Intermolecular nucleation

Crystal growth can only start after the crystalline phase has been nucleated, in contrast to a chemical reaction which may proceed on any single encounter of two reaction partners. This difference between the chemical reaction which sets the primary bonds and the crystallization which sets the secondary bonds in crystals of flexible linear high polymers makes the crystal nucleation to the central problem. From the different examples of crystallization during polymerization collected here one can derive five different nucleation processes A. an intermolecular nucleation followed by simultaneous polymerization and crystallization dose to the ceiling temperature, B. an intermolecular nucleation followed by simultaneous polymerization and crystallization far from the ceiling temperature, C. an intermolecular nucleation followed by successive pol3uner-ization and crystallization, D. and E. an intramolecular nudeation which may also show simultaneous or successive polymerization and crystallization. 

Fig. 4.15 Schematic pictures of (a) intermolecular nucleation and (b) intramolecular nucleation...

It should be noted fliat intermolecular nucleatitm could coexist with intramolecular nucleation. Intermolecular nucleation is often observed with short chains, rigid chains, polymerizing chains, or when chains are stretched. Recently, upon stretching network polymers, the transition from intramolecular nucleation to intermolecular nucleation was observed in Monte Carlo simulations (Nie et al. 2013). By analyzing the probability of adjacent chain-folding of those newly formed crystallites with a size between 50 to 200 parallel packed bonds at each step of stretching, an obvious reduction was observed in its evolution curve under each temperature as shown in Fig. 4.20a. The corresponding critical strain was considered to be the transition point under which intramolecular nucleation is the favorite and above which intermolecular nucleation becomes the dominant. 

Compared the critical strain with the onset strain of crystallization during stretching under each temperature as shown in Fig. 4.20b, it is fotmd that at low temperatures (the dimension-reduced T < 4.0) intramolecular nucleation dominates the initiation of polymer crystallization with a smaller strain than the critical value, and when temperature becomes higher, intermolecular nucleation begins to dominate the initiation of crystalhzation. 

In practice, intermolecular nucleation could coexist with intramolecular nucleation. Intermolecular nucleation is often observed with short chains, rigid chains, or when chains are stretched. Recently, upon stretching network polymers, the transition from intramolecular nucleation to intermolecular nucleation was observed in dynamic Monte Carlo simulations [59]. By analyzing the probability of adjacent chain folding... 

The tensile strength of a pure liquid is determined by the attractive intermolecular forces which maintain its liquid state the calculated tensile strength of water, for example, is in excess of -1000 atmospheres (7). In practice however, the measured threshold for initiation of cavitation is never more than a small fraction of that. Indeed, if the observed tensile strengths of liquids did approach their theoretical limits, the acoustic intensities required to initiate cavitation would be well beyond that generally available, and no sonochemistry would be observed in homogeneous media Cavitation is initiated at a nucleation site where the tensile strength is dramatically lowered, such as small gas bubbles and gas filled crevices in particulate matter, which are present in the liquid. 

In examining a crystalline structure as revealed by diffraction experiments it is all too easy to view the crystal as a static entity and focus on what may be broadly termed attractive intermolecular interactions (dipole-dipole, hydrogen bonds, van der Waals etc., as detailed in Section 1.8) and neglect the actual mechanism by which a crystal is formed, i.e. the mechanism by which these interactions act to assemble the crystal from a non-equilibrium state in a super-saturated solution. However, it is very often nucleation phenomena that are ultimately responsible for the observed crystal structure and hence we were careful to draw a distinction between solution self-assembly and crystallisation at the beginning of this chapter. For example paracetamol, when crystallised from acetone solution gives the stable monoclinic crystal form I, but crystallisation from a molten sample in the absence of solvent... 

Lansbury and his group have shown that amyloid formation is a nucleation-dependent process and that the nucleation step can be evaded by using seeds of preformed fibrils. The nucleation process is a rate-limiting step in amy-loidogenesis. ft is characterized by a lag phase. During the time required for nucleus formation, the protein appears to be soluble. Nucleus formation requires a series of association steps that are thermodynamically unfavorable because the resultant intermolecular interactions do not outweigh the entropic cost of association [60]. Once the nucleus has formed, further addition of monomers becomes thermodynamically favorable. The nucleation is concentration dependent [61] and shows the presence of hydrophobic cooperativity in the process [62]. 

Nucleation kinetics are experimentally determined from measurements of the nucleation rates, induction times, and metastability zone widths (the supersaturation or undercooling necessary for spontaneous nucleation) as a function of initial supersaturation. The nucleation rate will increase by increasing the supersaturation, while all other variables are constant. However, at constant supersaturation the nucleation rate will increase with increasing solubility. Solubility affects the preexponential factor and the probability of intermolecular collisions. Furthermore, when changes in solvent or solution composition lead to increases in solubility, the interfacial energy decreases as the affinity between crystallizing medium and crystal increases. Consequently, the supersaturation required for spontaneous nucleation decreases with increasing solubility, ° as shown in Fig. 7. 

The supramolecular assembly process can be controlled so that the precursor nuclei in solution adopt a structure that resembles the structure of the desired crystalline modification. " This concept has been used in the design of nucleation inhibitors to prevent growth of the stable polymorph and enhance the growth of the metastable polymorph. Davey and coworkers have explained the solvent dependent polymorph appearance of sulfathiazole by analyzing the intermolecular interactions in the various polymorphic structures, and comparing them with the supramolecular assemblies that could exist in the different solvents. In this case, however, the solvent dependent selective crystallization of a polymorph was not correlated with solubility. 

Because of their importance to nucleation kinetics, there have been a number of attempts to calculate free energies of formation of clusters theoretically. The most important approaches for the current discussion are harmonic models, " Monte Carlo studies, and molecular dynamics calcula-tions. In the harmonic model the cluster is assumed to be composed of constituent atoms with harmonic intermolecular forces. The most recent calculations, which use the harmonic model, have taken the geometries of the clusters to be those determined by the minimum in the two-body additive Lennard-Jones potential surface. The oscillator frequencies have been obtained by diagonalizing the Lennard-Jones force constant matrix. In the harmonic model the translational and rotational modes of the clusters are treated classically, and the vibrational modes are treated quantum mechanically. The harmonic models work best at low temjjeratures where anharmonic-ity effects are least important and the system is dominated by a single structure. 

In calculated intermolecular frequencies specifically carried out to point to the differences of cluster and liquid structural mismatch, Plummer (1973) showed that the free energy change for a 20-molecule clathrate is 57 kcal/mol, while the ice Ih of 20-molecule size has a 72 kcal/mol difference. The conclusion that this may be a reason for difficulties associated with Ih ice formation via homogeneous nucleation is worthy of further consideration. 

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