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much attention has been paid to the sub - micrometer scale thermal transportation along a nanowire mainly due to the scale - dependent carrier behavior upon nanoconfinement and their potential application in the thermoelectric devices and thermoresistive coating materials [ 1 - 7 ] .
one of the key problems is the temperature difference ( td ) between two ends of the nanowire [ 8 - 10 ] .
however , the td on the sub - nanometer scale ( or even on a few micrometers ) keeps rather small .
it will diminish to a very small value in less than 1 second , even if a highly thermal insulating material is employed .
it is because the power of thermal conduction from the end of the high temperature to that of the low temperature is much higher than the thermal dissipation if there is a considerable td . as the result
, only the td of 0.2 k was observed along a single wall carbon nanotube of 2 m .
even , the well - known thermoelectric candidate of bi nanowire produced a small td of 4 k along the length of 15 m .
the measurement of these small values of the tds requires some deliberately designed mems devices and complex procedures to make precise calibration of local temperatures . in this work , carbon nanowires ( cnws ) were suspended on a holey support film , and then pb nanoclusters were deposited on the sample in situ temperature variable transmission electron microscopic ( tem ) observation demonstrated the obvious td of up to 10 k along the cnw of less than 1 m . on the other hand , the present td permits the intuitivistic visualization of the nanoscale thermal inhomogeneity .
nanostructures of the low melting point nanoparticles ( pb , ga or even zn ) have long been featured for their thermal effects , such as the freezing behavior , phase oscillation between liquid and solid   and the liquid nanojet from the core expansion ( , see the supplementary materials also ) . in the normal heating carried out through broad contacts ,
the earlier mentioned thermal effects occurred abruptly ( , see the supplementary materials also ) .
however , it is only possible during controlled heating . in our work , heat is expected to input to the particle on cnw ( poc ) through the cnw , which limits the thermal input by changing the 2-dimensional ( d ) contact of the particle on the support ( pos ) to 1-d transportation .
the cnw was prepared in a radiofrequency plasma sputtering chamber , where a small nozzle to the high - vacuum chamber led the cnw onto the tem copper meshes with holey support films .
tem , high - resolution tem and electron energy loss spectra ( eels ) proved their amorphous structures ( see the supplementary materials also , ) .
the beam of pb nanoclusters was generated by a gas aggregation cluster source and deposited onto the copper mesh .
a tem of jeol 200cx was employed for the in situ observation , and the process was recorded by a digital video system .
figure 1a shows a tem image from the region of interest , where we can see the pb particles are distributed on the support film and on the cnw simultaneously .
the cnws with the diameters of 1020 nm are suspended on the pore , on which a pb nanoparticle with the size of about 130 nm sits .
the system was heated through a heating holder and the thermocouple sensor recorded the heating temperatures in a temperature - fixing mode .
the thermal conduction between the heating source and the copper mesh was enhanced by two pressed nickel grids .
the holey support film was attached to the copper mesh , and all the region in the support film was within a few micrometers from the copper grid .
therefore , we regard the temperature from the thermocouple meter as the temperature on the amorphous support .
pos was heated more effectively than poc due to the 2-d transporting routes ( see fig .
a is the tem image of the whole device , where we can see the nanowire is suspended on the hole of a porous carbon film .
it was directly taken from the phosphorus screen by a digital video machine when the system was heated to 350 c .
one of them is the abrupt change of the contrast , which can be seen in fig .
the exposure to the air coated an oxide shell on the pb particles before transferring to the tem .
after the particle is melted in the tem , the original crystalline pb core turns to liquid abruptly .
. it may be not clear enough for pos since the amorphous support film contributes to a noisy background sometimes .
2d , where some material from the melted core is evaporated soon due to the low heat of evaporation of pb .
the abruptly enhanced evaporation is subject to the transition to liquid , which shows the melting point has passed then .
appearance of the cavities also eliminates the influence of superheating due to close oxide coating .
a , b and c are the tem images taken at the time of 9 , 2340  and 3152  , respectively .
as recorded by the thermocouple , the corresponding heating temperatures are 200 , 300 and 325 c .
the irregular edges of the insets are due to the cut of the frames from the dv .
it shares the same scales bar as ( a ) figure 2 shows the evidence of melting retardation . here , we trace the change of two particles , one of which is poc and the other is pos ( fig .
figure 2a is the original image of the system at the temperature of 200 c .
no obvious signature of melting occurred in poc after 7 min of heating at 300 c . with increasing the heating temperature
it was read from the thermocouple meter , and it was the temperature of the support film , when the poc was just beginning to melt .
the melting of pos occurred before 300 c . assuming the equivalence of the melting points of all the pb particles , the evidence with a td of more than 10 k is present along the cnw .
one may argue that the melting retardation is due to the size effect of pb nanoparticles .
but the size effect makes little influence on the melting points of the nanoparticles larger than 10 nm , while the pb particles in the experiment are larger than 50 nm .
