Free volume and viscosity

The importance of free volume effects in diffusional processes at a molecular level should be further emphasized. An empirical relationship between viscosity and free volume was proposed by Doolittle ... 

Previous studies on paraffins, rhodamine dyes, and l,3-bis(N-carbozoyl) propane excimers have concluded that there is a relationship between km and polymer viscosity and free volume [103-105], Indeed, this dependence has been investigated in the context of decreasing free volume during methyl methacrylate polymerization [83,84], It has been shown that the nonradiative decay processes follow an exponential relationship with polymer free volume (vf), in which kra reduces as free volume is decreased [see Eq. (5)]. Here, k. represents the intrinsic rate of molecular nonradiative relaxation, v0 is the van der Waals volume of the probe molecule, and b is a constant that is particular to the probe species. Clearly, the experimentally observed changes in both emission intensity and lifetime for/ac-ClRe(CO)3(4,7-Ph2-phen) in the TMPTA/PMMA thin film are entirely consistent with this rationale. 

Here B is the Doolittle constant, since Brostow derived his equation starting from the Doolittle formula relating viscosity and free volume [44]. The reduced quantities are... 

The WLF Equation Section 8.2.7 illustrates how polymers soften and flow at temperatures near and above Tg. Flow, a form of molecular motion, requires a critical amount of free volume. This section considers the analytical relationships between polymer melt viscosity and free volume, particularly... 

The importance of viscosity and free volume in the molecular relaxation processes of excited dyes has been well documented in the case of polymethines, di and triphenylmethanes and coumarine dyesi3-2i. For dyes in which rotation-dependent non-radiative decay (knr) links the excited state conformation to the media free-volume, Vf, one can express knr in terms of solvent free volume as ... 

As the temperature is decreased, free-volume is lost. If the molecular shape or cross-linking prevent crystallisation, then the liquid structure is retained, and free-volume is not all lost immediately (Fig. 22.8c). As with the melt, flow can still occur, though naturally it is more difficult, so the viscosity increases. As the polymer is cooled further, more free volume is lost. There comes a point at which the volume, though sufficient to contain the molecules, is too small to allow them to move and rearrange. All the free volume is gone, and the curve of specific volume flattens out (Fig. 22.8c). This is the glass transition temperature, T . Below this temperature the polymer is a glass. 

In a series of papers, Diphant has been used to probe the microviscous properties of various polymer oils, and free volume parameters have been extracted. 4,88 90) In a comparative study of Excimer and TICT probes, it could be shown that the response of these probes is frozen out at lower temperatures, as can be expected from the large reaction volume necessary, whereas the TICT reaction still shows sizable rates at these high-viscosity conditions. (26) Moreover, this study also showed that the free volume fraction measured by the TICT probes is larger than that measured by Excimer probes. 

A modified version of the free-volume theory is used to calculate the viscoelastic scaling factor or the Newtonian viscosity reduction where the fractional free volumes of pure polymer and polymer-SCF mixtures are determined from thermodynamic data and equation-of-state models. The significance of the combined EOS and free-volume theory is that the viscoelastic scaling factor can be predicted accurately without requiring any mixture rheological data. 

Viscosity of Molecular Systems and Free Volume Theories. 124... 

Investigating the viscosity of a homological series of liquid normal paraffins, Doolittle [84] pointed out that the direct relationship between viscosity ( resistance to flow ) and free volume ( relative volume of molecules per unit free space ) is an intuitive hypothesis and the experimental dependence is described better by a logarithmic equation... 

Assuming that Ci, C2, and C3 are not affected by temperature, pressure, and dissolution of CO2, they can be determined from a viscosity-shear rate curve of the neat polymer. Namely, the coefficient, Ci, which is equivalent to n - 1, can be determined by the slope of the viscosity and shear rate curve. The values of C2 and C3 can be determined from data of viscosity vs. free volume fraction of the neat polymer. The data of free volume fraction required for determining C2 and C3 can be obtained from PVT data of the neat polymer at temperatures and pressures where the viscosity measurements of the neat polymer are performed. 

