Interplay Between Quantum Mechanics and Soft Matter in Physics Departments
Explore the interplay between quantum mechanics and soft matter in physics, focusing on electron interactions, polymer effects in batteries and electronics, and quantum models for classical behavior. Dive into topics like conformons, electron delocalization, and Hubbard models for hydrogen bond networks.
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Presentation Transcript
INTERPLAY BETWEEN QUANTUM MECHANICS AND SOFT MATTER P. PINCUS PHYSICS AND MATERIALS DEPARTMENTS UNIVERSITY OF CALIFORNIA, SANTA BARBARA CMMRC WASHINGTON, DC SEPTEMBER, 2013
OUTLINE & SCOPE Soft condensed matter physics is generally regarded as mainly classical ( =0) because it is typically concerned with objects at the nanoscale or larger. Some categories where QM plays a role include: (1)direct interplay between electrons and soft matter properties; (2) quantum models for classical behavior; (3) experimental tools to probe soft matter that rely in an essential way upon QM.
ELECTRONS AND SOFT MATTER o BATTERIES, PHOTOVOLTAICS, FLEXIBLE ELECTRONICS where polymers are essential elements o COORDINATION CHEMISTRY EFFECTS WITH TRANSITION METAL IONS AND SOFT MATERIALS .flexible lighting o COMPENSATION OF ELECTRONIC CHARGES BY IONIC CHARGES IN AQUEOUS MEDIA ..screening of Schottky barrier by dissolved salts in doping of conjugated polymers o CONDUCTIVITY OF CONJUGATED POLYMERS hopping o ELECTRON COUPLING TO BENDING MODES IN d=2..grapheme, o ELECTRON DELOCALIZATION AND POLYMER RIGIDITY
CONFORMONS-ELECTRON DELOCALIZATION AND POLYMER RIGIDITY ELECTRON DOPED CONJUGATED POLYMER CHAIN ELECTRON DELOCALIZATION STIFFENS GAUSSIAN POLYMER INTO A SEMI- FLEXIBLE CHAIN POLYTHIOPHENE TOY MODEL o TIGHT BINDING ELECTRON HOPPING MATRIX ELEMENT t all or nothing ?(?) = ??????( ?? + ?,? = ?,?,?.... is number of monomers per rigid segment ? ?), ? = Rigid segment--- conformon .. analogous to polaron o Loss of configurational entropy T/rigid bond
CONFORMONS AT LOW DOPING-RESULTS For r electrons (spinless for simplicity) in a conformon: o Optimal conformon length , 1/3 c + + (r ) t 12 10 c T o Using transfer matrix method to do stat mech for concentration c of electrons: 3 c For , Isolated one electron conformons c e 4 ( ( ) ) 12 Forc electrons. The chain stiffens and swells considerably. ( ( ) ) 12 c There are conformons each containing N c p r ..
QUANTUM MODELS Analog calculations using quantum models may be easier because of the finite state counting o HUBBARD MODEL FOR HYDROGEN BOND NETWORKS
HUBBARD MODEL FOR HYDROGEN BOND NETWORKS Water Structure
Ice H Bonds
Model- Basins Crystal field basins may be occupied by (0,1) protons. Strong Coulomb Repulsion Spinless Fermions
Single Molecule Energies U s-p hybridiztion U>V 2H2O OH- + H3O+ V
Hydrogen Bonds and the Hubbard Model Treat basins as Fermion states OH- t is matrix element to transfer a proton from one basin to another associated with a nearest neighbor O- - t H3O+ H-bond energy ~ -t2/V ~ 5kBT t ~ 10kBT Intermediate Coupling H Bond is proton resonating between two waters Hydrophobic Interaction
Quantum Soft Matter Probes o Magnetic resonance techniques Dynamic Overhauser effect to study motions o Neutron scattering techniques Spin Echo Small Angle Neutron Scattering SESANS
Spin-Echo Small-Angle Neutron Scattering (SESANS) Slides courtesy of Xin Li and Roger Pynn (Indiana University) Elastic scattering technique to investigate structure Real space correlation function
Neutron Alalogue of Differential Interference Contrast Microscopy Beautiful real-space images at about 1 micron resolution Wollaston Prism Eukaryotic Algae Two polarization states of light visit neighboring parts of a sample and interfere to produce contrast that depends on the phase difference between the paths.
SESANS L m B 2 2 cot L z ( ( ) ) Triangular regions have oppositely directed magnetic fields to change neutron wavelength 2 2 cot z L k m B Spin Echo length ( ( ) ) 0 2 SESANS measures a real-space correlation function as a function of z
SESANS & SANS Measure Different Transforms of the Debye Correlation Function Local Particle Density (r) Debye Correlation Function 1 V = + 3 ( ) ( ) ( r r' r' r )d r' V d r ( ) Q ( ) ( J r ) ( ) z ( ) r z = = 2 = 2 Q ( ) 4 I Qr r dr G dr 0 Fourier d 2 2 r z 0 Abel
Hard Sphere vs. Adhesive Hard Sphere Unpublished experiments at LANSCE by Xin Li and Roger Pynn Theoretical Predictions: T. Kruglov J. Appl. Cryst.38, 721 2005 Li et al. J. Chem. Phys. 132 174509 2010
We are usually completely wrong in predicting the future in science. However while waiting for unexpected discoveries, I believe that these categories merit some exploration. Thanks for listening!
