# Information Storage in Liquids with Ordered Molecular Assemblies

## Abstract

**:**

## 1. Introduction

## 2. Negative Entropy Residing in Molecular Assemblies

_{I}, are essentially “floating terms” and in principle can serve only as base lines for directional processes like those associated with transmission of information [3,5]. Statistical mechanics is a leading tool in this direction which can be also applied in statistical thermodynamics of gases and liquids at their steady state [5,6]. In the most common cases, where thermodynamic values are presented as the difference between two states of equilibrium , the absolute temperature, T, and its energy coefficients k (per molecule) or R (per mole), provide absolute scales for the energy involved in such transitions. The quantitative measures for the two types of entropy then become TΔS and TΔS

_{I}.

## 3. Information Capacity in Fluids

_{0}. In cases of liquids with ordered molecular assemblies prevailing at their steady state, the stored information of I > I

_{0}is correlated with the acquired negative entropy, –ΔS

_{I}= I − I

_{0}. The latter can be presented analogously to ΔS of classical thermodynamics, namely in units of J·mole

^{−1}·K

^{−1}. The corresponding energy stored in the negative entropy domains is then TΔS

_{I}, which has been defined as information capacity [7,8]. Quantitative evaluation of ΔS

_{I}entails an introduction of an experimental parameter which corresponds to the prevailing order. Subsequently, the information capacity, TΔS

_{I}

_{,}can be evaluated.

_{0}= I/I

_{0.}Both can be presented in terms of diversion from isotropy [1,2,3,4,5,6], as expressed in the fundamental Boltzmann Equation:

_{I}= RlnW = Rln I

_{I}= R ln W/W

_{0}= R ln I/I

_{0}

_{0}is the basal information at complete isotropy. Insertion of ordered regions into the liquid, i.e., induction of anisotropy, negative entropy is acquired due to I > I

_{0}as expressed in Equation 2 and energy amounting to –TΔS

_{I}is then accumulated:

_{I}= RT lnW/W

_{0}= RTln I/I

_{0}

_{I}= RT lnW

_{max}/(W

_{max}– I) = RT ln I

_{max}/(I

_{max}– I)

## 4. Information Storage in Solvent Envelopes

## 5. Chiral Solutions

**Figure 1.**Configuration of a right handed Moebius ring acquired by solvent molecules (Ι) surrounding a chiral solute (۞).

_{0}which corresponds to complete isotropy, as in racemic solutions, to I

_{max}which corresponds to a saturated chiral solution. Accordingly:

_{max}= α / α

_{max}

_{max}corresponds to saturated solution. Equation 4 is then extended to:

_{I}= RT ln I

_{max}/(I

_{max}– I) = RT ln α

_{max}/ (α

_{max}– α)

_{max}>> I or α

_{max}>> α, Equation 6 is reduced by a simple exponential approximation to the linear forms:

_{I}≈ RT I/I

_{max}= RT α / α

_{max}

_{I}, in chiral solutions remains corresponding to the energy evolved in the loss of order in the system. Furthermore, TΔS

_{I}is expected to increase linearly with α, namely with concentration, a key point in its experimental verification [7].

_{I}in chiral solutions can be achieved by heat release ensuing two independent processes; heat of dilution and heat of intermolecular racemization. However, these processes are, in general, of just a few Joules per mole, which fall near the border line of accuracy in conventional calorimetric measurements. With the availability of micocalorimetry instrumentations, in particular isothermal titration calorimetry, ITC [15,16], such processes can be now determined. These have up to now been applied to aqueous solutions of d- and l-amino acids and neat chiral liquids, which will be described below as specific examples.

_{I}component attributed to the disintegration of supramolecular chiral hydration assemblies [11].

_{I}can be alternatively released upon intermolecular racemization by mixing solutions of opposite enantiomers [7]. As hypothesized above, the released heat, Q, upon dilution or intermolecular racemization of chiral solutions, corresponds predominantly to the dissipation of the order in the chiral domains:

_{I}≈ RT α / α

_{max}= I

_{f}RT |α|

_{f}is defined here as the "information coefficient". As a coefficient it provides a constant which converts a measurable parameter to a distinct physical value. In our case, it translates the apparent |α| value, or its change, into the stored thermal energy, in units of RT. It formally corresponds to the reciprocal of |α|

_{max}(see Equation 7) and can be derived from the slopes of the linear dependence of Q on |α|, which are obtained experimentally [7]. I

_{f}values obtained for proline and alanine at different concentrations in water and their derived energy parameters, are presented in Table 1. As shown, this coefficient increases markedly with concentration. Other factors like temperature may also affect I

_{f}.

