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There are many ways (both in terms of variety and ingenuity) to generate a polymer chain. From time to time, new methods are invented and reported in scientific journals. Almost all these methods are geared towards reducing the
attrition problem and/or computational costs of generating a chain. In this applet, a sophisticate MC method, namely, the Configurational Biased Monte Carlo is used. You may be anxious to run the program now but it is important to know some background, however brief, in order to
utilize the method more effectively. I therefore urge you to read on.
Brief description will be given here that should give you sufficient knowledge to run the applet. The term 'biased' may at first sound a bit
'un-Monte Carlo' that destroys the flavor of randomness. However, this is precisely the approach that is used in this method: it has an ability to successively generate new beads in such a way that it tends to avoid region of space that is already occupied by other
beads. The chain generation process is step-wise in nature. In other words, only a bead is inserted, one at a time.
We begin by looking at an example of partially grown chain as shown below. The next bead that will be inserted is Bead 5 (figure on the left, as shown below). Before we decide where to place Bead 5 we first of all generate a number of links (CHOICE, show as green links) in random directions, each is connected to Bead 4. We then calculate the enrgy interaction, using the
Lennard-Jones formula, for each link as if Bead 5 is inserted on that link. This is referred to as a trial bead. In the example shown below we use CHOICE = 5.
The energy interaction for each trial bead is the sum of interactions between the trial Bead 5 and Beads 1 to 3. We do not need to consider Bead 4 becuase the energy between Beads 4 and 5 will be the same whichever direction Bead 5 will be taken. Once the total energies for all trial beads are calculated, a random number is used to decide which link will be selected for the
Bead 5. The probability of a selection will be weighted with the associated energy: trial beads with most favorable energy will be likely to be selected, while trial beads with high energy will be least likely to be selected. Diagram on the right show that one of the links is subsequently being selected for Bead 5. The procedue is repeated for Bead 6, 7, ... until a desire length N is achieved.
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