Calculate Polymer Melt Structure Factor - Help Needed

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In summary, the conversation discusses the calculation of the structure factor for a polymer melt, specifically dealing with the imaginary exponent in the equation. The individual is unsure of how to handle the exponent and suggests multiplying by the complex conjugate, but this would eliminate the exponential altogether. Another person suggests using Euler's formula and considering only the real part of the trig side, as it can make calculations easier. However, the first person is hesitant to throw out the complex part and is looking for further clarification.
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I'm trying to calculate the structure factor for a polymer melt: S(q)=[tex]\sum_{k}[/tex][tex]\sum_{j}[/tex][tex]\epsilon^{i*<q>*<r_{kj}>}[/tex], but I don't know how to deal with the imaginary exponent...(the rest of the variable don't really matter, because I'm confused about how to deal with the exponent, but q is the scattering vector, and r[tex]_{kj}[/tex] is the distance between vectors k and j) my first thought was to multiply by the complex conjugate, but doesn't that just get rid of the exponential altogether, leaving nothing for you to add? I don't understand how I can get any data if I multiply by the complex conjugate. Anyone have any suggestions?
 
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Use http://en.wikipedia.org/wiki/Euler%27s_formula" and consider only the real part of the trig side (i.e., the cosine). The exponential form makes some calculations easier.
 
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Thanks for responding!
I considered that, but it doesn't seem correct to just throw out the complex part...is there something I'm missing?
 

1. What is the purpose of calculating the polymer melt structure factor?

The polymer melt structure factor is a measure of the spatial arrangement of polymer chains within a melt. It provides important information about the physical properties and behavior of the melt, such as viscosity and mechanical properties. Therefore, calculating the structure factor is crucial for understanding and predicting the behavior of polymer melts.

2. How is the polymer melt structure factor calculated?

The polymer melt structure factor is typically calculated using Fourier transform methods. This involves taking the Fourier transform of the pair correlation function, which describes the probability of finding two polymer chains at a certain distance from each other. The resulting structure factor provides information about the spatial arrangement of polymer chains in the melt.

3. What factors can affect the polymer melt structure factor?

The polymer melt structure factor can be affected by a variety of factors, including the molecular weight and size of the polymer chains, the temperature and pressure of the melt, and the presence of additives or other components. Additionally, the method used to calculate the structure factor can also impact the results.

4. How can the polymer melt structure factor be used in practical applications?

The polymer melt structure factor has many practical applications in the polymer industry. It can be used to optimize polymer processing conditions, such as melt extrusion or injection molding, to improve the quality and properties of polymer products. It can also aid in the development of new polymer materials with desired properties.

5. Are there any limitations to calculating the polymer melt structure factor?

While the polymer melt structure factor is a valuable tool for understanding polymer melts, there are some limitations to its calculation. It assumes that the polymer chains are in a random-coil conformation, which may not always be the case. Additionally, the calculation may become more complex for systems with a high degree of entanglement or interactions between polymer chains.

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