Structured polymer melts

The actual mathematical form of this function will depend upon the nature (i.e., the constitution ) of the particular material. Most common fluids of simple structure water, air, glycerine, oils, etc.) are Newtonian. However, fluids with complex structure (polymer melts or solutions, suspensions, emulsions, foams, etc.) are generally non-Newtonian. Some very common... 

Boyer also reported a transition at still higher temperature, T p Tll + 50 1.47 g, which he named the intramolecular relaxation transition, which separates structured polymer melts from true liquids [Boyer, 1977, 1980a,b, 1985, 1987]. This high-temperature transition may be related to melting. Formally, liquids remain supercooled below the melting point, 1.5Tg [van Krevelen, 1997]. Detection of this temperature is contingent on the polymer achieving sulHcient crystalline content. For example, poly(vinyl chloride), usually treated as an amorphous polymer, shows Tm = 444 to 452 K when the crystalline content of the syndiotactic isomer is about 2wt% [Marshall, 1994]. 

Molecular dynamics of a macromolecular chain involves both cOTiformational and rotational motions. Along these lines, the backbone dynamics of poly(n-alkyl methacrylates) has been elucidated by advanced solid state NMR, which enables conformational and rotational dynamics to be probed separately [41], The former is encoded in the isotropic chemical shift. The latter is probed via the anisotropic chemical shift [14] of the carboxyl group with unique axis along the local chain direction. Randomization of conformations and isotropization of backbone orientation occur on the same time scale, yet they are both much slower than the slowest relaxation process of the polymer identified previously by other methods [40]. This effect is attributed to extended backbone conformations, which retain conformational memory over many steps of restricted locally axial chain motion (Fig. lb, c). These findings were rationalized in terms of a locally structured polymer melt, in... 

The properties of the final polymer (melting point, solubiUty, optical properties, etc) depend on the nature of the side chain incorporated into the structure, so that judicious choice of substituent can lead to material tailorabiUty. 

Further information on the effect of polymer structure on melting points has been obtained by considering the heats and entropies of fusion. The relationship between free energy change AF with change in heat content A// and entropy change A5 at constant temperature is given by the equation... 

Step I. The time dependent structure of the interface is determined. Relevant properties may be characterized by a general function H(t), which for the ca.se of polymer melts can usually be described in terms of the static and dynamic properties of the polymer chains. For example, with symmetric (A = B) amorphous melt interfaces, H(t) describes the average molecular properties developed at the interface by the interdiffusion of random coil chains as [ 1,6J... 

I. Bitsanis, G. Hadziioannou. Molecular dynamics simulations of the structure and dynamics of confined polymer melts. J Chem Phys 92 3827-3847, 1990. 

In order to complete the discussion of methodical problems, we should mention two more methods of determining yield stress. Figure 6 shows that for plastic disperse systems with low-molecular dispersion medium, when a constant rate of deformation, Y = const., is given, the dependence x on time t passes through a maximum rm before a stationary value of shear stress ts is reached. We may assume that the value of the maximal shear stress xm is the maximum strength of the structure which must be destroyed so that the flow can occur. Here xm as well as ts do not depend or depend weakly on y, like Y. The difference between tm and xs takes into account the difference between maximum stress and yield stress. For filled polymer melts at low shear rates Tm Ts> i,e- fhese quantities can be identified with Y. 

Though the accuracy of description of flow curves of real polymer melts, attained by means of Eq. (10), is not always sufficient, but doubtless the equation of such a structure based on the idea of relaxation mechanism of non-Newtonian polymer flow, correctly reflects the main peculiarities of viscous properties. Therefore while discussing the effect a filler has on the viscosity properties of polymer melts, besides the dependences Y(filler modifies the characteristic time of relaxation. According to [19], a possible form of the X versus

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Many papers deal with the crystallization of polymer melts and solutions under the conditions of molecular orientation achieved by the methods described above. Various physical methods have been used in these investigations electron microscopy, X-ray diffraction, birefringence, differential scanning calorimetry, etc. As a result, the properties of these systems have been described in detail and definite conclusions concerning their structure have been drawn (e.g.4 13 19,39,52)). 

A polymer coil does not only possess a structure on the atomistic scale of a few A, corresponding to the length of covalent bonds and interatomic distances characteristic of macromolecules are coils that more or less, obey Gaussian statistics and have a diameter of the order of hundreds of A (Fig. 1.2) [17]. Structures of intermediate length scales also occur e. g., characterized by the persistence length. For a simulation of a polymer melt, one should consider a box that contains many such chains that interpenetrate each other, i. e., a box with a linear dimension of several hundred A or more, in order to ensure that no artefacts occur attributable to the finite size of the simulation box or the periodic boundary conditions at the surfaces of the box. This ne-... 

As described in Sect. 1, the relevant length scales and time scales are a serious problem for any simulation of polymer melts [12,16-20] and, as discussed, a polymer coil has structures on different distance scales (Fig. 1.2) [17] and relaxations on different time scales. A brute force approach, consisting of a simulation of fully atomistic models of a sufficiently large system over time scales for which thermal equilibration could be reached at practically relevant temperatures, is totally impossible. Useful progress requires a different approach. 

Figures 5.3 and 5.4 are just two pieces of evidence that the bond fluctuation model is a reasonable starting point for describing the properties of polymer melts. Thus the next step has to be to incorporate suitable information about the chemical structure and the energetics of specific polymers into the model.

We now ask how well does the bond fluctuation model with these bond lengths and bond angle potentials reproduce the properties of real polymer melts quantitatively. First of all, it must be admitted that the model yields a qualitatively reasonable picture of the amorphous structure, as exemplified by... 

On the other hand, one strength of the approach is the availability of algorithms (such as the slithering snake algorithm) by which undercooled polymer melts can be equilibrated at relatively low temperatures. This allows the static properties of the model to be established over a particularly wide parameter range. Furthermore, the lattice structure allows many questions to be answered in a well-defined, unique way, and conceptional problems of the approach can be identified and eliminated. Last but not least, the lattice structure allows the formulation of very efficient algorithms for many properties. 

A rather crude, but nevertheless efficient and successful, approach is the bond fluctuation model with potentials constructed from atomistic input (Sect. 5). Despite the lattice structure, it has been demonstrated that a rather reasonable description of many static and dynamic properties of dense polymer melts (polyethylene, polycarbonate) can be obtained. If the effective potentials are known, the implementation of the simulation method is rather straightforward, and also the simulation data analysis presents no particular problems. Indeed, a wealth of results has already been obtained, as briefly reviewed in this section. However, even this conceptually rather simple approach of coarse-graining (which historically was also the first to be tried out among the methods described in this article) suffers from severe bottlenecks - the construction of the effective potential is neither unique nor easy, and still suffers from the important defect that it lacks an intermolecular part, thus allowing only simulations at a given constant density. 

Dodd, L. R. and Theodorou, D. N. Atomistic Monte Carlo Simulation and Continuum Mean Field Theory of the Structure and Equation of State Properties of Alkane and Polymer Melts. Vol 116,pp, 249-282,... 

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