# Tesi etd-12162007-113853

Thesis type
Tesi di dottorato di ricerca
Author
ZULLI, FABIO
URN
etd-12162007-113853
Title
Entanglement and Cooperativity: a Study of Polymer Dynamics at Different Time- and Length-Scales
Settore scientifico disciplinare
FIS/02
Corso di studi
FISICA
Commissione
Relatore Andreozzi, Laura
Parole chiave
• polymers
• polymer dynamics
• ESR
• entanglement
• cooperativity
• rheology
Data inizio appello
29/01/2008;
Consultabilità
parziale
Data di rilascio
29/01/2048
Riassunto analitico
In the first chapter, generalities of polymer sciences are presented. Particular attention has been payed to the phenomenology of the glass transition and of relaxation processes. In particular, the Rouse and reptation models for polymer dynamics of melts have been described.<br><br>The second chapter provides a general view of the theory of linear viscoelasticity.<br><br>An introduction to the theoretical aspects of electron spin resonance is provided in the third chapter. The different regimes of motion and diffusion models of probes are also detailed.<br><br>In the fourth chapter, details of experimental apparatuses are provided. Operational procedures followed during the measurements are also detailed.<br><br>Details of the synthesis, properties, and results of preliminary characterisation of the studied materials are given in the fifth chapter.<br><br>In the sixth chapter, the results of the linear viscoelastic characterisation of the investigated polymers are shown, and the chain dependence of rheological and thermal properties is discussed. The mass dependence of Vogel-Fulcher parameters $T_b$ and $T_0$, and $T_g$ has been analysed according to the free volume concept, and a coherent way of describing their molar mass behaviour is proposed here. Such a study led to the determination of the asymptotic values, in the presence of entanglement, of these physical quantities, which can be expressed in terms of several microscopic quantities. Moreover, the comparison of the fitting parameters, drawn from the functional relationship proposed here in order to describe the mass dependence of the parameters mentioned above, allowed to evaluate the ratio between the free volume pertinent to the polymer chain and to chain tail.<br>A study of the material parameter plateau modulus $G^0_N$ and of the mass dependence of zero-shear viscosity $\eta$ and steady-state shear compliance $J_e^0$ has also been carried out. In these cases, the discrimination between the Rouse and the entanglement regimes is apparent, and a correlation between macroscopic fitting parameters and microscopic quantities is carried out. It has thus been possible to determine the product $\zeta_0b^2$ of the monomeric friction coefficient $\zeta_0$ and of the dynamic segment length $b$ of the chains, as well as the ratio between the characteristic polymer masses $M_e$, $M_c$, and $M_c&#39;$.<br>The evidence presented is consistent with fitting laws suggested in the literature over the past years, however a comprehensive interpretation in terms of free volume is here proposed with a new coherent scenario for modified fitting laws, where the free parameters are connected to microscopic quantities. The consistency of this approach is demonstrated. These fitting procedures also allow an estimation of the length of the chain tails, which is in agreement with literature simulations.<br>Comparison of Vogel-Fulcher parameters $T_b$ and $T_0$ with William-Landel-Ferry parameters $c_1$ and $c_2$ allowed to test the thermorheological simplicity also of poly(alkyl acrylate) samples with side-chains of different length.<br>The linear viscoelastic response of polymers from a nematic azobenzene methacrylate and its copolymers with non-mesogenic methyl methacrylate was also studied. These samples showed thermorheological simplicity in the whole investigated temperature range, even across the nematic-isotropic transition. The analysis of the zero-shear viscosity confirmed a thermorheologically simple behaviour, which allowed an interpretation of the temperature dependence of the zero-shear viscosity in the framework of free-volume theory.<br>For all the investigated samples, the way the relaxation mechanisms approached their asymptotic behaviour was described in terms of fragility parameters, and a comparison of fragility of the samples was carried out. The analysis of fragility and temperature dependence of zero-shear viscosity provided a better understanding of the way the polymer architecture influences free-volume quantities and determines relaxation mechanisms.<br><br>In chapter seven, experimental master curves were reproduced by fitting procedures according to the Rouse and entanglement models by molar mass content of the melts. Different reptation theories have been compared, employing or not constraint release mechanisms. A new approach for a correct reproduction of experimental data is suggested, which takes into account the different mobility of the smallest chains. Such a study, carried out on a series of nearly monodisperse samples of different molar masses, confirmed the onset of entanglement at the entanglement mass $M_e$. The relationship between $M_e$ and the plateau modulus $G^0_N$ is also discussed.<br>A challenge was offered by the polydisperse nematic azobenzene methacrylate homopolymers and copolymers with non-mesogenic methyl methacrylate, because of their peculiar response, which does not exhibit entanglement plateau. To take into account the random composition of copolymers, the calculation algorithms were modified. In fact, one could expect that fluctuations from the average composition in short modes can change the monomeric friction coefficient. Therefore, a weighted monomeric friction coefficient was defined as an average of the azobenzene methacrylate and methyl methacrylate monomeric friction coefficients. Calculation of master curves provided very good fits and monomeric friction coefficients in accordance with literature findings. Very high values of $M_e$ were also confirmed by these calculations.<br>The data for $M_e$ found in this chapter were also studied in terms of coiling properties by means of the packing length approach. This approach allows to determine $M_e$ in terms of density, $b$, and molar mass of the repeating unit. The packing length concept was tested for the polymers characterised in this work, finding a good agreement with experimental data, even in the case of the very high $M_e$ of polymethacrylates.<br><br>In the eighth chapter, results of paramagnetic resonance characterisation are shown and discussed. The analysis carried out in poly(ethyl acrylate) and poly(propylene glycol) melts by means of the cholestane probe are reported and compared with studies on poly(alkyl acrylate) samples. Moreover, electron spin resonance investigations of the dynamics of the tempo probe dissolved in poly(propylene glycol) are also presented. The coupling degree of the probe dynamics to the relaxation mechanisms of the polymer is reviewed and discussed in terms of the different chain architecture and spin probes employed in the measurements. Sharp crossover between two different fractional regimes was observed at a temperature about $1.2T_g$ for the cholestane probe. Its nature, the onset of cooperative relaxation mechanisms, and the crossover to activated regimes are discussed. On the other hand, the dynamics of the tempo probe also shows crossovers between different dynamic zones, whose nature is also reviewed. The comparison between the dynamics of such different probes stresses which, and how, features of the dynamics of the probed polymer are affected by the tracer.
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