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IDEAL CHAIN - JAVASCRIPT - POLYMER CHEMISTRY HYPERTEXT
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<a href="Introduction.htm" class="chapter">INTRODUCTION</a><br /><br />
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<td>
<a class="toplink" href="MechanicalPropertiesIntro.htm">Mechanical Properties</a> 
</td>

<td width="20"></td>

<td>
<a class="toplink" href="MolecularWeightIntro.htm">Molecular Weight</a> 
</td>

<td width="20"></td>

<td>
<a class="toplink" href="PolymerModelingIntro.htm">Polymer Modeling</a> 
</td>

<td width="20"></td>

<td>
<a class="toplink" href="PolymerSolutionThermodynamicsIntro.htm">Solution Thermodynamics</a> 
</td>

</tr>
</table>


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<center>

<img src="polymers.jpg" />
<h2>
IDEAL CHAIN
</b>
</h2>
<h6>
<a class="hyperlink" href="JavascriptSeries.htm">JAVASCRIPT SERIES</a>
</h6>

</center> 


 

<br /><br />

The <b>ideal chain</b> or <b>freely jointed chain</b> is assumed.  Each monomeric addition
 can orient the new monomeric repeat group in any direction (no constraint on angle) and
 growing polymer chain can polymerize through space occupied by polymer (no 
<a class="hyperlink" href="ExcludedVolume.htm">excluded volume</a>).

<br /><br />

To grow each new monomer, spherical coordinates are used, setting r=1 and making θ and 
 φ random angles (in radians) from 0 to 2π.

<br /><br />

100 units are polymerized.  The displacement length (see <a class="hyperlink" 
href="EndToEndDistance.htm">End to End Distance</a>) is calculated and reduced to an
 integer.  The process rounds all numbers down.  


<br /><br />

Clicking a button below adds the number of polymers requested
 to the growing distribution.  Clicking "1 polymer" several times shows the randomness
 of the displacement lengths (end to end distances).  Clicking "1000 polymers" or "5000 polymers" adds polymers
 much faster.  

<ul>
<font size="-1">
For 5000, the browser program may give a message that a script
 is taking a long time, and ask if you want to abort the script.  If you choose "no"
 the polymerizations will continue.  For most computers, the total time should
 be less than a minute.
</font>
</ul>

<br /> 


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<input onClick="Walk50()" type="submit" value="50 polymers" />

<input onClick="Walk1000()" type="submit" value="1000 polymers" />

<input onClick="Walk5000()" type="submit" value="50000 polymers" />


<br /><br />





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<br /><br />


<br /><br />

The average length is <span id="avg"> - - - </span>.

<br /><br />

The number of polymers is <span id="totaln"> - - - </span>.

<br /><br /><br /><br />

An example for 1000 polymerizations: 

<br /><br />

<center> 
<img src="idealchain1000.gif" />
</center>

<br /><br />

An example for 5000 polymerizations: 

<br /><br />

<center> 
<img src="idealchain5000.gif" />
</center>

<br /><br />

An example with 25,000 polymerizations is shown below.  The probability density for a Maxwell Boltzmann
 distribution was added to the spreadsheet for comparison to distribution of values for displacement length.

<br /><br />

<center>
<img src="MBprobabilitydensity.gif" />
</center>

<br /><br />

In the graph below, "Norm" (blue) refers to the normalized values.  Norm values were calculated by
 taking the number of occurances, and dividing by 25,000.  The "theo" values are theoretical
 values calculated from the above probability density function. The only variable is "a".  
<br /><br />
Throughout the slideshow, the variable "a" changes, starting at 1 and ending at 5.25.  For
 each slide, the value of a is shown in the upper right corner.

<br /><br />

<center>
<img src="BDidealchain.gif" />
</center>

<br /><br />

The shape is similar, but not perfectly congruent, and tentatively the program is considered to have a flaw. 

<br /><br />

A <a class="hyperlink" href="JSidealchaintest.htm">second Ideal Chain</a> page was constructed.
 

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