Solvent and small-molecule motion

The next four chapters treat motion related to single polymer molecules. This chapter examines the solvent molecules surrounding the chains. Chapter 6 examines motions of modest parts of chains. Chapters / and 8 review rotational and translational diffusion of single chains through polymer solutions. 

It had long been assumed that the solvent in a polymer solution provides a neutral hydrodynamic background, and that the properties of the solvent in a solution, such as viscosity, are the same as the properties found in the neat solvent. We know now that this simple assumption is incorrect Just as the solvent can alter properties of the polymer, so also do polymers alter the properties of the surrounding solvent Translational and rotational mobilities of solvent molecules may be reduced or increased by the presence of nearby polymer chains. Models for polymer dynamics that assume that the solvent has the same properties as the neat liquid are therefore unlikely to be entirely accurate. 

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This section examines motion (diffusion, conductance, electrophoretic mobility) of rigid probes through simple solvents and small-molecule solutions. Experiments test the validity of Stokes law / and the Stokes-Einstein form D T/rjR. 

The original Kramers equation had a = 1 at all /, not the a 0.4-0.8 seen here at larger q. However, as seen in Chapter 5, solvent diffusion actually has the viscosity-dependence of Eq. 15.3 with an 7-dependent a, namely a = 1 at smaller qtoa = 2/3 at q larger than 5 cP. The small-molecule self-diffusion coefficient and the segmental diffusion time thus show consistent dependences on q. The spirit of the Kramers approach, namely that the rate of diffusion-driven molecular motions should track the solution fluidity q in the same way that the rates of solvent and small-molecule diffusion track the solution fluidity, appears to be preserved by experiment. 

The Walden rule is interpreted in the same manner as the Stokes-Einstein relation. In each case it is supposed that the force impeding the motion of ions in the liquid is a viscous force due to the solvent through which the ions move. It is most appropriate for the case of large ions moving in a solvent of small molecules. However, we will see here that just as the Stokes-Einstein equation applies rather well to most pure nonviscous liquids [30], so does the Walden rule apply, rather well, to pure ionic liquids [15]. When the units for fluidity are chosen to be reciprocal poise and those for equivalent conductivity are Smol cm, this plot has the particularly simple form shown in Figure 2.6. 

Multiparticle collision dynamics provides an ideal way to simulate the motion of small self-propelled objects since the interaction between the solvent and the motor can be specified and hydrodynamic effects are taken into account automatically. It has been used to investigate the self-propelled motion of swimmers composed of linked beads that undergo non-time-reversible cyclic motion [116] and chemically powered nanodimers [117]. The chemically powered nanodimers can serve as models for the motions of the bimetallic nanodimers discussed earlier. The nanodimers are made from two spheres separated by a fixed distance R dissolved in a solvent of A and B molecules. One dimer sphere (C) catalyzes the irreversible reaction A + C B I C, while nonreactive interactions occur with the noncatalytic sphere (N). The nanodimer and reactive events are shown in Fig. 22. The A and B species interact with the nanodimer spheres through repulsive Lennard-Jones (LJ) potentials in Eq. (76). The MPC simulations assume that the potentials satisfy Vca = Vcb = Vna, with c.,t and Vnb with 3- The A molecules react to form B molecules when they approach the catalytic sphere within the interaction distance r < rc. The B molecules produced in the reaction interact differently with the catalytic and noncatalytic spheres. 

Recent solid state NMR studies of liquid crystalline materials are surveyed. The review deals first with some background information in order to facilitate discussions on various NMR (13C, ll, 21 , I9F etc.) works to be followed. This includes the following spin Hamiltonians, spin relaxation theory, and a survey of recent solid state NMR methods (mainly 13C) for liquid crystals on the one hand, while on the other hand molecular ordering of mesogens and motional models for liquid crystals. NMR studies done since 1997 on both solutes and solvent molecules are discussed. For the latter, thermotropic and lyotropic liquid crystals are included with an emphasis on newly discovered liquid crystalline materials. For the solute studies, both small molecules and weakly ordered biomolecules are briefly surveyed. 

However, picosecond resolution is insufficient to fully describe solvation dynamics. In fact, computer simulations have shown that in small-molecule solvents (e.g. acetonitrile, water, methyl chloride), the ultrafast part of solvation dynamics (< 300 fs) can be assigned to inertial motion of solvent molecules belonging to the first solvation layer, and can be described by a Gaussian func-tiona) b). An exponential term (or a sum of exponentials) must be added to take into account the contribution of rotational and translational diffusion motions. Therefore, C(t) can be written in the following form ... 

In addition to the mobility of colloidal-sized probes, there is considerable interest in monitoring the motion of small molecules, including the solvent itself and also dye molecules. Once again, more is known about such mobilities in the case of transient gels, where it is now certain that "monomer segment mobility" effects are prerequisite to a correct dynsumical interpretation (102-105). Several papers in the present volume... 

In solution the barriers to conformational change are often small, even when the molecule has a built-in restriction on motion. Conformational barriers calculated for isolated molecules in the gas phase that reveal the nature of some of these barriers are likely to be good reflections of the real barriers in solvents such as chloroform. There usually are many conformations present at any time in such solutions and they are in equilibrium. The equilibria are likely to be much more restricted in polar media. It is very important for us to discover the extent of the equilibrium, that is, the number of conformations involved, the relative proportion of each, and the rate of transformation between them. Such a task is virtually impossible from theoretical considerations, and two major approaches using physical techniques, mainly nmr, are possible. These have been discussed in some detail for small molecules and can be summarized as follows. 

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