Orientador: René Alfonso Nome Silva / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-26T04:23:53Z (GMT). No. of bitstreams: 1 Zornio_BrunoFedosse_M.pdf: 1493558 bytes, checksum: 07565e7077eefa5f9f91f03dc9cc90d4 (MD5) Previous issue date: 2014 / Resumo: No final do século XIX Van¿tHoff empiricamente estabeleceu que a constante de velocidade de uma reação química é função exponencial da razão entre energia de ativação da reação pela energia térmica do ambiente (e portanto função da temperatura). Há uma variada ordem nas escalas de tempos reacionais, em especial, a constante de velocidade de reações lentas (por exemplo, reações bioquímicas não catalisadas) é difícil de determinar. Uma partícula difundindo em um meio viscoso que apresenta movimento aleatório ¿ com posição média (em um intervalo de tempo suficientemente grande) nula, e a variância da posição linearmente dependente em função do tempo ¿ é dita browniana, e quando submetida a um potencial bi quadrático é um bom modelo para descrição de reações químicas. A partir da dinâmica de Langevin (que serve para descrever a dinâmica de uma partícula browniana) é derivada a teoria de Kramers para meio viscosos - que relaciona o formato da curva potencial com a constante de taxa de reações químicas -. Experimentalmente pode-se recriar esse modelo utilizando pinças ópticas. Pinças ópticas são capazes de aprisionar partículas da ordem micrométricas em suspensão, pode-se recriar um potencial bi estávelutilizando uma pinça óptica dupla (com dois pontos de aprisionamento). Este estudo tem como objetivo avaliar a constante de taxa de um processo de transição entre poços de potencial de partículas brownianas teoricamente utilizando uma simulação de dinâmica de Langevin para sistemas em equilíbrio tanto quanto para sistemas antes de atingir o equilíbrio, assim como determinar experimentalmente utilizando microscopia ocoeficiente de difusão a partir da trajetória temporal de uma única partícula. Os resultados teóricos obtidos são bastante condizentes com os resultados experimentais descritos na literatura, assim como as predições da constante de taxa para tempos antes do equilíbrio apresentam correlação com o sistema em equilíbrio. Com relação à estimativa do coeficiente de difusão apresenta um erro sistemático associado ao tamanho da trajetória temporal de uma única partícula / Abstract: By the end of the XIX century, Van¿t¿ Hoff has empirically established that the rate constant of some chemical reaction is exponentially dependent by the ratio between the reaction activation energy and the environment thermal energy (and so on function of temperature). There is a wide variety in the reaction time scales, in particular, the rate constant of slow reactions (such as uncatalysed biochemical reactions) is difficult to determine. A diffusing particle in a viscous media which exhibit random motion ¿ with mean position (in a sufficiently large time series) is zero, and the position variance is linearly time dependent ¿ is called Brownian, and when is submitted in a biquadratic potential it¿s a good model to describe chemical reactions. By the Langevin dynamics (which serves to describe the Brownian particle motion) the Kramers theory for viscous media is derived ¿ that theory connects the potential energy shape with the chemical rate constant -. Experimentally it is possible to create this model using optical tweezes. Optical tweezers where capable to trap micrometrical beads in suspension, it can generate a bi-stable using a double optical tweezers (that is with two trapping points). The main objective of this essay is evaluate the rate constant a Brownian particles jumping between potential wells theoretically using Langevin dynamics simulations for the system at equilibrium and before reach the equilibrium, as determinate experimentally the diffusion coefficient of single particle time path using microscopy. The theoretical results is very consistent with experimental results described in literature, as well as the prediction of the rate constant for the system before reaches equilibrium are correlated with the rate constant for the system at equilibrium. For the diffusion coefficient estimative it was observed that there is a systematical source of errors, and its is related with the length of the time series of the single particle path / Mestrado / Físico-Química / Mestre em Química

