Documento PDF - UniCA Eprints - UniversitÃ degli studi di Cagliari.

More documents

Recommendations

Info

M O L E C U L A R D Y N A M I C SAa.1 molecular dynamicsMolecular dynamics (MD) is a computational techniquethat allows to calculate the atomic trajectories of a molecularsystem by numerical integration of Newton’s equationof motion, for a specific interatomic potential [112, 59, 60,61].In principle the dynamic of a system requires a quantummechanicaltreatment of constituents and the solution ofthe time dependent Schrödinger equation, that is possibleonly for extremely simple systems. Therefore, the applicationof approximations turns out to be essential.The first approximation used, is that of Born-Oppenheimer[113], that takes into account the heaviness of the nuclearmass with respect to the electronic one. The motion of thenuclei and the electrons can therefore be separated and theelectronic and nuclear problems can be solved with independentwavefunctions.The second approximation is to neglet the quantomechanicaleffects on the atoms, considering them as classicalparticles. In these conditions the Newton’s equation ofmotion F = ma = −∇V can be solved by calculating theforces as gradients of the potential energy function, thatdepends on the atomic coordinates.a.1.1Verlet algorithmEven in the classical approach, due to the complicatednature of the systems, typically there is no analytical solutionto their equations of motion and they must be solvednumerically. In particular, in the Verlet algorithm [114] thebasic idea is to write two third-order Taylor expansions forthe positions r(t), one forward and one backward in time:r(t + ∆t) = r(t) + v(t)∆t + ......(t)∆t 2 + (1/6)b(t)∆t 3 + O(∆t 4 )(A.1)73
74 molecular dynamicsr(t − ∆t) = r(t) − v(t)∆t + ......(t)∆t 2 − (1/6)b(t)∆t 3 + O(∆t 4 )(A.2)Adding the two expressions the position at later time isobtained:r(t + ∆t) = 2r(t) − r(t − ∆t) + a(t)∆t 2 + O(∆t 4 ) (A.3)where a(t) is the force divided by the mass:a(t) = −(1/m)∇V (r(t))(A.4)Velocities are not directly generated. One could computethe velocities from the positions by using:v(t) =r(t + ∆t) − r(t − ∆t)2∆t+ O(∆t 2 ) (A.5)The error associated to this expression is of order ∆t 2 ratherthan ∆t 4 .A more used and efficient method for the integrationof the equation of motion is the Velocity Verlet algorithm[115]. In this case the positions are calculate at time t + ∆t:r(t + ∆t) = r(t) + v(t)∆t + 1 2 a(t)∆t2(A.6)The velocities are calculated at one half timestep t + ∆t2 :v(t + ∆t2 ) = v(t) + 1 a(t)∆t (A.7)2Forces and accelerations are computated at t + ∆t:a(t + ∆t) = −( 1 )∇V (r(t + ∆t))m (A.8)At last, we obtain the velocity at the time t + ∆t:v(t + ∆t) = v(t + ∆t2 ) + 1 a(t + ∆t)∆t (A.9)2The Velocity Verlet algorithm has the advantage to be stableand to allow the use of relatively large timesteps (1 fsfor most of the calculations in this thesis), requiring a lowercomputational time.
Page 1 and 2:
Università degli Studi di Cagliari
Page 4:
A C K N O W L E D G M E N T SI woul
Page 7 and 8:
example of a novel class of systems
Page 10 and 11:
C O N T E N T S1 introduction 11.1
Page 12 and 13:
L I S T O F F I G U R E SFigure 1.1
Page 14 and 15:
List of FiguresxiiiFigure 2.15 Init
Page 16 and 17:
List of FiguresxvFigure 4.6Figure 4
Page 18:
Figure 5.7Figure 5.8Figure A.1Figur
Page 21 and 22:
2 introduction1-3 eV) and the trans
Page 23 and 24:
4 introductionorder in such a compl
Page 25 and 26:
6 introductionprocesses that need t
Page 27 and 28:
8 introduction1.2 physical factors
Page 29 and 30:
10 introductionrecovered by the int
Page 31 and 32:
12 introductionA cheap and environm
Page 33 and 34:
14 introductiondensed phases [63, 7
Page 36 and 37:
P 3 H T - P O LY ( 3 - H E X Y LT H
Page 38 and 39:
2.1 mechanism of assembling and mor
Page 40 and 41:
2.2 p3ht assembling and intermolecu
Page 42 and 43: 2.3 p3ht crystalline bulk phases 23
Page 44 and 45: 2.5 nanocrystalline p3ht 25Figure 2
Page 46 and 47: 2.5 nanocrystalline p3ht 27Table 2.
Page 48 and 49: 2.6 conclusions 29Figure 2.13.: Ini
Page 50 and 51: P O LY M E R / S E M I C O N D U C
Page 52 and 53: 3.3 adhesion of a single p3ht molec
Page 54 and 55: 3.4 p3ht/zno interface 35surface (t
Page 56 and 57: 3.5 p3ht/zno interface: low deposit
Page 58 and 59: 3.6 p3ht/zno interface: high deposi
Page 64 and 65: 3.7 effective model for the transpo
Page 66 and 67: 3.8 conclusions 47As for the low te
Page 68 and 69: T E R N A RY Z N O / Z N P C / P 3
Page 70 and 71: 4.1 self assembling of znpcs on zno
Page 72 and 73: 4.2 polymer interaction with znpcs
Page 74 and 75: 4.3 electronic and optical properti
Page 76 and 77: 4.3 electronic and optical properti
Page 78 and 79: 4.4 conclusions 59ties. The absorpt
Page 80 and 81: I N T E R A C T I O N B E T W E E N
Page 82 and 83: 5.2 solvent thf interaction with zn
Page 88 and 89: 5.3 conclusions 69γ L/L ∼ 0.112
Page 90 and 91: C O N C L U S I O N SIn this thesis
Page 94 and 95: A.1 molecular dynamics 75a.1.2The t
Page 96 and 97: A.2 the force field 77Finally, τ t
Page 98 and 99: A.2 the force field 79Waals interac
Page 100 and 101: A.3 methods 81tional Theory (DFT) l
Page 102 and 103: B I B L I O G R A P H Y[1] http://w
Page 104 and 105: ibliography 85[17] J. D. Servaites,
Page 106 and 107: ibliography 87Zakeeruddin, and M. G
Page 108 and 109: ibliography 89Phys. Chem. Chem. Phy
Page 110 and 111: ibliography 91[65] D. J. Binks and
Page 112 and 113: ibliography 93cells,” Energy Envi
Page 114 and 115: ibliography 95[97] C. Ingrosso, A.
Page 116 and 117: ibliography 97298.15 k,” Journal
Page 118 and 119: ibliography 99charges. am1-bcc mode
Page 120: colophonThis document was typeset u
show all

Documento PDF - UniCA Eprints - UniversitÃ degli studi di Cagliari.

Create successful ePaper yourself

Delete template?

Save as template?