Fluctuation free volume

Rheological properties of the oligoethylsiloxane-based compositions with additives are of vital importance for the selection of maintenance conditions of various items, but they have not been studied yet. No data on such composition-fluidity relationships (unconfined fluctuating free volume and viscous flow activation energy values) are available. 

Overall membrane compression Lipid-domain interface fluctuations Free volume fluctuations Local depressions and distortions Transient hydrophobic pores Transient hydrophilic pores Foot-in-the-door hydrophilic pores Composite hydrophilic pores Membrane enzyme changes Membrane macromolecule protrusion changes Rupture and REB not actually described (5) Suggested alternative to transient pores (6) Transport of nonpolar species (7) Possible precursors to hydrophilic pores (8, 9) Possible precursor to hydrophilic pores (10) Key to quantitative descriptions (10-16) Candidate metastable pores" Candidate metastable pores Coupling to membrane macromolecules (17) Candidate signaling change mechanism... 

It is considered that is determined by the properties of the supermolecular structure of epoxy polymers, namely, by the degree of local order in them. This assumption arises due to the well-known succession of relationships between the diffusion process and d [28], between the diffusion process and the fluctuation free volume [119], and between and the cluster structure [120]. Therefore, the fractal dimension of the cluster structure of crosslinked polymers [105, 110], estimated from Equation (11.27), is taken to be d. Since the D value is determined for an Euclidean space with d = 2, it was also assumed in Equation (11.27) that d = 2. The d value was found for a three-dimensional space therefore, a graph [121] for converting d from three- to two-dimensional space was used in subsequent calculations. The D values were further calculated from Equation (11.8) in terms of the AO and AS hypotheses. Figure 11.13 shows the dependences of D on calculated from Equations (11.8) and (11.39). The dependences of D on and the absolute magnitudes of D are in good agreement, especially when the AO hypothesis is used. 

The Fractality of the Fluctuation Free Volume of Glassy Polymers... 

The fluctuation free volume in crosslinking epoxy polymers has a fractal structure and the microvoids formed in the matrix are simulated by Df dimensional spheres. The size of a microvoid is considered as the volume that is necessary for its formation and is a consequence of the accumulation of thermal fluctuations. 

It has been established that the structure of an amorphous polymer is fractal with a fractal dimension (df) (2 < df < 3). Therefore we ought to expect, that the fluctuation free volume should also have fractal properties. The purpose of this chapter is to investigate the fractality of the fluctuation free volume in glassy polymers and epoxy polymers are... 

As can be seen in Figure 15.2, the dependence (15.3) is correct for the epoxy polymers investigated and confirms the self-similarity of a cluster of microvoids of fluctuation free volume. The interval of the scale of the self-similarity, with allowance for correlations between Df and fractal dimension of the structure of the polymer df may be assumed. This interval coincides with a similar interval for the structure of an amorphous polymer which is distributed from several units up to several tens of Angstrom (5-50 A) [1, 4]. 

Let us consider the physical sense of the parameter Df. It is obvious that the value of Df obtained from the slope of a straight line. In N -ln rif (Figure 15.1), is the average of the values. Nevertheless the microvoids of the fluctuation free volume form a DF dimensional fractal cluster. 

The cluster model assumes availability in the amorphous polymers structure of local order domains (clusters), consisting of several densely packed collinear segments of different macromolecules (amorphous analog of crystallite with stretched chains). These clusters are connected between themselves by tie chains, forming by virtue of this physical entanglements network, and are surrounded by loosely packed matrix, in which all fluctuation free volume is concentrated [107],... 

FIGURE 11.20 Schematic illustration of the spatial structure of the smallest representative subvolume derived from the volume fluctuations detected by PALS, (VVs) =1, at high temperatures (T 2Tg, the a -process) and at Tg (the cooperative a-process) and its relation to particle mobilities. Shown are empty spaces (represented by empty areas), which constitute the fluctuating free volume and particles (spheres). The larger empty spaces are probed by o-Ps (holes). Circles with dots represent particles considered at their movement near a hole, filled circles are particles with higher mobihty, and open circles are particles with lower mobility. The arrows indicate the possible movement of particles. (From Dlubek et al. [2006a].)... 

