Grading: 50% Homework assignments and 50%
Computer assignments
2
Course Syllabus
Intra and intermolecular interactions: ionic, covalent, and metallic bonding; van der Waals, charge-charge, charge-dipole, and dipole-dipole, hydrogen bonding, pi-pi stacking, and hydrophobic interactions
Molecular mechanics: mathematical description of molecules and their interactions (force fields)
Energy minimization: Simplex, Newton Raphson, steepest descent, conjugate gradient, simulated annealing
Statistical mechanics: ensembles, Boltzmann distribution, partition function, entropy and free energy, thermodynamic properties from statistical mechanics, molecular simulations
Molecular dynamics: Newton’s equations of motion, periodic boundary conditions, thermostats, integrators, ensembles
3
Course Syllabus (cont…)
Monte Carlo: Monte Carlo integration, importance sampling, Markov chains, detailed balance, biased sampling, ensembles
Calculation of equilibrium/dynamic properties: radial distribution functions, autocorrelation functions, transport properties, free energy computation
Stochastic simulations: Langevin and Brownian dynamics; Gillespie algorithm, hydrodynamics
Interactions between surfaces: Hamaker constants, Poisson-Boltzmann equation, Debye-Huckel theory, DLVO theory
Polymer physics: distributions and scaling properties, Flory-Huggins theory, lattice polymers, Rouse theory
Self-assembly: critical micelle concentration, DNA hybridization, membranes, phase behavior versus micellization
4
Reference Materials A. R. Leach, "Molecular Modeling: Principles and Applications", Addison
Wesley Longman, Essex, England (2001)
D. Frenkel and B. Smit, "Understanding Molecular Simulations: From
Algorithms to Applications", Academic Press, San Diego, California (1996)
M. P. Allen and D. J. Tildesley, "Computer Simulation of Liquids", Clarendon
Press, Oxford (1990)
D. Chandler, “Introduction to Modern Statistical Mechanics”, Oxford
University Press, Oxford (1987).
G. D. J. Phillies, “Elementary Lectures in Statistical Mechanics”, Springer-
Verlag, New York (2000)
K. A. Dill and S. Bromberg, “Molecular Driving Forces”, Garland Science, New
York (2002)
J. Israelachvili, “Interfacial and Surface Forces”, Academic Press, London (1991)
5
Lecture 1 Intra and intermolecular interactions
6
Types of forces Intramolecular forces
Ionic bond
Covalent bond
Metallic bond
Intermolecular forces
Charge-charge interactions
charge-dipole, Dipole-dipole interactions
Dispersion/London interactions
Pi-pi stacking interactions
Hydrogen bonding
Entropic forces (not fundamental)
Hydrophobic interactions
Depletion interactions …
Compare to fundamental forces defined by physicists
• Gravity • Electromagnetism • Strong interaction • Weak interaction
7
Ionic bonding
When two atoms of widely different electronegativities combine
E.g. KBr (Br holds tighter to its outer pair of electrons than K)
K -> K+ + e- I = +420 kJ/mol
Br + e- -> Br- I = -325 kJ/mol
Net effect is energy gain of 95 kJ/mol (unfavorable)
But attraction between opposite ions K+ and Br- in a lattice reduces energy
Energy of one ions pair = -589 kJ/mol => net effect now becomes favorable
Infact, ions are rarely found in pairs but form an infinite lattice (KBr crystal) so net electrostatic attraction even larger = -672 kJ/mol
€
U =q1q24πεε0
1r r q1
q2
ε0: permittivity of vacuum; ε: dielectric constant
Coulomb law:
8
Covalent bonding
Chlorine has seven valence electrons 3s23p5
The two 3p orbitals in the two Cl atoms share the single unpaired electron by overlapping in between the two atomic centers (bonding orbital)
That way nucleus-electron attraction maximized and nucleus-nucleus repulsion minimized (screening)
Two atoms of large and similar electronegativities prefer to share the electrons => that way both atoms attain full valence shells
9
Metallic bonding
Consider Na: Single electron in 3s orbital, and
3p orbitals empty
If the 3s orbitals share the two unpaired
electrons in the regions, the 3p orbitals still
remain empty (unfavorable)
Also, if this sharing occurs between the atoms,
the (+)ve charge on nucleus on either side of
the pair will become very accessible to the
electrons from other Na atoms
Other Na atoms join the chain, and so and so
forth, a lattice forms (Na lattice)
Electrons shared between chain of Na atoms are
considered “delocalized”
Elements with similar but low electronegativities (metals) form metallic bonds
10
Charge-charge intermolecular interactions
Two charges q1 and q2 interact through Coulomb law:
But charge-charge interactions are much weaker in biological systems (WHY??)
