Re: [ESPResSo] orientational order parameter

[Markus Deserno]

Hi,

> martina pannuzzo wrote:
>> a few days ago, i sent a mail but i got no aswer;maybe i was unclear. I
>> am simulating the lipid vesicles with the mbtools but the order
>> parameter is not convincing.in the state more ordered i get a
>> orientational order parameter value close to the lowest possible -0,45.
>>  when the temperature increase the oop increase. there appears to be a
>> reversal of the sign. I attached a picture to make the idea.
>>
>
> First, let me state that I am not an expert on the mbtools, but I did
> work on membranes during my PhD thesis.
>
> I do not see any error in what you describe. To my understanding, the
> nematic order parameter of a vesicle should be close to -0.5. Have a look
> at the definition: If all lipids point to the same direction, S has a
> value of 1. If all lipids point to random directions (and a vesicle can be
> seen as that), S whould be -0.5.

I am confused by that. Are you sure, Olaf?

Yes, if all lipids point in the same direction, then the order
parameter is 1, assuming (I believe) that during calculation we
tell the system to measure the angles with respect to that
magic axis.  However, if all lipids point evenly in all
different directions (i.e., if they are completely random),
then I expect an order parameter of 0.

A negative order parameter only occurs for "anti-alignment",
i.e., if lipids preferentially point AWAY from some given axis.
Say, there is a north-south-axis, but all lipids point
towards the equator.  Since this is a somewhat curious state
to achieve, I indeed do not understand how it shows up in
Martina's simulations.

But maybe I'm just confused about order parameters?

> The parameter is not defined locally, i.e. it does not take into account
> the nieghbourhood of lipids. Instead, it is defined globally over all
> lipids.

Yes. typically people calculate these things for a flat membrane
and pick as the external axis the normal of that membrane.  If you
have nontrivial shapes and calculate the lipid order parameter
for them, then you're entangling properties of the lipid phase
with properties of the aggregate shape, and I'm not convinced that
this is a clever thing to do.

Best,

Markus Deserno