Carbon Nanotubes Addition Effects on MgB2 Superconducting Properties

2.1. Carbon doping and critical temperature (T_c)

Several systematic carbon doping studies of Mg(B_1-xC_x)₂ have been performed in single crystals (Lee et al., 2003; Kazakov et al., 2005), polycrystalline wires fabricated by chemical vapor deposition (CVD) (Wilke et al., 2004, 2005a), and B₄C-doped (Avdeev et al., 2003; Wilke et al., 2005b). All these studies indicate a monotonic decrease of T_cand the lattice parameter a for increasing x, while the lattice parameter c remains constant.

For single crystals, the solubility limit of C in MgB₂ was estimated to be about 15 ± 1%, which is substantially larger than that reported for the polycrystalline samples. A dramatic decrease in T_c was also observed with C-substitution, followed by complete suppression of superconductivity for x>0.125. This solubility limit is usually not reached in bulk samples. A comparison of the critical temperature as a function of the nominal C-content for different carbon sources is displayed in Figure 1.

The reduction in T_c resulting from C addition using CNT sources is much lower than in the previous cases, suggesting that C substitution is lower than the concentration given by Mg(B_1-xC_x)₂. The T_c decrease is even lower when using SWCNT as a source of carbon indicating a very low doping level.

As an example, it is possible to calculate the actual C content substituting B into the MgB₂ structure, using the lattice parameters obtained from XRD: the shift in the a-axis lattice parameter can be used as a calibration for the actual amount of C (x) in the Mg(B_1-xC_x)₂ structure in comparison with the fitting of neutron diffraction data (Avdeev et al., 2003) or single crystal data (Kazakov et al., 2005). The dependence of a-axis lattice parameter as a function of the nominal DWCNT %at content is plotted in Figure 2. The corrected x values obtained were used to plot the same data as open squares in Figure 1, indicating that not all C is incorporated into the MgB₂ structure. A similar behavior is observed for all CNT samples, indicating that actual C-substitution tends to saturate for nominal CNT contents larger than 10%at. The actual C-doping varies according to the CNT type, synthesis temperature or other synthesis parameters (i.e. pressure or magnetic field). This C-substitution level determines not only the T_c but other superconducting properties such as H_c2, as will be described in section 2.2. Nevertheless, we will continue using the nominal content as the parameter to describe most effects to make it easier the comparison with other author’s results.

It is important to mention that not only the nominal carbon content x but also other synthesis parameters affect the superconducting properties like T_cdue to the amount of C substituting B in the structure. All parameters studied up to now are listed at the beginning of next section.

2.2. Simultaneous enhancement of critical currents and fields

2.2.1. Critical currents (J_c)

Since the first work devoted to the study of the effect of the addition of CNT on the critical current density of MgB₂ (Dou et al., 2003), several parameters have been studied:

• the amount of "x" for a particular CNT type : MWCNT (Dou et al., 2003; Shekhar, 2007), DWCNT (Serquis et al., 2007), SWCNT (Serrano et al., 2009 ; Vajpayee et al., 2010)

• the effect of CNT type (Serrano et al., 2008) and size (Yeoh et al., 2005, 2006)

• the effect of sintering conditions such as temperature (Yeoh et al., 2004), pressure (Yuan et al., 2005), ultrasonication of precursors (Yeoh et al., 2006) or the application of magnetic field during sintering (Li et al., 2007)

Most researchers performed magnetization loops measurements to determine J_c(H) in bulk samples using the Bean critical state model (Bean, 1962) assuming full penetrated samples for a long parallelepiped:

Jc(H)[A/cm2] = 20×ΔM(H)[emu/cm3](a−a23b)[cm]E1

where a and b are the lengths of the parallelepiped edges perpendicular to the magnetic field and ΔM is the width of the magnetization characteristic at the applied magnetic field H.

Figure 3 shows the dependence of J_cwith the applied magnetic field at 5 and 20 K for samples prepared with different amount of single (SW) (Serrano et al., 2009), double (DW) (Serquis et al., 2007) and multi-walled (MW) (Shekhar et al., 2007) CNT (see inset for the later case). Some flux jumps were frequently reported at 5 K in regions up to 2 T, and these data were not included in the corresponding figures. It can be observed that in all cases the addition of CNT progressively improves the overall J_c(H) performance, reaching an optimum for the x=0.10 sample, where J_cis higher than for any other composition in all the reported temperatures and fields. When the amount of added CNT is over 10%at the performance deteriorates. However, many other authors also reported that the optimum addition is around 10%at, although in some cases the critical current densities are not higher than for other compositions in the whole range of temperatures or applied fields.