**Table 1.**Information capacity of 1M proline and alanine in water, at 30° [7].

Resident solute | Liberated heat upon point racemization, Q, (J·mole^{−1}) | I_{f}RT (J·mole^{−1} ·optdeg^{−1}) | I_{f} (optdeg^{−1}) | Information capacity, RT α/α_{max}, estimated (kJ·mole^{−1}) |
---|---|---|---|---|

L-Proline | 19.2 | 18.0 | 7.1·10^{−3} | 0.3 |

D-Proline | 26.4 | 22.6 | 9.0·10^{−3} | 0.3 |

L-Alanine | 2.5 | 104.7 | 4.2·10^{−2} | 1.2 |

D-Alanine | 2.6 | 108.9 | 4.3·10^{−2} | 1.2 |

## 6. Neat Chiral Liquids

_{3}CHD-OH, to its common non chiral form CH

_{3}CH

_{2}-OH.

## 7. Micellar Aggregates

## 8. Transient Information Acquired by Fluorescent Solutes

^{−12}s) is ensued, trapping the excited fluorescent molecule in its lowest vibrational level of the first excited state for approximately 10

^{−8}s. At this time interval, reorientation of the solvent envelope takes place. Immediately after emission of the fluorescence photon the solvent envelope relaxes back to its original configuration. This sequence of solvent reorientation upon electronic excitation is outlined in Figure 2 for the common case of a fluorescent aromatic molecule. As shown, the excited state is characterized (classically) by a transient dipole which induces relatively strong polarization in the surrounding solvent molecules. The ensuing electrostatic attraction between the excited molecule and the polarized surrounding solvent molecules is displayed by an energetic shift in the emission spectrum to longer wavelengths, i.e., lower energy. For example, in the case of tryptophan, a fluorescent amino acid, the maximum of the emission spectrum shifts from 320 nm to 355 nm when measured in a hydrophobic solvent and in water, respectively [22]. This typical 35 nm shift of the fluorescence spectrum, corresponds to 8 kcal/mole, which is invested in the strong electrostatic interaction of the excited molecules with water. A very small fraction of it, presumably in the range of several cal per mole, corresponds to TΔS

_{I}of the acquired order which precedes the full relaxation to the ground state. Thus, the instantaneous emission leaves the solvent coating around the previously excited molecule (d in Figure 2) in an ordered configuration which stores the equivalent information. This transient configuration relaxes spontaneously to the less ordered original configuration (a in Figure 2) by releasing heat amounting to TΔS

_{I}. Experimental resolution of this quantity encounters the high background of the simultaneous heat liberations (b to c in Figure 2) which are by far more intensive. It can, in principle, be approached by analyzing heat release ensuing a pulse excitation or pulse extinction of a steady state excitation.

**Figure 2.**Cycling of solvent configuration in a fluorescence process. A fluorescent solute, e.g., an aromatic molecule (a), is excited (b) and then relaxes to a polar excited state (c) which lives for about 10

^{−8}s, when the surrounding solvent molecules reorient themselves. Upon fluorescence emission, the solvent shell transiently preserves an ordered configuration with an acquired information capacity (d) which relaxes spontaneously to the initial configuration.

## 9. Chiral Conductivity

**Figure 3.**Signal transmission along a right handed nerve fiber and a left handed nerve fiber which can be either wires or planar sheets (displayed in the magnified section).

## 10. Information Processing

## 11. Conclusions

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Shinitzky, M. Information Storage in Liquids with Ordered Molecular Assemblies. *Entropy* **2011**, *13*, 1-10.
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Shinitzky M. Information Storage in Liquids with Ordered Molecular Assemblies. *Entropy*. 2011; 13(1):1-10.
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**Chicago/Turabian Style**

Shinitzky, Meir. 2011. "Information Storage in Liquids with Ordered Molecular Assemblies" *Entropy* 13, no. 1: 1-10.
https://doi.org/10.3390/e13010001