Region IV occurs in the temperature range above T v where the knee in (vft> appears. Here the calculated (vh) and ah remain constant or may even show a decrease. From the continuous expansion of Vf we expect that the true hole size increases further. This different behavior shows that above T v the o-Ps lifetime parameters do not adequately mirror the fluctuating free volume via snapshots, and owing to this, PALS fails. We have attributed this effect to structural motions where the relaxation time decreases with increasing temperature, becoming comparable to and then decreasing below the mean o-Ps lifetime. 

The value of polymers fluctuation free volume can be calculated according to the equation [52] ... 

FIGURE 2.7 The dependence of relative fluctuation free volume/ on relative fraction of loosely packed matrix (Pj for PC (1) and PAr (2) [47],... 

Kozlov, G. V, Sanditov, D. S., Lipatov, Yu. S. (2004). Structural Analysis of Fluctuation Free Volume in Amorphous State of Polymers. In Achievements in Polymers Physics-Chemistry Field. Zaikov, G. E., Berlin, A. A., Zlotskii, S. S., Minsker, K. S., Monakov, Yu. B. Ed. Moscow, Khimija, 412 74. 

In Ref. [25], the asymmetrical periodic function is adduced, showing the dependence of shear stress x on shear strain (Fig. 4.2). As it has been shown before [19], asymmetry of this function and corresponding decrease of the energetic barrier height overcome by macromolecules segments in the elementary yielding act are due to the formation of fluctuation free volume voids during deformation (that is the specific feature of polymers [26]). The data in Fig. 4.2 indicate that in the initial part of periodic curve from zero up to the maximum dependence of x on displacement x can be simulated by a... 

In the Eq. (4.21), the coefficient (3 + 5) takes into accoimt conformational molecular changes contribution to AS, k is Boltzmann constant,7 is a polymer relative fluctuation free volume. 

If to consider the yielding process as polymer mechanical devitrification [36], then the same increment of fluctuation free volume is required for the strain achievement. This increment AY can be connected with as follows [50] ... 

Let us consider, which processes result to necessary for yielding realization fluctuation free volume increasing. Theoretically (within the frameworks of polymers plasticity fractal concept [35] and experimentally (by positrons annihilation method [22]) it has been shown, that the yielding pro-... 

The comparison of and values is adduced in Fig. 4.14, from which their satisfactory correspondence follows. This is confirmed by the conclusion, that crystallites partial meehanical melting (disordering) is necessary for fluctuation free volume growth up to the value, required for polymers mechanical devitrification realization [51]. 

In its turn, polymer structure entropy change AS, which is due to fluctuation free volume, can be determined according to the Eq. (4.21). Comparison of the Eqs. (4.21) and (4.46) shows that entropy change in the first from them is due to change probability and to an approximation of constant the values /( ) and AS correspond to each other. Further polymer behavior at deformation can be described by the following relationship [84] ... 

As it is known [9], polymer viscosity at viscous flow depends on relative fluctuation free volume value, which can be estimated according to the Eq. (2.19). In Fig. 6.3 the dependence of parameter characterizing polymer... 

Landell-Ferry Free Volume fwFL> Fluctuation Free Volume uc. ittid Free Volume for Thermal Expansion fa p- The effect of system variables on solubility is discussed in Handbook of Solvents, 2001. Miller (1968) noted that the concept of free volume is easy to grasp, but, quantitatively, its definition runs into snares. Is free volume the specific volume of the liquid (solution) minus the volume of the molecules computed from Van Der Waals radii, or minus the volume swept out by the segments as they rotate, or is it some other volume The free volume is generally, but necessarily, about 2.5% for all polymers. 

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