Figure 4 displays the dependence of J_cwith different amount of MWCNT (Dou et al., 2003), DWCNT (Serquis et al., 2007) and SWCNT (Vajpayee et al., 2010) added to MgB₂ samples under an applied field of 4 T and temperatures of 5 and 20 K. It is interesting to note that the critical current densities are very similar between x = 0,025 and x = 0,10 for each type of sample, but the J_cimprovement tends to be more notorious for x = 0,10 at higher temperatures and fields. The best composition for a certain field and temperature may also change with the sintering temperature. Samples included in Figure 4 were prepared at 800, 900 and 850 °C for MW, DW and SW, respectively. A study about the dependence with sintering temperature (Ts) in MgB₂ samples with MW CNT (Yeoh et al., 2004) indicated that when the Ts is 900 °C or higher, the nanotubes tend to dissolve and are incorporated into the MgB₂ matrix, decreasing T_cbut increasing the irreversibility field (H_irr). This effect will be discussed in the next subsection, since it is correlated with the H_c2improvement. Therefore, the larger the amount of C-doping the smaller is the J_c(H) slope improving the performance at higher fields. On the contrary, the J_cdecrease for x > 0,10 may be due to both an even larger decrease in T_cand a probable deterioration of interconnectivity between grains. This deterioration of grain connectivity was denoted by a large normal resistivity value (i.e. ρ(40K) ~ 200 μΩcm) for the DW sample with x = 0,125.

Figure 5 shows the dependence of J_cwith the applied magnetic field of samples prepared with the same amount of single (SW), double (DW) and multi-walled (MW) CNT.

For comparing the absolute values it is important to take into account the pure MgB2 sample used as reference since this can be a good parameter to check the influence of variables other than composition, such as connectivity, that may result from the sintering process. Consequently, the best performances (i.e. Jc values and Jc(H) dependences) are obtained for MW (diameter 20-30 nm) (Yeoh et al., 2005) and DW (diameter 1.3–5 nm) (Serquis et al., 2007). These two samples (both heat treated in flowing high purity Ar at 900 for 30 minutes) presented the largest C-doping (smallest a lattice parameter) and Yeoh et al. suggested that it is not the diameter but the MWCNT length the responsible for allowing a more homogeneous C-incorporation by avoiding the nanotubes agglomeration. This explanation may not apply to DW CNTs, which have a length ≤ 50 μm. However, it is highly probable that synthesis parameters that promote a more homogeneous CNT distribution and improve connectivity (avoiding agglomerates at grain boundaries) are the key for Jc performance.

2.2.2. Upper critical fields (H_c2)

The H_c2(T) dependences are usually determined from four probe transport measurements. Since the involved fields are frequently very high for standard laboratory test equipments, several groups performed measurements at large High Magnetic Field facilities. As an example, measurements of DW and SW CNT samples were performed in the mid-pulse magnet of NHMFL-LANL, capable of generating an asymmetric field pulse up to 50 T. Figure 6 exhibits the temperature dependences of H_c2and H_irr, defined as the onset (extrapolation of the maximum slope up to the normal state resistivity) and the beginning of the dissipation, respectively, of the R versus H data for samples with several DWCNT contents, at temperatures between 1.4 and 34 K. The criteria to define H_c2and H_irr are exemplified in the inset of figure 6.

In all superconducting materials, an H_c2enhancement is expected when disorder is increased (e.g., by doping). The reason is that the reduction in the electronic mean free path produces a decrease of the effective coherence length, driving the superconductor to the “dirty limit”. This effect is especially large in C-doped MgB₂, and additionally an anomalous H_c2(T) upward curvature is also noted in the present data and reported many times. This positive curvature is related to the existence of two-gaps in MgB₂, (π-band and σ-band) and predicted by some theoretical models.

These models for a two gap superconductor in the dirty limit (Golubov et al., 2002; Gurevich, 2003) consider that nonmagnetic impurities affect the intraband electron diffusivities Dand D, and the interband scattering rates and . An implicit H_c2dependence on temperature can be obtained from the Usadel equations, derived taking into account only the intraband effect.

a0[lnt+U(h)][lnt+U(ηh)]+a2[lnt+U(ηh)]+a1[lnt+U(h)]=0E2

where, t=T/Tc0is the reduced temperature

In Refs. (Gurevich, 2003; Serquis et al., 2007 ; Serrano et al., 2008)) Tc0 = Tc(g=0) is defined, where g the interband scattering parameter. This value corresponds to the clean limit MgB2 sample.