In the thesis work we investigate four problems connected with dynamical processes in condensed medium, using different techniques of equilibrium and non-equilibrium statistical mechanics. Biology is rich in dynamical events ranging from processes involving single molecule [1] to collective phenomena [2]. In cell biology, translocation and transport processes of biological molecules constitute an important class of dynamical phenomena occurring in condensed phase. Examples include protein transport through membrane channels, gene transfer between bacteria, injection of DNA from virus head to the host cell, protein transport thorough the nuclear pores etc. We present a theoretical description of the problem of protein transport across the nuclear pore complex [3]. These nuclear pore complexes (NPCs) [4] are very selective filters that monitor the transport between the cytoplasm and the nucleoplasm. Two models have been suggested for the plug of the NPC. The first suggests that the plug is a reversible hydrogel while the other suggests that it is a polymer brush. In the thesis, we propose a model for the transport of a protein through the plug, which is treated as elastic continuum, which is general enough to cover both the models. The protein stretches the plug and creates a local deformation, which together with the protein is referred to as the bubble. The relevant coordinate describing the transport is the center of the bubble. We write down an expression for the energy of the system, which is used to analyze the motion. It shows that the bubble executes a random walk, within the gel. We find that for faster relaxation of the gel, the diffusion of the bubble is greater. Further, on adopting the same kind of free energy for the brush too, one finds that though the energy cost for the entry of the particle is small but the diffusion coefficient is much lower and hence, explanation of the rapid diffusion of the particle across the nuclear pore complex is easier within the gel model. In chemical physics, processes occurring in condensed phases like liquid or solid often involve barrier crossing. Simplest possible description of rate for such barrier crossing phenomena is given by the transition state theory [5]. One can go one step further by introducing the effect of the environment by incorporating phenomenological friction as is done in Kramer’s theory [6]. The “method of reactive flux” [7, 8] in chemical physics allows one to calculate the time dependent rate constant for a process involving large barrier by expressing the rate as an ensemble average of an infinite number of trajectories starting at the barrier top and ending on the product side at a specified later time. We compute the time dependent transmission coefficient using this method for a structureless particle surmounting a one dimensional inverted parabolic barrier. The work shows an elegant way of combining the traditional system plus reservoir model [9] and the method of reactive flux [7] and the normal mode analysis approach by Pollak [10] to calculate the time dependent transmission coefficient [11]. As expected our formula for the time dependent rate constant becomes equal to the transition state rate constant when one takes the zero time limit. Similarly Kramers rate constant is obtained by taking infinite time limit. Finally we conclude by noting that the method of analyzing the coupled Hamiltonian, introduced by Pollak is very powerful and it enables us to obtain analytical expressions for the time dependent reaction rate in case of Ohmic dissipation, even in underdamped case. The theory of first passage time [12] is one of the most important topics of research in chemical physics. As a model problem we consider a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space we derive a very general expression of the survival probability and the first passage time distribution, irrespective of the statistical nature of the dynamics. Also using the prescription adopted elsewhere [13] we define a bound to the actual survival probability and an approximate first passage time distribution which are expressed in terms of the position-position, velocity-velocity and position-velocity variances. Knowledge of these variances enables one to compute the survival probability and consequently the first passage distribution function. We compute both the quantities for gaussian Markovian process and also for non-Markovian dynamics. Our analysis shows that the survival probability decays exponentially at the long time, irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant [14]. Although the field of equilibrium thermodynamics and equilibrium statistical mechanics are well explored, there existed almost no theory for systems arbitrarily far from equilibrium until the advent of fluctuation theorems (FTs)[15] in mid 90�s. In general, these fluctuation theorems have provided a general prescription on energy exchanges that take place between a system and its surroundings under general nonequilibrium conditions and explain how macroscopic irreversibility appears naturally in systems that obey time reversible microscopic dynamics. Based on a Hamiltonian description we present a rigorous derivation [16] of the transient state work fluctuation theorem and the Jarzynski equality [17] for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is valid for a general non-Ohmic bath.