© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

10.5.5 Other Temperature-Dependent Properties

There are a great many temperature-dependent materials properties of nanomedical relevance, but there is only space here to mention just a few:

1. Denaturation and Combustion -- Protein denaturation and reduced receptor-ligand fidelity may occur at temperatures as low as 50-100°C. It is true that not much happens to a block of diamond dropped into boiling water,²⁸⁰ but the maximum combustion point for diamond in air is ~800°C,⁶⁹¹ and carbon nanotubes start to burn in air at ~700°C.¹⁸⁵⁷ At low temperatures, receptor-ligand binding may occur with greater fidelity but more slowly, and there are various unusual biological effects that occur at low temperature -- for example, the lens of the human eye becomes opaque when cooled to below freezing [G. Fahy, personal communication, 1997].

2. Speed of Sound -- Acoustic waves travel at different speeds in cold and hot media, potentially affecting medical nanorobot sensing, energy transmission, communication and navigation. In general, the speed of sound (v_sound) in liquids depends upon the adiabatic bulk modulus B and density r, both of which are temperature-dependent, as v_sound = (B/r)^1/2 (Eqn. 4.30). The temperature dependence of the speed of sound in pure water at 1 atm has been carefully studied and is approximated fairly well by:²¹⁵⁵

{Eqn. 10.25}

where T is temperature in K. Thus the speed of sound increases with rising temperature up to a peak at 347 K (74°C), then decreases thereafter. For practically all other liquids, v_sound decreases with rising temperature over the entire range in which the material remains a liquid.²¹⁵⁶ (In most liquids, v_sound increases linearly, though only very slightly, with pressure. For example, v_sound in benzene rises ~17% when pressure is increased from 1 atm to 500 atm;²¹⁵⁶ see also Section 10.3.3.) The speed of sound in water-ice just below the freezing point, estimated from Eqn. 4.30, is ~1000 m/sec. The speed of sound in dry air at 1 atm increases with rising temperature and is approximated by:¹¹⁶⁴

{Eqn. 10.26}

3. Energy Absorption -- Acoustic absorption and attenuation coefficients change with temperature, affecting the efficiency of acoustic power transfer. Absorption per unit of radio frequency (rf) energy in tissue during diathermic heating also varies with temperature.

4. Surface Tension -- The surface tension of liquids at the airliquid interface tends to decline as temperature rises, falling to zero at the boiling point. For instance, the air-liquid surface tension for a 48% volumetric ethanol-water mixture (96 proof, U.S. spirit) is 30.10 x 10^-3 N/m at 20°C but 28.93 x 10^-3 N/m at 40°C;⁷⁶³ values for pure water are given elsewhere (Section 9.2.3).

5. Dielectric Constant -- The electrical properties of materials may be temperature-dependent. For example, the dielectric constant of water declines with rising temperature and is crudely approximated by:²¹⁵⁷

{Eqn. 10.27}

for temperatures in kelvins from T = 273-373 K (0-100°C), for rf frequencies up to 100 MHz, and at 1 atm pressure. The dielectric constant of ice at 0°C is virtually the same as that of water (88.0), but decreases rapidly with decreasing temperatures below 0°C, and with increasing frequency; by 0.1 MHz, k_ice ~ 2-4 with little influence of temperature.²¹⁵⁷ Relative permittivity decreases by a large factor for many other substances as they change state at the freezing point; for example, k falls from 35 for liquid nitrobenzene at 279 K to 3 for solid nitrobenzene at 279 K.⁷²⁷ In general, nonpolar liquids have a small dielectric constant (e.g., 1.5-2.5) that is nearly independent of the temperature, whereas polar liquids have a larger value that declines rapidly as temperature rises.²⁰³⁶

Last updated on 24 February 2003