,

a₀, a₁, and a₂were determined in ref. (Gurevich, 2003).

Another equation was derived when taking also into account the interband effects:

2w(lnt+U+)(lnt+U−)+(λ0+λi)(lnt+U+)+(λ0−λi)(lnt+U−)=0E3

where

,

w, λ₀ are constants that depend on _mn(m,n = π,σ) (values obtained from ab initio calculations) (Golubov et al., 2002; Braccini et al., 2005).

In this case we optimized the diffusivity ratio =D/ Dand interband scattering parameter to fit the measurements using the equation (Eq. 3).

Figure 7 shows the dependence of H_c2as a function of the reduced temperature t = T/T_c0, where T_c0= 39 K, of some selected samples with and without CNT addition. Other C-doped

samples are included for comparison (Serrano et al., 2008; Braccini et al., 2005). The lines are fits to the data with the model proposed using the fitting parameters described above.

The upward curvature signaled as a characteristic of the presence of two gaps is apparent in these H_c2(T) data.

Figure 8 displays the H_c2(0) extrapolations as a function of x for DW (Serquis et al. 2007) and SW (Serrano et al. 2007) in comparison with data for other C-doped samples (Wilke et al., 2004). We observe that H_c2(0) increases with x and has a maximum for 10 at% for DW and 5 at% for SW. For a larger x values a decrease in H_c2 was found, probably due to a larger T_cdecrease and an increase in the resistivity of the samples. Earlier MgB₂ carbon doped data (Wilke et al. 2005) also indicates an initial rapid rise for lower C contents that then slows down, reaches a maximum at intermediate carbon concentrations, and decreases for larger C contents and the same behavior was reported for MgB₂ single crystals.

The CNT additions produce a larger C incorporation than SiC, probably because of the higher synthesis temperature, resulting in samples with lower T_c. The DWCNT 10 at% sample has the highest C content into the lattice, indicating that using this kind of inclusions is an easier way to incorporate C. This allows to reach a record H_c2value for this sample. Earlier MgB₂ carbon doped data from Wilke et al (Wilke et al., 2005b) also indicates an initial rapid rise for lower C contents that then slows down, reaches a maximum at intermediate carbon concentrations, and decreases for larger C contents and the same behavior was reported for MgB₂ single crystals. The H_c2(0) of CNTdw10 is close to the maximum H_c2value as a function of x. A decrease in H_c2(0) was also observed for a larger x value (see Fig. 8)), in agreement with other reported data (Senkowicz et al., 2007).

4.1. Introduction

In Section 2.2 we have shown that the main effect of DW CNTs addition is the simultaneous increase in the critical current density and the upper critical field H_c2. However, it is not clear if these two effects are connected. In fact, the vortex physics underlying this performance improvement has not been so far understood. In this section, we present a very recent work (Pasquini et al., 2011), where the role of CNT addition is investigated by studying the magnetic relaxation in bulk MgB₂ samples.

As was mentioned in Section 2.1.1, if a superconducting sample is fully penetrated by the magnetic field B, the magnetization m is proportional to the density current J flowing in the sample that, in the ideal critical state approximation is the critical current density J_c. However, due to the thermal activated motion, this "measurable" critical current is lower than the "true" J_c0. The main quantity governing the creep of vortices is the activation barrier U(J,T,B). In a magnetic relaxation experiment both the magnetization m and J_cdecay in time as

and then

where Cc~ Jc/τ0or C~m m/τ0can be approximated as constants.

The activation barrier is expected to be described by the general expression (Blatter et al.,1994; Geshkenbein et al., 1989)

where U_c(T,B) is the pinning energy and μ is a critical exponent characteristic of the particular creep regime.

In High Temperature Superconductors (HTSs), the creep drastically reduces the measured current density, so J_c<<J_c0. A large number of glassy creep regimes in this limit have been proposed theoretically (Blatter et al., 1994; Yeshurum et al., 1996) and many of them observed experimentally (Thompsom et al., 1994, 1997), whereU(J,T,B)≅g(T,B)J−μ.