it eliminates the influence of the size - dependent melting point and consolidates the presence of the earlier mentioned td . as stated earlier , the td of up to 10 k between the two ends of less than 1 m has been demonstrated .
such a td is unexpectedly high since it turns out a thermal insulting performance of 10 k / mm
. it could not be the result from the dominance of thermal transportation along cnw , as shown by the top calculation curve in fig . 3a .
if only the thermal transportation due to the td contributes to the heat flow of the poc , the td can cease to almost zero shortly .
for example , if we increase the heating temperature from 573 to 623 k from one end of the cnw , the td reduces to 0.1 k in ten milliseconds .
the heavier mass of the poc contributes little to the td . after considering the overall sources of thermal input and thermal dissipation of the poc , the irradiation is found to be an effective thermal dissipation route .
firstly , the convection through the air is excluded due to the high - vacuum environment .
final dissipation source of the irradiation can be described by the stefan - boltzmann law , where s is the area of poc ,  of 0.43 is the emission coefficient of the grey body ( oxided pb ) and  is the constant .
although the irradiation effect is often omitted in the thermal measurement at a few hundred celsius degrees , it is actually related to the surface area . in the experiment ,
a huge pb particle is attached on the cnw , leading to a much larger surface than the original cnw and a larger irradiation thermal dissipation .
the calculation considers the cnw thermal input , the irradiation dissipation and the temperature increase from heating .
one can find the td increases with increasing the size of poc . during heating from 673 to 723 k ,
the stable td is still smaller than 0.5 k when the diameter is equal to that of cnw .
while poc becomes a ball with the radius of 65 nm , the td of 4.5 k can be expected .
the particle with the radius of 100 nm leads to a td of nearly 10 k. the calculation validates the presence of the obvious td in the experiment .
it provides the td of more than 1 k at room temperature , which can be compared with the previous study .
a assuming the heating temperature of 623 k at one end of the cnw and particle radius of 65 nm , we calculated the temperature at the other end .
the calculation gives the result without considering the irradiation by the smooth line and shows the result considering the irradiation by the red triangular - dot curve .
b describes the influence of the radius of the pb particle on its temperature and the td along the nanowire .
the decreasing curve plots the temperature of the pb particle against its radius and the rising curve plots the td . the left axes of both the insets are the pb particle s temperature and the right axes are the td .
the heating temperature is assumed 723 k. ( color figure online ) effective thermal dissipation in the cold end generates the obvious td .
the absorption of the heat of melting makes much less contribution than the thermal input from td driven thermal conduction .
the fixed melting point of the poc during heat absorption increases its temperature abruptly , which ceases by the enhanced input immediately .
4a4d , the evaporation of the pb core increases with increasing the heating temperature . here
the evaporation of the poc becomes as obvious as that of pos after the heating temperature of 350 c .
a , b , c and d are the tem images taken at the heating temperatures of 310 , 350,400 and 450 c , respectively .
the evaporation rate estimated from the images agrees to the estimation from the bulk value of heat of vaporization .
assuming the particle radius of 65 nm and the evaporation rate of , the influence of the evaporation on the td is assessed , resulting in the round - dot curve ( irradiation + evaporation ) and the box curve ( only irradiation ) in ( e ) .
the obvious td has been demonstrated along an amorphous cnw of less than 1m decorated by the pb nanoparticles .
the melting and the evaporation of the on cnw - pb particle are retarded by the confined thermal transportation along the cnw .
, in which c , m and s are the specific heat , the mass and the surface area of the poc respectively.s , l and  are the cross section , the length and the thermal conduction coefficient of the cnw .
t is the temperature and td is the td between the two ends of the cnw .
the first item is the thermal input from the cnw conduction ; the second item is the irradiation of the grey body ,  = 0.43 is the emission coefficient of the oxided pb ; the third item describes the evaporation dissipation , where ev = 2.9 ev stands for the heat of evaporation of lead .
the thermal conductivity of 0.2 w / k m is used according to the previous measurement and the sp3 ratio ( less than 10% ) of the current cnw .
the online version of this article ( doi:10.1007/s11671 - 009 - 9455-y ) contains supplementary material , which is available to authorized users .
this work was financially supported by the national natural science foundation of china ( grant no . 90606002 , 10674056 and 10904065 ) , the national key projects for basic research of china ( grant no .
the authors acknowledge mr . jianming hong ( nanjing university ) for the technical assistance and dr .
pb nanoclusters were deposited onto a suspended carbon nanowire ( cnw ) , where in situ temperature variable observation was carried out by a transmission electron microscope . 
 the heating temperature was up to 450 c . 
 both the melting and evaporation of the pb nanoparticles on the cnw were retarded when compared to the particles on the support frame . 
 the obvious temperature difference of up to 10 k along the cnw of less than 1 m was demonstrated . 
 it was attributed to the irradiating dissipation - dependent on the surface area of the decorating pb particle by calculation.(see supplementary material 1 )