Dielectric constant of water is large
Electrostatic screening by the salt
€
U =q1q24πεε0
1r
€
U ~ q1q2exp(−κr)
rinverse Debye
length
ε0: permittivity of vacuum; ε: dielectric constant
11
Electrostatic interactions at work
Compaction of genomic DNA through histone proteins
Properties of DNA
Salt bridges in proteins (Barnase)
between Asp and Arg
12
Charge-dipole interactions
Can be repulsive and attractive depending upon the charge sign and position of the charge relative to the dipole
In reality, dipoles are free to rotate and choose favorable positions, therefore charge-dipole interactions are always attractive (Boltzmann averaging)
+ +
–
r Electrostatic energy depends as 1/r2 if the charge interacts with a fixed dipole
Electrostatic energy depends as 1/r4 if the charge interacts with a free dipole (HOMEWORK)
Hydration of ions
θ
€
U =qµ4πεε0
cosθr 2
; µ = qll
(HOMEWORK)
13
Dipole-dipole interactions (Keesom forces)
Can be repulsive and attractive depending upon the charge sign and position of the charge relative to the dipole
Again, dipoles are usually free to rotate and choose favorable positions, and the average Boltzmann averaged energy is always negative
We can also have induced-dipole/
dipole interactions (1/r6)
Electrostatic energy depends as 1/r3 if two dipoles interacts with each other
Electrostatic energy depends as 1/r6 if the dipoles free to rotate
+
–
r
14
Hydrogen-bonding: Special case of dipole-dipole interaction
Special type of dipole-dipole bond that exists between an electronegative atom and a hydrogen bonded to another electronegative atom (O-H···N)
Weaker than covalent and ionic bond
Typical length of a hydrogen bond ~2 Angstroms
H-bonding in DNA H-bonding in α-helix
15
Instantaneous dipole-induced dipole (dispersion/London forces)
One of the most basic interactions between atoms (even spherical ones)
Weak at room temperatures (<kBT) but can strong enough to condense gases at lower temperatures
H2 molecule (average)
H2 molecule (instantaneous view)
H atom (instantaneous view)
What happens when another H2 molecule approaches?
OR
Also 1/r6 dependence?
Homework problem: Prove this
16
Van der Waals interactions (dispersion + Keesom forces)
Large magnitude range for dispersion interactions (0.05-40 kJ/mol)
Increases with the size of the atoms (no. of electrons)
CHCl3 61.2°C CCl4 76.8°C
Boiling Points
Example 2:
Example 1:
17
van der Waals interactions at work
Attractive interactions between carbon nanotubes which makes their separation so difficult
Geckos feet that allows to walk upside down
Liquefaction of gases (nitrogen,methane, etc)
Crystallization of many proteins
18
Pi-Pi Stacking Interactions
Attractive interaction between stacked aromatic rings through mutual overlap of the p orbitals of Π-conjugated systems
As strong a driving force as H-bonding for DNA double helix formation
Can also have other Pi interactions: cation-Pi; sigma-Pi; etc
19
Hydrophobic Interactions
Effective attraction that arises between nonpolar molecules in water solvent - this minimizes the disruption of the favorable H-bonded network of water molecules
Mostly an entropic effect
Hydrophobic collapse of protein folding Lipid bilayer formation