In those cases the temperature dependence of the measurable J_cis dominated by creep while the J_c0(T) dependence is negligible. On the other hand, in traditional type II superconductors the current decay is very small, so (J_c0-J_c)<<J_c0, therefore equation (Eq. 5) take the traditional Anderson-Kim (A-K) linear dependence (Anderson et al., 1964)

In these very low creep superconductors an experimental confirmation of glassiness, which regardless of the specific approach always involves detecting tiny deviations from the Anderson-Kim model, is extremely challenging.

From this basic point of view, MgB₂ is a very particular system, as the intermediate T_c and moderate anisotropy makes the creep effects smaller than in HTS but larger than in conventional superconductors. The influence of thermal fluctuations in the vortex physics is measured by the Ginzburg number G_i=(1/2)(kT_c/H_c²ξ³γ^-¹)². For YBa₂Cu₃O_7-δ this is as large as G_i~ 10^-2, and even larger for the more anisotropic Bi-based compounds, while for NbTi, the paradigmatic strong-pinning conventional superconductor, G_i~10^-8. For MgB₂, depending on the doping level we have G_i~10^-4-10^-5. This is just in the middle between the extreme cases. The first consequence is that in magnetization measurements, the A-K limit is not necessary valid in the whole temperature range, and the measured J_cis expected to be in the intermediate range (J_c0-J_c)≲J_c.

In the rest of the section we present a creep study in bulk MgB₂ samples as-grown and doped with different doses of carbon nanotubes. In subsection 4.2 experimental relaxation rates are presented, and the general behaviour is described. In subsection 4.3 we review some fundamental concepts and formulas concerning creep rates and activation energies to perform in subsection 4.4 a careful analysis of results that allows us to identify the region where the A-K model is valid. In 4.5, the pinning energies U_c, true critical current densities J_c0, and correlation volumes V_care estimated and compared. Conclusions are summarized in 4.6.

4.2. Relaxation rates

Samples used in this study were prepared by solid-state reaction with magnesium (-325 mesh, 99%) and amorphous boron (99%) as starting materials (Serrano et al., 2008). The powders were ground inside a glove box and pressed under 500 MPa into small pellets with

dimensions of 6 mm in diameter and 4 mm in thickness, wrapped together with extra 20%at Mg turnings (99:98% Puratronic) in Ta foil and then placed in an alumina crucible inside a tube furnace in flowing Ar=H₂ at 900 °C for 30 min.

The relaxation measurements were carried out in a Quantum Design model MPMS XL 7T SQUID based magnetometer. Time-dependent data were taken with a protocol similar to that described in ref. (Civale et al., 1996). A scan length of 3 cm was used in order to minimize the effects due to the non-uniformity of the applied magnetic field that was applied parallel to the longest axis of the sample. For each relaxation measurement, the samples were first cooled and stabilized at the measurement temperature. Then the field was first raised up to 6T and then lowered to the measuring field to assure that the sample was fully penetrated. Intermediate measurements were performed in the upper and lower magnetization branches to subtract the reversible magnetization. We checked for and ruled out any effects due to the magnet self relaxations (H variations during the measurement time) that could lead to spurious changes in the magnetization of the samples.

The experimental critical current density J_c(t) has been calculated from the measured magnetic moment using equation (Eq. 1), as in previous sections.

As reported in section 2.2., the response for samples with DWCNT additions between 1% and 10% at temperature far below T_cis very similar and the "measured" critical current density J_cis optimal in this range of doping. This fact is illustrated in Figure 3, where J_cobtained from typical magnetization loops in samples with different doses of DWCNT is plotted as a function of the applied magnetic field H at T = 5K and 20K. The response for samples with 1 at% and 10 at% addition of DWCNT is very similar. At low temperature (5 K), CNT addition enhances J_cmore than twice for all the measured range of H. On the other hand, at high temperature (20 K) the response of pure and CNT samples is quite similar but CNT addition continues being efficient at fields higher than H = 2T.

The magnetic relaxation has been measured in pure MgB₂ samples and samples with DWCNT doses between 1 at% and 10 at% in the range between 5K and 25K. The corresponding relaxation rate S=-d(ln(J))/d(ln(t)) has been obtained as the slope of the ln J vs ln t graph. Results for H =1T (full symbols) and 3T (open symbols) are shown in Figure 12.

Samples with doses of 2.5% and 5% of carbon nanotubes have also been measured and display similar results, not shown in the figure for clarity.

As was described in the introduction, the S values are intermediate between those measured in low and high T_cmaterials. With this moderate relaxation, the temperature dependence of J_c(t) (Figure 3) cannot be explained assuming a T independent J_c0at low temperature. An intrinsic J_c0(T) dependence must to be taken into account.