VISCOSITY OF SEVERAL LIQUID HYDROCARBONS AS A FUNCTION OF TEMPERATURE, PRESSURE, AND FREE VOLUME. HOGENBOOM D L WEBB W DIXON J A... 

A plasticiser is a material incorporated in a plastic to increase its workability and flexibility or distensibility. The melt viscosity, elastic modulus and Tg of a plastic are lowered by a plasticiser addition. There are several theories to explain plasticiser effects such as the lubricity, gel, and free volume. Plasticisers are essentially nonvolatile solvents and therefore, polymer and plasticiser compatibility is very important and the solubility parameter difference (A8) should be less than 1.8. When present in small amounts plasticisers generally act as antiplasticisers, (i.e., they increase the hardness and decrease the elongation of polymers). Figure 6.12 illustrates the effect of plasticiser on modulus. Increasing concentration of the plasticiser shifts the transition from the high modulus (glassy) plateau region to the low, i.e., to occur at lower temperature [9]. 

It can be observed from both tests at constant shear stress and constant shear rate that the melt viscosity is reciprocal of temperature. The melt viscosity is relatively related to the structure and free volume, whereby the increase in temperature might result in the enhancement of free volume and the improvement of chain mobility. Thus, viscosity gradually decreased exponentially with rising temperature. It is well known that the value of flow activation energy reflects the temperature-sensitivity of viscosity so, higher E or Ea leads to higher sensitivity of the blends to temperature. It can be seen from the values of E and Ea that E. increases with increasing... 

Perhaps the most direct observation of the relation between relaxation times and free volume, as expressed in its most general form by equation 49, is obtained from viscoelastic" " (or viscosity or dielectric ) measurements repeated over a period of time during the spontaneous contraction of a glassy sample that occurs after quenching it to a temperature near or below Tg, as portrayed in Fig. 11 -7. As the volume decreases, the relaxation times increase. Since the contraction takes place at constant temperature and pressure, the change in ar can be entirely attributed to collapse of free volume as a function of elapsed time. Moreover, since the occupied volume should remain constant at constant T and P, experimental measurements of the decrease in v provide the decrease in ly directly. Thus, during such an isothermal contraction at temperature T, the fractional free volume at time t is... 

Where t is the tensile viscosity, V and Vf are the total volume and free volume of the system respectively, and A and B are constants. 

There are a number of important concepts which emerge in our discussion of viscosity. Most of these will come up again in subsequent chapters as we discuss other mechanical states of polymers. The important concepts include free volume, relaxation time, spectrum of relaxation times, entanglement, the friction factor, and reptation. Special attention should be paid to these terms as they are introduced. 

In discussing Fig. 4.1 we noted that the apparent location of Tg is dependent on the time allowed for the specific volume measurements. Volume contractions occur for a long time below Tg The lower the temperature, the longer it takes to reach an equilibrium volume. It is the equilibrium volume which should be used in the representation summarized by Fig. 4.15. In actual practice, what is often done is to allow a convenient and standardized time between changing the temperature and reading the volume. Instead of directly tackling the rate of collapse of free volume, we shall approach this subject empirically, using a property which we have previously described in terms of free volume, namely, viscosity. 

The iatroduction of a plasticizer, which is a molecule of lower molecular weight than the resia, has the abiUty to impart a greater free volume per volume of material because there is an iucrease iu the proportion of end groups and the plasticizer has a glass-transition temperature, T, lower than that of the resia itself A detailed mathematical treatment (2) of this phenomenon can be carried out to explain the success of some plasticizers and the failure of others. Clearly, the use of a given plasticizer iu a certain appHcation is a compromise between the above ideas and physical properties such as volatiUty, compatibihty, high and low temperature performance, viscosity, etc. This choice is appHcation dependent, ie, there is no ideal plasticizer for every appHcation. 

Melt viscosity is also affected by pressure (43,67,68). The compression of a melt reduces the free volume and therefore raises the viscosity. For example, the viscosity of low density polyethylene increases by a factor of roughly 10 over a static pressure range of 34—170 MPa (5,000—25,000 psi). 

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