Again, at H = 1 T the decay in time is quite similar in all the doped samples with doses between 1% and 10%. However, same unexpected results appear. The S(T) curve at H=3T is similar for pure and CNT samples in all the temperature range. Furthermore, at H=1T the pure sample that has a lower J_c(associated with a lower pinning) has also a lower relaxation (associated with a higher pinning energy U_c).

We have proceeded to analyze the relaxation data in a pure and a 10 at% CNT samples to get an understanding of the causes of this puzzle. The procedure and results are described in the subsections 4.3 and 4.4.

4.3. Creep and activation energies in the Anderson-Kim approximation

In the general case (Blatter et al., 1994), the relaxation rate S is related with the pinning energy by

As was mentioned in the introduction, the A-K approximation assumes (Jc0−J)<<Jc0or(J/Jc0)~1, that lets to the linear dependence of eq. (Eq. 6) between the activation barrier U and the density current J. The integration of eq. (Eq. 4) in this limit gives the well known logarithmic decay of the experimental critical current density with time.

and allows to estimate Uc(T,B)/kTunder the supposition thatJ~Jc0_.

An alternative method combines Eq. 4 and Eq. 6 to obtain a linear dependence between J and ∂J/∂t that, under the condition lnCJ<<Uc(T,B)/kTresults in (Pasquini et al., 2011)

Due to the numerical differentiation, this method has a greater error in the calculation of the pinning energy, but allows estimating J_c0(B,T).

A mayor difficulty to directly decide the validity of the A-K approximation from the relaxation data at a single temperature is the extremely large time needed to reliably determine the linear relationship (Eq. 8) (i.e. the logarithmic decay with time of the current density). However, the resulting fitting parameter J_c0(B,T) must be consistent with the A-K assumption (Jc/Jc0)~1and the resulting fitting parameter Uc(T,B)must be consistent with (Eq. 7). If these two conditions are not fulfilled then some of the assumptions was wrong and we can conclude that the AK description is not valid.

In the following section, we apply the above procedure to MgB₂ relaxation data, determining the temperature region where results are consistent.

4.4. Data analysis in MgB₂ samples

As can be observed in the inset of Figure 12, it is not possible to identify in all the cases a low T region with a linear relationship between 1/S and 1/T, characteristic of a temperature independent pinning energy. For this reason, experimental data where separately analysed at each temperature assuming a linear dependence between U and J, i.e. the validity of the A-K approximation.

At each temperature J_c(t) has been plotted has a function of ln t and ln (-∂J/∂t). The fitting parameter A(T) = (kTJ_c0(T))/U_c(T)) has been extracted from the slope using equations (Eq. 8) and (Eq. 9), and J_c0(T) from the intercept using (Eq. 9) (Pasquini et al., 2011).

In Figure 13 the estimated true critical current density J_c0is compared with the measured critical current density J_c(the first point measured in the J_c(t) relaxation) by plotting (J_c0-J)<<J_c0as a function of temperature for a pure and a 10%doped sample, at H=1 T and 3T.

Taking a 10% criterion to determine the limit of the A-K condition (J_c0-J)<<J_c0, the resulting J_c0(t) is consistent below the temperature where each experimental curve crosses the doted horizontal line.

In figure 14 the resulting pinning energies obtained from the slope of eq. (Eq. 8) (squares) and (Eq. 9) (circles) are plotted as a function of temperature and compared with T/S (asterisks) for a pure and a 10%doped sample, at H=1 T and 3T. Results have been restricted to the consistent T region obtained by the above analysis.

As can be observed (with exception of the lower temperatures data in the undoped sample at H= 1 T) pinning energies obtained from the three methods are very similar, and this validates the fitting procedure, including the estimation of J_c0(T) from (Eq. 9).

Observing the resulting T dependence in Figure 14 it seems that, in most of the cases, pinning energies remain nearly constant at low temperatures. The unexpected drop in U_cat the lower temperatures data in the undoped sample at H= 1 T, together with the inconsistence of the analyzed data, could imply the presence of another relaxation mechanism, perhaps associated with macroscopic flux jumps. In the data measured at H=1 T a drop at a higher temperature far below the irreversibility line is also observed.

On the other hand, a continuous decrease occurs in the critical current density. This can be observed in figure 15, where the true critical current density is plotted in the studied range for the same samples.

The previous analysis excludes the creep study in the high temperature region using the A-K approximation. Successful procedures have been developed to analyze creep data in high T_c superconductors (Maley et al., 1990; Civale et al., 1996) in the limit J_c<<J_c0, but they are not suitable for intermediate creep regime. However, in the present subsection we showed that, from the present study at low temperatures, a good insight about the role of doping can be obtained.

4.5. Discussion

Consistent with the relaxation rates, at H=1 T there is a clear decrease of U_c after CNT addition, whereas at H=3 T the doping has not an evident effect in the pinning energies.

The parameter U_cis associated with the pinning energy of a pinning volume that, in a single vortex pinning regime, is defined by the disorder parameter (T) and the superconducting coherence length (T) (Blatter et al., 1994). In section 2.2 we have shown that DWCNT addition enhances H_c2(T) by doping the B site, i.e. reduces (T). On the other hand, it is expected that doping increases disorder. Therefore, these two consequences of DWCNT doping will compete and define the effect in the pinning energies and critical currents.

The fact that the doping effect in the pinning energies is field dependent is a clear indication of a collective pinning regime.

In a collective regime, the pinning volume is determined by the competition between elastic and pinning energies and each volume V_cof the vortex system is collectively pinned with energy U_c. The Lorentz force over a volume V_cis F_L~(1/c)BJ V_cand, in a rough estimation, the pinning force is F_p~ U_c/ξ. When J reaches the critical current density J_c0, the pinning and Lorentz forces are balanced and therefore the following relationship is obtained:

In section 2.2, we have presented H_c2 measurements in pure and DWCNT MgB₂ samples and we have found (Serquis et al., 2007 ) that H_c2(T) fits very well the function proposed in ref (Braccini et al,. 2005). We have estimated ξ(T) from H_c2(T) for the as grown samples and for samples with 10% DWCNT. Using this ξ(T) dependence we have estimated V_c(T,B) from our data. Results are shown in Figure 16, where V_cis plotted as a function of temperature a H(T) = 1 T (right axis) and 3 T (left axis) for both samples.

The estimated numerical values (~10^-¹⁵ cm³) imply that the correlation radius is larger than the main vortex distance, in agreement with a collective pinning regime of vortex bundles.

Doping additionally reduces the correlation volume, consistent with the increase in the critical current density.

From the comparison of data taken at H = 1 T and 3 T, in both pure and CNT samples, the correlation volume at H= 3T is approximately three times smaller than that obtain at H = 1 T and both J_c0and U_cdecrease with B. This field dependence for U_cdoes not correspond with that predicted by the classical collective pinning theory for the activation energy of vortex bundles when pinning arises from random point defects (Blatter et al., 1994). However, this discrepancy is not surprising, as we know that the strong pinning in these MgB₂ samples arises from a variety of larger defects rather than atomic-size disorder.

4.6. Conclusions

Magnetic relaxation in bulk MgB₂ samples as-grown and with DWCNT doses between 1% and 10% in the range between 5K and 25K has been measured and the corresponding critical current density has been calculated. The current decay in time is quite similar in all the doped samples with doses between 1% and 10%.

A careful creep analysis has been carried out in a pure sample and in one with 10% of carbon nanotubes at H= 1 T and 3 T.

The analysis has been performed under the Anderson-Kim approximation, valid in the limit where the measured critical current density J_cis similar to the “true” one J_c0that would be present in the absence of creep phenomena. In these samples, even at the loweest temperatures it is necessary to include an explicit field and temperature dependence of both the pinning energies U_c(T,B) and true critical current densities J_c0(T,B).

These pinning properties have been obtained as fitting parameters from the experimental data for two different methods. The consistence of the fitting parameters with the A-K limit has been required to delimit the region of validity of the analysis.

In the valid region, the pinning energies and critical current densities have been estimated and compared. The dependence with magnetic field, together with numerical estimations of the pinning volume, indicate the presence of a collective pinning regime of vortex bundles. There is a decrease in the pinning energies that implies an increase in the relaxation rates as a consequence of DWCNT addition. However, the true critical current densities increase, due to a decrease in the collective pinning volumes.

We conclude that the origin of the main changes in the pinning properties with doping are the reduction of the coherence length (that decreases the pinning energies ) and the increase in the disorder parameters (that increase the critical current and decrease the pinning volume).

The strong temperature dependence of the coherence length is probably the main reason to the observed temperature dependence in the pinning properties. At the lower temperatures, thermal instabilities that originate macroscopic flux jumps could also play a role.

A method to analyse the relaxation data in the high temperature region, beyond the A-K approximation, is necessary and will be object of a future work.